SOURCES, EFFECTS AND RISKSOF IONIZING RADIATION
United Nations Scientific Committee on the
Effects of Atomic Radiation
UNSCEAR 2012
Report to the General Assemblywith Scientific Annexes

Scientific Annexes

UNITED NATIONSNew York, 2015

NOTE
The report of the Committee without its annexes appears as Official Records of the General
Assembly, Sixty-seventh Session, Supplement No. 46 (A/67/46).
The designations employed and the presentation of material in this publication do not imply
the expression of any opinion whatsoever on the part of the Secretariat of the United Nations­
concerning the legal status of any country, territory, city or area, or of its authorities, or­concerning the delimitation of its frontiers or boundaries.
The country names used in this document are, in most cases, those that were in use at the time thedata were collected or the text prepared. In other cases, however, the names have been updated,
where this was possible and appropriate, to reflect political changes.

UNITED NATIONS PUBLICATION
Sales No. E.16.IX.1
ISBN: 978-92-1-142307-5
eISBN: 978-92-1-057798-4© United Nations, December 2015. All rights reserved, worldwide.
This publication has not been formally edited.
Information on uniform resource locators and links to Internet sites contained in the present
publication are provided for the convenience of the reader and are correct at the time of issue.
The United Nations takes no responsibility for the continued accuracy of that information or forthe content of any external website.

ANNEX B
UNCERTAINTIES IN RISK ESTIMATES FORRADIATION-INDUCED CANCER

91

ANNEX B: : UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER

93

CONTENTSI.

INTRODUCTION ................................................................................................................................... 95

II. FUNDAMENTAL CONCEPTS ............................................................................................................ 96
A. Statistical concepts of uncertainty ....................................................................................... 96
B. Epidemiological concepts ....................................................................................................... 98
III. SOURCES OF UNCERTAINTIES IN RADIOEPIDEMIOLOGICAL STUDIES ............................ 99
A. Uncertainties in health effect information ........................................................................ 99
B. Uncertainties in exposure and dose assessment ............................................................ 99
C. Uncertainties in risk assessment ......................................................................................... 101
1. Impact of uncertainty in health effect information on risk
estimates and statistical power of epidemiological studies.............................. 101
2. Impact of exposure uncertainty ................................................................................... 102
3. Impact of model uncertainty* ...................................................................................... 105
IV. UNCERTAINTIES IN TRANSFERRING RISK QUANTITIES FROM GIVEN STUDIES TO
OTHER EXPOSURE CONDITIONS OR POPULATIONS OF INTEREST ......................................... 106
A. Transfer to another population or time period ............................................................. 106
B. Transfer to risks from LSS to other exposure conditions ............................................ 107
V. UNCERTAINTIES OF SELECTED RISK EVALUATIONS ............................................................. 108
A. Solid cancer risks after external exposure to cumulative doses of theorder of 100 mGy above typical background exposure ............................................. 109
B. Thyroid cancer after radiation exposure during childhood ...................................... 110
C. Lung cancer after residential exposure to radon .......................................................... 111
VI. KEY RESEARCH NEEDS .................................................................................................................... 112
VII. CONCLUSIONS ................................................................................................................................... 113
ACKNOWLEDGEMENTS .......................................................................................................................... 114
APPENDIX A. FUNDAMENTAL CONCEPTS ...................................................................................... 115
APPENDIX B. SOURCES OF UNCERTAINTY IN RADIOEPIDEMIOLOGICAL STUDIES .......... 139
APPENDIX C. UNCERTAINTY IN TRANSFERRING RISK QUANTITIES FROM GIVEN STUDIESTO OTHER EXPOSURE SITUATIONS OR POPULATIONS OF INTEREST .................................... 211
APPENDIX D. UNCERTAINTIES IN SELECTED RISK EVALUATIONS .......................................... 241
REFERENCES ............................................................................................................................................... 285

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 95

I. INTRODUCTION
1.
Cancer risks* of exposure to ionizing radiation are much better known than those of most othercarcinogens. The Committee has previously summarized the results of numerous epidemiologicalstudies of populations exposed to moderate to high doses of radiation exposure [U11, U12]. However,as discussed in annex A, at lower doses (generally below an absorbed dose* of about 100 mGy fromlow-LET* radiation), the uncertainties* associated with epidemiological studies become increasingly
large and tend to mask any possible effect. The estimation of risk from such exposures requires
judgements against a backdrop of different sources of uncertainty and ongoing scientific debate. The
uncertainties involved in these judgements and hence the estimation of risk need to be properly
addressed and communicated in order to improve understanding by decision-makers and others.
2.
In order to support its findings and provide a more rational basis for discussions of the risk fromradiation exposure, the Committee has prepared this scientific annex on the uncertainties in estimates ofrisk following exposure to ionizing radiation. Many epidemiological studies of the health effects* ofradiation exposure derive risk estimates with confidence intervals* that express only the impact ofstatistical fluctuations of the data in the frame of the risk model* chosen. Other specific sources of
uncertainty, such as those due to incomplete knowledge of exposures, or factors and mechanisms
influencing the development of the disease, must also be addressed in order to more realisticallydescribe the current state of knowledge. A main purpose of this annex then is to describe the current
state of knowledge on (a) the various factors influencing estimates of risk from radiation exposure; and(b) the methodologies to integrate information on different sources of uncertainties so as to describe
uncertainties on estimates of risk from radiation exposure more comprehensively than have previous
reports of the Committee.
3.
This scientific annex includes: (a) an evaluation of current knowledge on the impact of various
sources of uncertainty on estimates of risk from radiation exposure and how they may be treated;(b) a comparison of frequentistic and Bayesian interpretations of uncertainty and probability forderiving information from new data; (c) a discussion of uncertainties in transferring risk estimatesderived from a study to another population or a situation of interest; and (d) three examples of
evaluations of cancer risk to demonstrate the structure and analysis of uncertainty. The main text of theannex is supported by four detailed technical appendices that provide more extensive discussion. A
glossary supports the interpretation of terms for both this annex and annex A.
4.
Uncertainty analyses in the field of risk estimation for radiation exposure have up to now
focussed mainly on the risk of cancer. Consequently, much of the material summarized in this annex
relates to radiation-induced cancer. The methods outlined, however, are equally well applicable to theanalysis of other radiation-induced health effects.
5.
The estimation of risks to human health from exposure to ionizing radiation is mainly based on
epidemiological studies either of large exposed populations (cohort studies) or of the exposure
distribution of persons with and without the disease of interest (case–control studies). There are also
many radiobiological studies, including animal experiments, related to the effects of exposure toionizing radiation [U11, U12]. These studies provide some insight into the mechanisms and processes
that are involved in carcinogenesis after exposure to ionizing radiation. However, the studies cannot yet
be used to improve quantitative estimation of the risks for humans of radiation exposure.

96 UNSCEAR 2012 REPORT

6.
Risk estimates are derived generally for a group of people, defined by sex, birth year, ethnicity,
occupation, smoking behaviour or other characteristics, and to specified exposure conditions. However,whether or not an individual will be affected depends on further, unknown factors, such as genetic orfamilial predisposition, pre-existing illnesses or pre-cancerous lesions, repair capacity, or
immunological characteristics. At present, the possibilities for determining individual sensitivity arestill limited and there is insufficient understanding of its interaction* with radiation exposure. Therefore
this report does not treat the assessment of individual sensitivity to radiation exposure.

II. FUNDAMENTAL CONCEPTS
7.
This chapter recapitulates some fundamental statistical concepts, including types of error* anduncertainty, and statistical inference,* as well as key concepts and terminology of epidemiology.
Appendix A provides more detailed explanatory material on these concepts and on methods forquantifying and analysing uncertainties.

A. Statistical concepts of uncertainty
8.
The difference between an estimate of a quantity of interest* (e.g. a dose or the excess relativerisk* per unit dose in some exposed population) and the true but unknown value of that quantity iscalled the “error”, which itself cannot be observed or quantified. “Uncertainty” refers to the probability
distribution of the possible errors and “uncertainty analysis” to the characterization of the error
distribution taking account of all known sources of uncertainty.
9.
Uncertainty in estimation of cancer risk from radiation exposure comes from several sources,
including the inherently random nature of processes that lead to cancer, limitations in data, and the useof idealized models to describe the nature of the risks in both an exposed and a non-exposed population.
10. Uncertainties are composed of mixtures of systematic and random errors.* The nature of thedifferent types of error contributing to the uncertainty is important. Errors that are statisticallyindependent between individuals are called “unshared errors”,* while correlated ones are called “sharederrors”.*
11.

There are two types of unshared errors:(a) “Measurement error”* is independent of the true value, and typically arises when using an
imprecise (but unbiased) measuring device. The main determinants of the measurement error arecharacteristics of the measurement device, the study protocol and skill of the measuring personnel.
In the case of measurement error, the variance of the observed values* exceeds that of the true
values by the variance of the measurement error. It is known that the regression coefficients in a
dose–response analysis will be biased towards zero depending on the importance of measurement
errors in the dose estimates. Measurement errors are also called “classical errors”.
(b) “Assignment error”* arises when individuals are assigned representative values, often as aresult of grouping, and is independent of the assigned value. Assignment errors describe random
inter-individual variability* of true values about a single value assigned to every individual

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 97

belonging to a distinct group. The variance of the assigned values will be less than that of the truevariance by the variance of the individual peculiarity in the values about a given assigned value.
When dose values are assigned in a dose–response analysis, the regression coefficients tend to beunbiased. Assignment errors are also called “Berkson errors”.*
12. Shared errors include shared measurement errors (such as the use of an improperly calibrated
measuring device) and shared assignment errors (such as mis-specification of values for parameters
used in computation of observed values). Shared errors almost inevitably lead to biased estimates of thequantity of interest, and failure to account for them can lead to overconfidence in deriving risk
estimates.
13. Statistical inference is critical in characterizing and quantifying uncertainty in both estimation ofrisk from radiation exposure for specific studies and in projection of risk to other populations andexposure scenarios. Statistical inference is based on data (observations) and models used to analyse thedata. The probability density function* for the data given a model,  , its parameters, β, and the valuesof any explanatory variables, Z, is denoted by f (data | , β , Z ) . When viewed as a function of theparameters given the data, the model and the values of the explanatory variables, the probability density
function is called the likelihood* function (L), which plays a central role in statistical inference. A
hypothetical and unrealistic example would be the likelihood of a set of breast cancer incidence data
being observed in a cohort of women given a model of the incidence rate* that, say, were:I = β1 a (1 + β2 d)Here, the age, a, and the dose, d, would be explanatory variables, and best estimates of the parameters
β1 and β2 would be determined, e.g. by identifying the maximum of the likelihood function of theobserved data.
14.

There are two main approaches of statistical inference:(a) “Frequentist” inference* uses observed data and aims at establishing the probability of thetruth of statements about quantities of interest given the data and the model used to analyse thedata. Frequentist probability can be interpreted as the relative frequency* in a hypothetical set of
realizations given the true parameter values of the assumed model;(b) “Bayesian” inference interprets probability as a measure of the degree of belief or state ofknowledge concerning the true values of the quantities of interest. With this interpretation, one’s“prior” state of knowledge about the quantity of interest can be explicitly updated with new
information to make Bayesian probability statements about one’s “posterior” state of knowledge.
From this probability density function of possibly true values, a central value (usually thearithmetic mean, median or mode) and a 90% or 95% credible interval* can be obtained. A reviewof the application of Bayesian methods in epidemiology can be found in [G17].

15. Although the two concepts are fundamentally different, they often lead to similar conclusions,especially when their implementation is well-informed by the scientific context or when the data arestrong enough to make the choice of the prior distribution less relevant.
16. Frequentist methods for quantification and assessment of uncertainties have generally served wellin the estimation of risk in specific exposed populations, such as the survivors of the atomic bombingsin Japan. However, Bayesian methods become more appropriate with increasing complexity, such as
when estimating uncertainties in deriving cancer-specific risks from limited data or in doses calculatedusing complex Monte Carlo dosimetric modelling systems. They also become more important in

98 UNSCEAR 2012 REPORT

making informed but qualified judgements about risk estimates so that they may be applied
appropriately to address important societal questions.
17. Depending on the objective of an assessment, it may be necessary to distinguish variability fromuncertainty. Variability describes the variation of values between individuals, while uncertainty refers
to the variation in values due to unexplained stochastic processes or the state of knowledge about
imperfectly known fixed quantities.
18. The Committee recommends that uncertainty in the measurements, variables, and models used toestimate exposures, doses and risks—both for specific individuals and for groups—be defined asprobability density functions, representing the analyst’s state of knowledge, with account being taken of
the dependencies or correlations between the distributions.
19. “Uncertainty propagation”* is the process of combining all contributing components into an
overall statement of uncertainty about the estimate of the quantity of interest. Monte Carlo uncertainty
propagation* is preferred to closed-form algebraic solutions for all but the very simplest models. If it isnecessary to distinguish between the variability of dose or risk among individuals and the uncertainty
about values of fixed quantities, a two-dimensional Monte Carlo approach to uncertainty propagation is
the preferred approach. This produces (a) sets of possibly true values of fixed quantities that are shared
among groups of individuals; and (b) alternative realizations of possibly true sets of individual values
representing the variability in the quantity of interest.
20. A “sensitivity analysis” of the effect of changes in values of the model input on its output
determines which parameters or processes have the largest influence on a model result or on theuncertainty in that result.

B. Epidemiological concepts
21. Cohort studies, which involve the long-term follow-up of an exposed population having
individually characterized exposures, can provide unbiased risk estimates for various outcomes.
Analyses typically focus on how rates for the outcome of interest depend on radiation exposure
allowing for “modifying” factors such as sex or age at exposure. The strength of cohort studies arises
from the fact that rates of the disease of interest can be computed directly from the follow-up data.
However, such studies are challenging to establish and costly to maintain over the long follow-up
period needed, and lack statistical power for studying rare outcomes. Also, competing risk factors canoften not be explicitly taken into account.
22. Case–control studies identify cases for an outcome of interest in a population together with acontrol sample of disease-free individuals from the same population. Cases and controls are matched on
factors such as sex, or vital status at the age and time of diagnosis of the cases to reduce the chance thatobserved differences in the exposure distributions between cases and controls are due to factors otherthan radiation exposure. Such studies can be retrospective and can be undertaken with smaller
population groups than those required for cohort studies. Thus they cost much less than cohort studies,but without careful design, risk estimates are likely to have more bias* than those from cohort studies.
23. Epidemiological studies of radiation-induced health effects are observational and may suggest
associations between some exposure and an outcome of interest. However, a single epidemiologicalinvestigation is unlikely to establish unequivocally a cause–effect relationship,* in part because of thepossible impact of risk factors that are correlated with both the outcome of interest and the exposure

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 99(“confounding factors”).* Nevertheless, the consistency of results of many independent studies coupledwith plausible* biological reasoning can be convincing. Guidelines suggested by Bradford–Hill [H14]
are often used to judge the confidence that a risk factor (e.g. radiation exposure) might cause increased
incidence in a population of health outcomes (e.g. cancer).

III. SOURCES OF UNCERTAINTIES IN RADIOEPIDEMIOLOGICALSTUDIES24. This chapter discusses the sources of uncertainty in analysing the results of epidemiologicalstudies of populations exposed to ionizing radiation, specifically the uncertainties in information on
health effects, in information on exposure and dose assessment. It considers the impact of these
uncertainties and uncertainties in the dose–response model on risk assessment. Appendix B provides
more detailed explanation, technical information and review.

A. Uncertainties in health effect information
25. Sources of uncertainty in information on health effects can be broadly classified into two groups:(a) “Selection bias” occurs when the study population is not representative of the population of interest.
Examples are discussed in appendix B. Readily available information on disease status and exposure
history, and truly random cohort or case–control sampling can help avoid this; and (b) “Informationbias” involves erroneous or incomplete information about disease and exposure. Examples include
cases recalling their exposure history differently than non-cases (recall bias), and subjects who may
have left the geographical study area (ascertainment or follow-up bias). Previous UNSCEAR reports[U11, U12] have given examples of the ways in which errors can arise when assessing diseasefrequencies. Appendix B discusses various examples of information bias and how they have beenaccounted for in major radioepidemiological studies.
26. Failure to adjust for confounding factors can distort risk estimates. For example, increases incancer rates and decreases of exposure levels over time might suggest that normalized risks (expressedin terms of risk per unit dose) are increasing when actually improvements in medical diagnostics are
helping to detect cancers earlier and before these cancers would otherwise manifest. Confounding is
usually dealt with at the analysis stage, either by incorporating such factors into the regression model orby stratifying the data according to levels of the confounding factor. Cigarette smoking is one of themost serious potential confounding factors that have to be dealt with in epidemiological studies of thehealth effects of radiation exposure (radioepidemiological studies); clearly this is especially importantwhen analysing diseases that are known to be related to smoking [U12].

B. Uncertainties in exposure and dose assessment
27. Uncertainties in the assessment of exposure and dose may affect the evaluation of the statisticalsignificance of the dose response, the shape and steepness of slope, and the width of the confidence

100 UNSCEAR 2012 REPORTinterval. Common errors and mistakes in dose estimation can arise, for example, with measurements,
laboratory procedures, record keeping, programming, data input, and computation. Sources of such
errors must be addressed before estimating doses for epidemiological evaluation. Rigorous quality
assurance/quality control procedures should include checks of model inputs, equations, intermediate
results and individual dose estimates with calculations performed by different persons using
independent computational platforms. If common errors and mistakes are not detected and corrected,
expressions of uncertainty in dose estimation may be invalid. In general, some form of mathematicalmodelling is required to estimate the radiation dose to specific organs and tissues of the human body,
because these cannot be measured directly. Assumptions made and uncertainties introduced by themodelling need to be taken into account in the analysis.
28. For external exposure to photons with an energy of more than 0.03 MeV, uncertainty in theestimation of organ dose is generally less than that for internal exposure. However, the more thatmodels must be employed to estimate individual exposure and dose, the greater the anticipateduncertainty. The uncertainty varies from low for workers who wore individual dosimeters, to verylarge, e.g. when only the source term of an atmospheric release might be relatively well-known andmodelling of atmospheric dispersion and radionuclide deposition is needed to estimate doses.
Depending on the radiation type and the number of unknown variables, uncertainty in estimates oforgan dose from external exposure to photons of less than about 0.03 MeV can be considerable.
29. Doses due to internal exposure must be determined indirectly using mathematical models that
describe the distribution of the radionuclides in the body (biokinetic models) and delivery of dose overtime (dosimetric models). The models used are similar to the widely used models developed by theInternational Commission on Radiological Protection for calculating dose coefficients for radiation
protection purposes [I9, I13, I16]. Various methods are used to quantify the uncertainties in each stageof the dose calculation for internal exposure.
30. For radionuclides emitting photons or electrons of sufficiently high energy, measurements of theradiation leaving the human body allow a direct determination of the absorbed dose rate* in the body orin a specific organ such as the thyroid. Models for the time course of uptake and the biokinetics
following the uptake are needed to assess the cumulative dose.
31. The types of measurement used to estimate dose from internal exposure depend on whether the
exposure setting is environmental, occupational or medical. For environmental exposure settings, dose
assessments for internal exposure are often based on measurements of radionuclide concentrations inenvironmental media. If such measurements are not available for a specific location, models must use
measurements made at other locations and times. Furthermore, the diet of specific individuals is seldom
monitored directly, and thus the uncertainty in estimates of intakes by ingestion may be larger than in
the doses per unit intake estimated by biokinetic and dosimetric models.
32. In occupational settings, doses can be derived from bioassay analysis using biokinetic models andassumptions about when intakes occurred, as well as from measurements of radionuclides in theenvironment and models of intake rates. An important source of uncertainty in estimating doses due toinhalation is the physico-chemical form of the inhaled material. The magnitude and uncertainty ofintakes derived from bioassay data depend mainly on the solubility of the inhaled material in the lung.
Mistaken assumptions regarding the rate of dissolution and uptake to blood can lead to significant
systematic errors* in estimated intakes and doses, especially those derived from measurements ofradionuclides in urine.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 101

33. In medical settings, often the quantity of radionuclides administered is known. In these cases theuncertainty in the dose estimation is dominated by uncertainties in the biokinetic and dosimetricmodels.
34. Because biokinetic models are generally designed to assess doses for representative members of
exposed populations, uncertainty in the structure of biokinetic models represents a shared error in an
epidemiology study. However, uncertainties of the parameter values for these models can be bothshared and unshared. For retrospective assessments, bioassay data generally provide additional
information about parameter values that will reduce uncertainties on dose estimates. However, there areparameters that do not strongly influence bioassay quantities, but may nevertheless significantly affectdose estimates. An illustrative example of this is long-term binding of inhaled plutonium to bronchial
airways of the lung; here, a small bound fraction (in the order of a few per cent) can increase absorbed
doses to bronchial cells from inhaled plutonium by over two orders of magnitude [B12]. Over the past
decade, Bayesian methods have proved useful in refining estimates of intakes and quantifying theuncertainties on intakes and doses estimated from bioassay data [D4].
35. Uncertainties in the absorbed fractions calculated using dosimetry models arise because of
uncertainty in the positions of source and target tissues, and in the geometry and masses of thesetissues. It is necessary to perform Monte Carlo radiation transport calculations for a set of phantoms
that represent particular combinations of source and target geometries in the determination of theuncertainty distribution of interest. Estimation of uncertainty in absorbed fractions may need to accountfor a systematic difference between the idealized (reference) phantom and the average individual in the
population of interest.
36. Uncertainties of dose estimates in various major epidemiological studies are discussed inappendix B. A limited number of studies have used parameter uncertainty analysis to quantify
uncertainties on doses per unit intake. None of them distinguish variability from uncertainty in the
distributions derived for model parameters since many of these studies were not intended for
epidemiological purposes.

C. Uncertainties in risk assessment
1. Impact of uncertainty in health effect information on risk estimates andstatistical power of epidemiological studies
37. Uncertainty in health effect information, namely, selection bias, information bias, the effect ofconfounding factors and changes in information over time may lead to systematic errors in theestimates of risks from radiation exposure and/or affect the precision of these risk estimates. Statisticalmethods have been developed to deal with multiple sources of bias. However, concerns have beenraised about the methodological basis for such approaches (see discussion in [G16]). To date, thesemethods have been used infrequently in epidemiological analyses.
38. Studies with low statistical power, typically owing to small sample size and/or low radiation
doses, usually yield indeterminate results whether or not there is a true underlying association between
radiation dose and the disease of interest. However, confidence intervals at, say, the 95% level, eachobtained from one of a very large number of independent studies, will over the long term give asignificant result at least 5% of the time regardless of whether or not there is a true association between

102 UNSCEAR 2012 REPORT

radiation dose and disease. For these reasons, the evidence regarding risk from radiation exposure relies
heavily on studies of high statistical power with, when possible, replications of study findings indifferent exposed populations.
39. Combining data from several existing studies is a useful way to improve risk estimates or gain
insights into the patterns of risk in different populations. There are two primary approaches: metaanalyses* of published findings and combined analyses using original data.
40. Meta-analyses use data from existing studies without re-analysing the data. The published results
are averaged with weights determined by the precision of the findings and in some cases judgements as
to the overall quality or comparability of the specific studies. A concern is whether the variations
between studies, either in the control for confounding factors or in modifying factors that influence therisk from radiation exposure, could lead to incompatibility in the results across the studies. A statistical
approach that is often used in meta-analyses is the “random-effects” model that takes account not onlyof uncertainties within the studies, but also between the studies [L27]. Typically, the confidence
interval for the overall risk estimate is wider under a random-effects model than in a straightforward
meta-analysis (“fixed-effect” model), particularly if there is strong evidence of heterogeneity in thefindings between the studies.
41. Combined analyses involve joint analyses of the original data pooled from various studies. With
access to the data from the individual studies, it is possible to use the same approach to analyse all of
the data; for example, by using common exposure categories and by applying the same form of
adjustment for confounding factors. This should enhance the compatibility of the findings across thestudies. Since a combined analysis is easier to perform if the individual studies are of a similar design, aprospective approach whereby studies are constructed around a common protocol may be moreadvantageous than a retrospective pooling exercise. Questions not in the original studies may also be
addressed. For example, based on studies with comparable protocols, Darby et al. [D3] were able tolook at how radon-related risks varied between continuing smokers, ex-smokers and never-smokers.
Nevertheless, if there is statistically significant heterogeneity in estimates of risk between studies,careful examination is required of the possible reasons for this heterogeneity before deciding whether it
is sensible to pool all or even part of the data.

2.

Impact of exposure uncertainty

42. Uncertainty in dose estimates is a recognized and important source of potential bias and increased
uncertainty in the estimation of risk from radiation exposure. While the nature of the impact of
uncertainty in dose estimates on risk estimates is understood reasonably well, it is important tounderstand how the different types of dose uncertainty can affect risk estimates and the limits ofexisting approaches. More effort is needed to improve practical methods to ensure that risk estimatesproperly account for the impact of uncertainty in dose estimates.
43. In practice, the magnitude of systematic errors—expressed either as a proportion or as an absolutevalue—may vary according to the level of dose, possibly in a complex fashion. Consequently, theimpact of these errors would need to be evaluated on a case-by-case basis. Generally this involves
sensitivity analyses, in which different assumptions are made about the form and magnitude of thesystematic errors. For example, in analysing the United Kingdom National Registry for Radiation
Workers, Muirhead et al. [M21, M22] explored the impact of dose recording practices by conducting
sensitivity analyses that excluded some or all of the correction factors applied to recorded doses.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 103

44. Shared errors in the estimation of dose increase uncertainty in estimates of risk from radiation
exposure and can result in biased estimates of the risk. The shared errors in the estimation of dose arerarely considered for two reasons: (a) dose estimates rarely, if ever, include information on the natureor likely magnitude of shared errors; and (b) even if useful information on shared errors is provided
there are no well-established methods for incorporating this information into risk estimation. In someanalyses of nuclear industry workers, including of workers at Oak Ridge National Laboratory (ORNL)[S25] and at Hanford [G8] in the United States, account was taken not only of correction factors toallow for differences between recorded doses and organ doses, but also for the uncertainty in these
correction factors [T2]. In essence, these analyses took account of shared errors that arose fromapplying the same correction factors to doses for groups of people. Methods to effectively use twodimensional Monte Carlo dosimetry systems providing information on shared errors in estimating doses
for risk estimation are in the early stages of development. Thus, the main aim in dealing with sharederrors in dose estimation is to develop methods to ensure that their effect is reflected in the uncertainty
on estimates of risk from radiation exposure.
45. Differential measurement errors, such as when greater efforts are made to determine the dose for
persons with the disease of interest than for persons without it, can introduce serious and unpredictablebias. While it may be possible to assess whether risk estimates have been underestimated—or
overestimated—as a consequence of differential errors, quantifying the impact on dose–response
analyses is almost impossible without a detailed understanding of the structure and magnitude of theseerrors. Avoiding such errors is a major concern in study design.
46. How non-differential unshared errors in the estimation of dose affect risk estimates is wellunderstood and methods for dealing with them are well-developed, at least for relatively simple
situations. For example, risk estimates based on observed doses that include unshared measurement
errors are biased toward zero, while if dose errors result from assignment error then there is little or nobias in the risk estimates [C7, H18, S6].
47. An example of measurement error occurs when individual dosimeter readings are used to estimate
individual doses to occupationally-exposed workers over a certain period; the error reflects a (random)lack of precision in each of the individual measuring devices. Here, assuming a multiplicative error
model for dose and a linear dose–response model, the effect of error in the estimated dose is to flatten
the fitted dose response gradually with increasing dose, creating an apparent negative curvature and abias toward reduced slope [C7]. Similarly, if the true dose–response relationship were linear–quadraticwith positive curvature, the fitted curve might show a reduced, zero, or even negative curvature.
48. A statistical method, regression calibration,* can be used to adjust the doses and, at least
approximately, adjust the risk estimate uncertainty for the effects of unshared errors in the dose
estimates. The basic idea underlying regression calibration is rather intuitive: each measured (orassigned) individual dose is replaced by the expected value of the true individual dose given themeasured (or assigned) dose and the distribution of true individual doses in the population [C7].
However, the distribution of true individual doses in the population is strictly not known and has to be
replaced by an assumed distribution, which can be based, e.g. on a validation study for the dose
estimates. If an additive and unshared non-differential measurement error and the true dose*
independently have normal distributions, with variances σC2 and σ2 respectively, then in linear
regression the correction for measurement errors would increase the slope of the dose–response curveby a factor of 1+ σC2 /σ2. Schafer and Gilbert discussed other error structures that can be approachedanalytically [S6]. In a recent analysis by Pierce et al. [P6] of the Life Span Study (LSS) of the survivorsof the atomic bombings in Japan, the correction for measurement errors with geometric standard
deviations in the range 35% to 40% increased estimates of the risk per unit dose by 12% to 14%.

104 UNSCEAR 2012 REPORT

49. Except in the simplest situations, computations for regression calibration can be challenging.
Considerable research, often in the context of studies of radiation-induced health effects, is facilitating
its use in solving real problems. One line of research is the development of methods to perform
regression calibration with fewer assumptions about the distribution of true doses in the population.
50. Regression calibration was originally developed to handle situations in which all of the dose error
came from unshared either measurement or assignment error. However, in reality the unshared errors inradiation dose estimates come from a combination of the two types. Methods for handling this more
realistic situation have been studied using a generalized model for unshared errors that can include bothmeasurement and assignment errors.
51. While regression calibration and related methods to address unshared dose errors rely onfrequentist methods, Bayesian methods provide an attractive, conceptually simple approach tocharacterize the influence of dose error on risk estimates (see, e.g. [L14]). The Bayesian approach
involves specifying a dose–response model together with a prior distribution on the relative likelihoodof specific parameter values. The data are then used to update the state of knowledge about possible
values of the parameters. Recent advances in Monte Carlo-based Bayesian computational methods havemade it possible to obtain samples from the posterior distribution of model parameters for many of themodels of interest in studies of radiation-induced health effects. The information in these samples canthen be used to provide estimates with credible uncertainty intervals for parameters of interest. In
principle, the basic Bayesian approach can be extended to allow for unshared and shared dose errors by
incorporating information on the nature of the dose errors and prior probabilities for parameters
associated with these errors. However, further development of practical Bayesian methods applicable tolarge radiation studies is needed before they can be routinely used in estimation of risk from radiation
exposure.
52. With increased awareness of the importance of dose uncertainties, the need for better ways tocharacterize uncertainties in individual dose estimates has become more obvious. A general statement
about the average relative uncertainty in the dose estimates (e.g. 30% uncertainty) or statement of theuncertainty for individual doses, is not sufficient to properly assess the impact of dose uncertainty on
risk estimation. Some indication of the relative contributions of measurement and assignment error to
the dose estimates would be helpful. Information on shared errors is rarely provided, partly because ofdifficulties in determining their likely magnitude, but also because methods for using such information
are still under development.
53. Over the past decade, dosimetrists have begun to develop complex Monte Carlo dosimetry
systems that provide multiple realizations of individual dose estimates based upon a characterization of
uncertainties about the individual’s exposure situation and in the dosimetric models. These systems aim
to capture the effect of both shared and unshared errors. One of the biggest challenges is the removal of
the effects of unshared measurement error, otherwise risk estimates will likely be biased and theuncertainty of those estimates understated.
54. Proper use of the dose realizations from such systems requires weighting that combines
information about realization-specific risk estimates using likelihood-based weights. A relatively
simple approach to obtain risk estimates would be to compute a likelihood-weighted average of therealization-specific risk estimates. Somewhat better estimates can be obtained using Monte Carlomaximum likelihood (MCML) calculations, in which one computes the profile likelihood for theparameter of interest for each realization and uses the average of these functions for inference about theparameter. Stayner et al. [S25] used data on cancer mortality in the cohort of ORNL nuclear workers toillustrate the use of the MCML method to adjust for shared errors.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 105

55. Bayesian analyses that combine information from both the outcome data and the dose realizations
from such systems with prior information on the risk model parameters, while fraught withcomputational challenges, have the potential to provide more information on risk uncertainty than
MCML or related frequentist approaches. However, little work has been done to develop such methods
or to address the computational and data management issues to apply them to relatively large andcomplex data sets from many radioepidemiological studies.

3.

Impact of model uncertainty*

56. Models are designed to give a simplified description of the main processes or an assessment of
key parameters of complex processes. The results of various models may approximate a given data set
equally well but yet give different estimates for some quantities of interest. Evaluating the results fromseveral models provides insight into the information contained in the data and possible artefacts
introduced by specific models. Evaluating several models increases confidence in results that arecommon among them and that exhibit good quality of fit. Taking into account several models generally
results in uncertainty intervals that are wider than those given by the single models.
57. Generally, the impact of model assumptions is small for upper dose categories (if they havesufficient statistical power) and for the central regions of the co-variables considered in a study, such as
birth year, age at exposure, age at diagnosis or death, or smoking rate. At low doses and at the bordersof the range of the co-variables considered, however, the impact might be quite large. For example, inan analysis of Preston et al., for survivors aged 60 at the time of the atomic bombings in Japan and who
received a colon dose of 1 Gy, considering the incidence of solid cancer at age 70, the estimates ofexcess relative risk using two preferred models differed by a factor of 2.5 [P14]. In another example,
for the risk of fatality from lung cancer among male Mayak workers at age 50 following an exposure toplutonium between the age of 20 and 40 years with a cumulative dose of 0.1 Gy, the estimates of ERR
using preferred empirical and mechanistic models differed by a factor of four [J3].
58. Quantification of model uncertainty is complicated by the fact that it represents a conceptual
uncertainty; however, one approach is to represent model uncertainty in an uncertainty analysis by
assigning discrete probabilities to plausible alternative model structures.
59. Model that are too simplistic obviously describe the data poorly, while models with too many
parameters may result in uncertainties of estimated quantities of interest too large to be real or may
produce spurious effects. So-called “information criteria” have been derived to optimize the number ofmodel parameters and select between different models. Criteria frequently used are the Akaike
information criterion* (AIC) [A3, A4, B25, C10], derived from information theory, and the Bayesian
information criterion* (BIC) derived from Bayesian statistics [S10, Y2]. Walsh suggested theapplication of the information criteria in analyses of radioepidemiological data [W2].
60. Multi-model inference* is a methodology that combines results for a quantity of interest that were
derived from the same data with different models. Weights based on an information criterion are
assigned to probability density functions derived from different models. There is a large body of
publications on model uncertainties (for summaries, see [B25, C10, H15]). However, applications in thefield of radiation research are rare.
61. In some cases, publications of multi-model inference in the field of risk from radiation exposure
demonstrated that uncertainty intervals derived by multi-model inference are wider than those derived
from well-fitting descriptive models by up to a factor of two or even more; in other cases, results thatwere significant in a well-fitting descriptive model were no longer significant when more models were106 UNSCEAR 2012 REPORT

considered [K2, W4]. The Committee notes that neglecting model uncertainties may lead toconsiderable over-confidence in risk estimates, and considers that multi-model inference techniquesshould be used in future risk evaluations, and that model uncertainties should be explored using both
empirical and mechanistic models.

IV. UNCERTAINTIES IN TRANSFERRING RISK QUANTITIES FROM
GIVEN STUDIES TO OTHER EXPOSURE CONDITIONS OR
POPULATIONS OF INTEREST
62. This chapter discusses the transfer of risk estimates derived from observational studies to draw
inferences for other populations of interest who may be exposed under different conditions from theobservational studies. Appendix C provides more detailed explanation, technical information andreview, including consideration of the uncertainty in the dose and dose-rate effectiveness factor(DDREF), and in modifying factors to estimate risks from exposure to high-LET radiation, lowerenergy photons and low-energy electrons.

A. Transfer to another population or time period
63. The UNSCEAR 2006 Report [U12] considered that the best way to transfer estimates of risk fromradiation exposure between populations was unknown, and that currently the most useful and relevant
information came from multinational comparisons of cancer-specific, radiation-related risk. If two
populations have distinctly different age-specific baseline rates* for a given cancer site, additive andmultiplicative projections of risk from one irradiated population (e.g. the LSS cohort of the atomic
bombings survivors) to a second population yield discordant risk estimates. Though not necessarily
correct, results of the projections differ little if the two populations have similar baseline rates.
64. Both additive and multiplicative projections are plausible in terms of possible biologicalmechanisms. If exposure to ionizing radiation—and other possible risk factors—act mainly as cancer
initiators, then one might expect the effect of the exposure to be approximately additive. If this were thecase, the dose-specific excess absolute risk* (EAR) would be expected to be relatively independent of
the baseline rate* and the same for the two countries. In contrast, to the extent that differences inbaseline rates reflect differential population exposure to cancer promoters, the dose-specific EAR might
be expected to be proportional to the baseline rate. Thus, if this were the case, the dose-specific excess
relative risk (ERR) would be expected to be about the same for the two countries [N7]. However,mechanisms of carcinogenesis are not sufficiently well understood to allow a decision on theappropriate risk transfer model. Instead, comparisons of estimates of risk from radiation exposure
derived from different epidemiological studies are used (see, e.g. [N19, P11]). Uncertainty about the
choice of projection model needs to be incorporated into estimates of radiation-related risk for the
population of interest, particularly for public policy purposes such as radiation protection or
adjudication of compensation claims for possible radiation-related cancer.
65. Useful site-specific data on baseline cancer rates as functions of attained age are readily available
for many populations [I5]. Information on radiation-related cancer risk as functions of age is available
from studies of exposed populations, including the LSS cohort and numerous studies of medically andANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 107

occupationally-exposed populations [N19]. The relationship between the two sets of data varies byorgan site and population, and is not straightforward. For example, age-specific baseline rates of female
breast cancer are markedly lower in Japan compared to those in the United States, but radiation-related
excess absolute risks are comparable between the LSS study cohort and medically irradiatedpopulations in the United States. Assuming the dose-specific ERR to be the same for the LSS and for
the United States population results in a risk estimate for the United States population that is four times
higher than that obtained using an additive transfer model (table 1). Baseline rates for gastric cancer, on
the other hand, are much higher in Japan than in the United States, yet radiation-related excess relative
risks are similar in the two countries [N19]. Appendix C of this annex discusses these and further
examples in more detail.
66. Estimates of risk from radiation exposure obtained from epidemiological studies apply to theperiod of observation in those studies. For most members of a cohort study, the observation period does
not, in general, extend up to the end of their lives. In order to derive lifetime risk* estimates,
extrapolations have to be performed that are based on the time dependencies seen during theobservation period. Attained age is the independent variable most closely associated with extrapolating
risks over a lifetime. Radiation-related risks tend to decrease exponentially with age attained. Annex Aof the UNSCEAR 2006 Report of the Committee [U12] summarizes a number of quantities that areused to describe lifetime risks.
Table 1. Best estimates and 90% confidence intervals of excess cancer rates per unit dose in the
United States based on different transfer models of LSS risk factors
The risk projection applies to age 70 after exposure at age 30

CancerRisk quantity
on which transfer is based

Extrapolated excess rate per unit dose(cases per 104 PY Gy)

Breast cancer

ERR per unit dose
EAR per unit dose

36 (23, 54)
9.2 (6.8, 12)

Gastric cancer

ERR per unit dose
EAR per unit dose

1.2 (0.8, 1.7)
9.5 (6.1, 14)Colon cancer

ERR per unit dose
EAR per unit dose

8.2 (4.6, 12)
8.0 (4.4, 12)

B. Transfer to risks from LSS to other exposure conditions
67. In this annex, the Committee uses a value of 0.1 Gy as an upper value of the low-dose range for
low-LET radiation, and doses up to 1 Gy are called moderate, while doses above 1 Gy are called high.
Low dose rate* is used to express doses-rates for low-LET radiation below 0.1 mGy/min averaged over
one hour. Although the Committee had previously reviewed the evidence related to transferring risk
estimates derived from studies of acute exposures* at moderate or high doses to exposure situations at
low doses or low dose rates, it did not quantify uncertainty. The United States BEIR VII analysis
derived a distribution of the dose and dose-rate effectiveness factor (DDREF) with a mode of 1.5 and a
95% credible interval of 1.5 to 2.3 [N19]. However, the resulting uncertainty distribution wasconsidered to be misleadingly narrow and a wider distribution was used subsequently. The Committee
considers that the present knowledge of the DDREF may be expressed by a ratio of the 95th percentileof the uncertainty interval to the 5th percentile of at least a factor of four.

108 UNSCEAR 2012 REPORT

68. In the past decade, a number of reports have shown evidence that the biological response toexposures at low dose is different from that at moderate and high dose (in terms of DNA double-strand
repair, gene expression and abundance of proteins). Because carcinogenesis following low doses is notcompletely understood, estimates of cancer risks from radiation exposure are necessarily more
uncertain when extrapolating from moderate- or high-dose studies to low dose.
69. Despite the increasing statistical power of epidemiological studies, the statistical power of single
studies of cancer risk after protracted exposures* with cumulative doses of at most a few hundred
millisieverts is still low. Nevertheless, a meta-analysis of cohorts with prolonged occupational exposure
has indicated that risks per unit dose are not inconsistent with those derived from the LSS cohort of theatomic bombing survivors [J5].
70. Estimates of cancer risks from exposure to ionizing radiation are based primarily on analyses ofdata on dose response in the Japanese atomic bombing survivors, who mainly received an acuteexposure to high-energy photons. In estimating cancer risks from exposure to other types of radiation(e.g. neutrons, alpha particles, and lower-energy photons and electrons), estimated risks for the atomic
bombing survivors must be modified to address the dependence on radiation type. An exception
involves the risk of lung cancer from inhalation of radon and its decay products, where the risk fromradon exposure can be estimated directly from epidemiological data, without the need to estimate
absorbed dose and the biological effectiveness of alpha particles. 1
71. Modifying factors to represent the effectiveness of different radiation types compared with highenergy photons can be applied to estimates of absorbed dose at the site of an organ or tissue to obtain abiologically significant dose on which the risk of cancer at that site is assumed to depend [K6]. The
Committee has discussed values for these modifying factors and their uncertainties that were developedfor use in estimating cancer risks from actual exposures on the basis of data on relative biologicaleffectiveness* (RBE) obtained from radiobiological studies. Modifying factors for some radiation types
can also be estimated from epidemiological data. The Committee has reviewed published analyses ofmodifying factors and their uncertainties for radiation types of most general concern (neutrons, alphaparticles, lower-energy photons, and low-energy electrons) and for inducing cancer in humans(appendix C to this annex).

V. UNCERTAINTIES OF SELECTED RISK EVALUATIONS
72. The Committee has considered three examples of risk evaluation that summarize the present stateof knowledge, estimate the value of various quantities that express risk and indicate the impact ofdifferent sources of uncertainty:(a) Solid cancer after external exposure to radiation with cumulative doses of the order of
100 mGy above that from exposure to typical levels of background radiation;(b) Thyroid cancer after radiation exposure during childhood;(c) Lung cancer after residential exposure to radon decay products.
1

In radiation protection, the dependence of cancer risks on radiation type is represented by the quality factor (Q) and radiation
weighting factor (wR). Point values of Q and wR are defined by the ICRP for use in calculating the radiation protection quantities:
dose equivalent, equivalent dose, and effective dose. However, Q and wR are not intended for use in estimating cancer risks from
actual exposures of identified individuals or groups.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 109

For each of the first two cases, two calculations were performed. One was based on a recent major
study. The second was based on extrapolating risk using data from other studies. This aims to show
how the more recent studies have improved knowledge on the specific risk under consideration. Moredetails on the risk evaluations are given in appendix D.

A. Solid cancer risks after external exposure to cumulative dosesof the order of 100 mGy above typical background exposure
73. Risk estimates for the combined group of solid cancers are usually based on comparatively large
numbers of cases thereby increasing statistical power and reducing statistical uncertainty. However, thegroup comprises a large number of different cancer sites and types. Carcinogenic processes and causal
associations with radiation exposure vary substantially between individual sites.
74. Overall, there is a strong body of evidence on solid cancer risks after external irradiation withcumulative doses exceeding 100 mGy based upon sophisticated analyses of data from the atomic
bombing survivors and a growing number of other studies of people with occupational orenvironmental exposures.
75. Most work on sources of uncertainty beyond that on statistical sampling error has focussed on
dosimetric errors, notably in the LSS and the international workers study [S25]. Uncertainty from othersources, such as procedural aspects of conducting the study or insufficient information on potential
confounding factors, are often noted qualitatively, but usually not formally incorporated into risk
estimation.
76. The Committee considered a risk evaluation for a population of workers who began work at age
30 and were occupationally exposed to low-LET radiation from the ages of 30 to 44 with a total dose of
100 mGy. Two approaches were taken to estimate radiation-related solid cancer risks and associateduncertainties:(a) The first relies on a study of the United Kingdom National Registry of Radiation Workers(NRRW) for the risks of all cancers combined and considers possible age-related changes in themagnitude of the so-called “healthy worker effect” [M21]. The results indicate that the expectedbaseline lifetime risk of developing a solid cancer (other than non-melanoma skin cancer) is 40.3
(95% CI: 38.5, 41.4) per 100 exposed workers, with an expected risk of an exposure-associatedcancer of 1 (95% CI: 0.07, 1.97) per 100 exposed workers. This indicates that roughly 2 (95% CI:
0.2, 4.8) per cent of all the cancers are expected to be associated with the exposure. This proportion
was found to be essentially constant for all ages at diagnosis.
(b) The second characterized the effect of radiation exposure on solid cancer rates using sitespecific and age-dependent risk models derived primarily from LSS cancer incidence data but
excluding any consideration of the NRRW results [K7]. The estimate of radiation-related lifetime
risk at age 45 was 0.81 (95% CI: 0.32, 1.6) per 100 exposed workers, and a total number of
expected cases (baseline plus radiation-related) of 41.8 (95% CI: 38, 44) cases per 100, leading to
an attributable fraction* of 1.9 (95% CI: 0.8, 3.7) per cent (table 2). The uncertainty in the DDREF
dominates the uncertainty in these estimates.

110 UNSCEAR 2012 REPORT

Table 2. Estimates of exposure-related risk of cancer incidence, based on the BEIR VII/NCI risk
assessment methodology, for United Kingdom nuclear workers who received an absorbed dose of
100 mGy between the ages of 30 and 44 with no additional occupational exposure
StatisticaMean

95% credible interval
Lower

Upper

Total cancer casesa

41.8

38.6

43.5

Excess cancer casesa

0.81

0.32

1.6

Attributable fraction (%)

1.9

0.8

3.7

Total cancer cases and excess cases are expected values for an assumed population of 100 workers with follow-up from age 45

through to the end of life. The number of cases includes all solid tumours, except non-melanoma skin cancer.

77. The two approaches agree very well on a lifetime excess cancer rate of 1 case among 100 United
Kingdom exposed workers after a total dose of 100 mGy between ages 30 and 44. Thus the new studyof the United Kingdom NRRW data increased confidence in the transfer of risk estimates for all cancers
from the LSS cohort to other populations. Although this approach took into account uncertainties due tothe risk transfer from Japanese to United Kingdom populations, and from exposures ranging from acuteto protracted, the calculated uncertainty interval (0.3 to 1.6 cases) is considerably smaller than theinterval derived from the NRRW study alone (0.07 to 1.97 cases). (The large uncertainty for the NRRW
study is due to its limited statistical power, in spite of its large size—177,000 workers). Whether or not
the uncertainty interval based on the risk transfer is too narrow cannot be answered presently.

B. Thyroid cancer after radiation exposure during childhood
78. Previous UNSCEAR reports concluded that the thyroid is highly susceptible to the carcinogenic
effects of external exposure to radiation during childhood, and thyroid cancer risks remain elevated formany decades [U12]. The excess risk* decreases strongly for older ages at exposure. Evidence of the
carcinogenic effects of exposure to 131I came from studies of individuals exposed to radiation from the
Chernobyl accident during childhood or adolescence. A number of epidemiological studies resulted inconsistent estimates of the ERR for thyroid cancer after an exposure during childhood or adolescencewith a thyroid dose of 1 Gy. It was emphasized that medical surveillance of thyroid diseases escalated
in the affected countries after the accident, increasing the number of thyroid cancer cases reported inregistries.
79. Two new analytical studies on children who received external exposures during medical treatment
resulted in risk estimates either similar [B11] to the previous study of the same cohort, or in a lower
estimate of the ERR per unit dose [A1] (probably because of a decrease of risk with the longer followup times). The new study after the Chernobyl accident investigated data for a longer time since
exposure than before and also tended to have a lower estimate of the ERR per unit dose.
80. Methods to correct estimates of thyroid cancer risk for the large random dose errors in two studies
have been implemented [K10, L14]. For these cases, corrected estimates of the ERR per unit dose arelarger by a factor of about three than those using a regression calibration with mean values forindividual dose. Shared errors can influence the dose response further, but the impact remains to beevaluated explicitly. The Committee emphasizes that reliable risk estimates are normally derived fromstudies that have reliable dose estimates, and thus are less affected by dose uncertainties.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 111

81. The impact of the choice of model on risk estimates has been analysed in two studies with morereliable dose estimates [W3]. At 12 years after exposure, ERR estimates for young ages at exposure
appear to be strongly influenced by the baseline modelling, while EAR estimates were more stable.
82. The Committee evaluated thyroid cancer risk for a hypothetical group of Ukrainians who were
10 years of age at the time of the Chernobyl accident. Their cumulative thyroid dose was assumed to be
200 mGy almost exclusively due to incorporation of 131I. Surveillance of thyroid diseases in the group
was assumed to correspond to the situation one to two decades after the accident in parts of Ukrainewith higher levels of deposition. Two approaches to analyse risk and uncertainties were again used:(a) A first approach used only studies conducted before the accident. According to the best
estimates, the baseline rate of 14 cases of thyroid cancer during the lifetime of 10,000 males would
be increased by the radiation exposure to about 20, while the baseline rate of about 60 cases during
the lifetime of 10,000 females would approximately double (table 3). Baseline rates are larger for
females than for males, and the rate ratios (relative risks)* from radiation exposure were also
assumed to be larger for females than for males. The 95% credible interval for the radiationassociated rate ranges for males from 1.2 to 21 per 10,000, and for females from 11 to 210 per
10,000. The large uncertainty is dominated by the statistical uncertainty in the estimate of the ERR
per unit dose for acute exposure followed by the uncertainty in the DDREF. In these calculations,
the ERR was assumed to be independent of time after exposure.
(b) Studies conducted after the accident have, however, demonstrated high ERR values at a few
years after exposure that decrease over the following one or two decades. Furthermore, in the first
approach, above, the ERR was used to transfer risk from the LSS to the hypothetical Ukrainian
population. However, studies conducted after the accident indicate that the EAR for thyroid cancer
may also be appropriate to transfer thyroid cancer risk. Risk projections based on the EAR modeltransfer were higher than those based on an ERR model transfer, generally by a factor of two. It
may be noted that the difference here is because of an uncertainty in the risk model, and not
because of an uncertainty in the transfer model. If the EAR model estimate for the EAR is replacedby the product of the ERR and the baseline in the LSS, then the difference in the lifetime risks ofthe two transfer models is relatively small.
Table 3. Estimates of hypothetical numbers of rates of thyroid cancer (best estimates and 95% credibleintervals) among 10,000 Ukrainians, who were of age 10 years at the time of the Chernobyl accident andreceived a thyroid dose of 200 mGy from incorporation of 131I, using the BEIR VII models [N19]Sex

Baseline (per 10,000)

Excess (per 10,000)

Total (per 10,000)Males

14 (–)

6.6 (1.2, 21)

20 (15, 35)

Females62 (–)

59 (11, 210)

121 (73, 272)

C. Lung cancer after residential exposure to radon
83. The main health effect from inhalation of radon decay products is an increased risk of lungcancer. More than 20 analytical studies (mostly case–control studies) of lung cancer and residential
exposure to radon, and three pooled analyses of the individual data of the European [D3], North
American [K15] and Chinese studies [L30] have been published. These pooled studies consistently
showed an approximately linear increase in the risk of lung cancer with increasing long-term radon
exposure.

112 UNSCEAR 2012 REPORT

84. The greatest challenge in such studies is to assess radon concentrations accurately for the relevant
period of interest (from 5 years to about 35 years before lung cancer was diagnosed or, for the controls,
before the date of their interview). Usually radon is measured for one year in one or two rooms of thecurrent home and of all other dwellings inhabited by the cases and controls during the period of interest.
Uncertainty in the exposure assessment arises from detector measurement error, the use of current
measurements of radon concentrations in air to reflect past levels for up to 30 or more years ago, spatial
variations within a home, missing radon concentration measurements, and failure to link radon
concentration measurements with subjects’ occupancy patterns.
85. So far, the largest and most informative study on lung cancer and indoor radon is the pooled
analysis* of 13 European case–control studies [D3]. It includes 7,148 cases and 14,208 controls, allwith detailed information on smoking histories and radon measurements in homes that the individual
had occupied during the previous 15 years or more. The risk estimates were formally adjusted formeasurement (year-to-year variability of measurements) and assignment (imputation of missing values)
errors using regression calibration. Without these adjustments, the estimate for the ERR per unit
average radon concentration was 0.08 (95% CI: 0.03, 0.16) per 100 Bq/m3. After adjustment the ERR
estimate per unit average radon concentration increased to 0.16 (95% CI: 0.05, 0.31) per 100 Bq/m3.
86. Several other methods have been applied to account for the uncertainties in exposure assessment
such as those associated with deriving doses from track-etch measurements or from direct
measurements of radon in air, or with using a study design that limits participants to long-term
residents. Other methods include conducting sensitivity analyses that limit subjects to those with moreaccurate information, or improving the exposure assessment by linking it with spatial and temporal
occupancy patterns. Applying these methods consistently increased the estimate of excess relative riskof lung cancer by around 50% to 100% (see appendix B). In addition, uncertainty in the assessment ofpotential confounding factors, such as smoking, may distort estimates of the true risk. The true ERR per
unit radon concentration could thus be somewhat higher, even after correction for year-on-year
variation in measured radon concentrations [W8].

VI. KEY RESEARCH NEEDS
87. Research is needed to identify sources of measurement error, which leads to over-estimation of
random variability of true dose in a cohort, and develop procedures to either remove them or accountfor them using regression calibration on each realization of a set of possibly true doses.
88. Because of the complex nature of risk analyses making full use of Monte Carlo uncertainty
propagation to produce multiple realizations of cohort dose sets, there is a need to develop anddistribute tools to make efficient implementations of these computationally intensive methods readily
available to researchers. Guidelines would be useful to help researchers evaluate when shared errors indose reconstruction models are likely to have a marked effect on dose response or its uncertainty.
89. Many exposures to ionizing radiation involve low-LET radiation at low doses or low dose rates orradiation types other than high-energy photons. To improve estimates of cancer risk and theiruncertainties for such situations, further research is needed to quantify risks at low-dose and low-doserate exposures to low-LET radiation and modifying factors to represent the effectiveness of radiation
types other than high-energy photons in inducing cancer in humans, and their uncertainties. A
particularly important need is further research on the biological effectiveness of lower-energy photons,
especially X-rays of various energies, given their common use in medicine.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 113

90. While most studies of radiation-induced health effects focus on a single model to analyse theradiation dose response and quantify the uncertainty of the risk estimate, alternative models can also
often describe the data. In general, not allowing for uncertainty about the form of the risk model
underestimates uncertainty in estimates of the quantities of interest. There is a need to develop methods
that incorporate uncertainty about the form of the model for radiation dose response.
91. New approaches are essential to improving understanding of radiation-related health risks and to
reduce uncertainty of risk estimates at doses of general concern. One of these approaches is toincorporate radiobiological knowledge by analysing epidemiological data with models ofcarcinogenesis. The identification of a possible marker of radiation-induced cancer and performing
measurements of the marker in a large epidemiological study is another approach that may also
improve knowledge of low-dose radiation-induced health effects.

VII. CONCLUSIONS
92. Estimates of cancer risk from exposure to ionizing radiation derived from radioepidemiologicalstudies are uncertain because of the power of the study, the intrinsic stochastic variability of cancer
cases, imprecise characterization of risk factors, and the effects of risk factors other than radiation
exposure that can distort results unless properly addressed. Reports of estimates of risk from radiation
exposure should include a clear and thorough discussion of limitations of the data and a realistic
assessment of how these limitations might affect the results.
93. In recent years, increased attention has been paid to the uncertainty in risk estimates associatedwith uncertain estimates or measurements of dose. Failure to account for dose uncertainty can lead tobiased risk estimates (often underestimates) and to overly optimistic statements about the confidence inthese estimates. The different effects of errors in individual doses result from measurement or theassignment of representative values. There is increasing awareness that shared dose errors may bias risk
estimates or underestimate the uncertainty of these estimates. In many situations, regression calibration(in which observed dose estimates are replaced by their expected values given what is known about theindividual and the population dose distribution) is a relatively straightforward and often quite effective
method for dealing with random individual dose errors. The development of multiple-realization
dosimetry systems and computationally intensive Bayesian methods that make full use of the dose
realizations to allow for the effects of dose uncertainty on risk estimates are topics of great interest.
There is a need to develop practical methods for such analyses.
94. Risk analyses are based on models that describe the health effects of interest. These analyses
typically involve only a single model, even though various models can describe the data withcomparable quality but imply different values of risk. Neglecting model uncertainties may considerably
underestimate the total uncertainty of risk estimates. Multi-model inference is a method that considers
multiple models in risk analyses. The Committee suggests that future risk evaluations use multi-model
inference techniques.
95. The contribution of the different sources of uncertainty in transferring risk estimates from anepidemiological study to another population or exposure situation of interest depends on the objectiveof the specific risk assessment. Usually, only a few factors dominate. For example, for protracted
uniform whole-body irradiation and risk for all cancer sites combined, the uncertainty in transferring
LSS risk estimates to low-dose and low-dose-rate exposure is usually an important contributor. Forinternal exposure of single organs, the uncertainty in the absorbed organ dose and in the organ-specific114 UNSCEAR 2012 REPORT

risk coefficients may dominate. Uncertainty in transferring risk coefficients from one population toanother are of importance when these populations exhibit large differences in the baseline rates of
disease. Additional uncertainties must be considered when using estimates of the excess relative risk to
calculate the likelihood that the manifestation of a diagnosed cancer in a specific individual can be
attributed to radiation exposure.
96. Selected examples of risk evaluations have shown that lifetime risks are well studied for all solidcancers combined after acute and after protracted exposure with cumulative whole-body absorbed dosesof greater than about 100 mGy and for lung cancer after living for decades in homes with radon
concentrations of greater than about 100 Bq/m3 above average. Addressing known sources of
uncertainty, the 95% credible intervals span about an order of magnitude. However estimates of sitespecific cancer risks have larger uncertainties still, as shown by an example evaluating thyroid cancer
risk after an absorbed dose to the thyroid of 200 mGy in childhood.

ACKNOWLEDGEMENTS
The Committee would like to acknowledge: P. Jacob, F.O. Hoffman, C. Land, and D. Preston, who
prepared the substantive material for the Committee’s scrutiny; I. Apostoaei, N. Harley, D. Kocher,
M. Kreuzer, R. Michel, C. Muirhead, and H. Zeeb for their contributions; and L. Dobrzyński (Poland),
who critically reviewed drafts for the Committee.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 115

APPENDIX A. FUNDAMENTAL CONCEPTSI.

STATISTICAL CONCEPTS OF UNCERTAINTY ............................................................................ 115
A. Basic concepts and terminology ......................................................................................... 115
B. Approaches to statistical inference .................................................................................... 119
C. Quantifying uncertainty ......................................................................................................... 125
D. The distinction between variability and uncertainty................................................... 126
E. Accounting for dependences among uncertain model inputs andassumptions ............................................................................................................................... 128
F. Uncertainty propagation and sensitivity analysis......................................................... 128

II. EPIDEMIOLOGICAL CONCEPTS .................................................................................................... 134
A. Cohort studies............................................................................................................................ 135
B. Case–control studies ............................................................................................................... 137
C. Geographical correlation studies........................................................................................ 138

I. STATISTICAL CONCEPTS OF UNCERTAINTY

A. Basic concepts and terminology
A1.
Uncertainties on estimates of risk from radiation exposure include both those that arise indeveloping models and in estimating parameters based on a specific data set and those that arise when
the resulting risk estimates are used to assess risks for some other population.
A2.
Uncertainty in the characterization of cancer rates and risk estimation arises from a number ofsources. The inherently stochastic nature of the processes leading to the response is a primary andomnipresent source of uncertainty in any attempt to describe radiation-induced health effects.
Additional uncertainty arises because the amount of data available to characterize the risk is limited oreven, in some cases, non-existent. Furthermore since risk estimates are virtually always based on
idealized (and incomplete) models, the choice of model is another source of uncertainty in risk
estimation. When risk estimates are based on data, imprecise specification of risk factors, particularly
measures of dose or exposure, can be an important source of uncertainty in the resulting risk estimates.

116 UNSCEAR 2012 REPORT

A3.
Additional uncertainties arise when risk estimates developed on the basis of a population
exposed in a particular way (for example, survivors of the atomic bombings in Japan who received
acute, relatively high-dose exposures) are used to assess the risk in a different population (for example,
workers in the German nuclear industry who received low-dose-rate chronic exposures,* or children
who undergo CT scans). Sources of such uncertainties are described later in this report.
A4.
Because of the importance of the relationship between the characterization of the dose–
response function and the inherent, but often ignored, uncertainties in measuring or estimating radiation
doses, the report gives considerable attention to methods of adjusting for dose uncertainties and toquantifying uncertainties in risk estimates that arise from using uncertain dose estimates.
A5.
In this document the term “uncertainty” refers to the distribution of the possible true values ofa quantity of interest. The actual difference between the true value of a quantity of interest and an
estimate or measurement of that value, which is here called an “error”, is generally unobservable.
Uncertainty analysis concerns the characterization of the distribution of the possible true values taking
into account all known sources of uncertainty.
A6.
In all but the simplest cases uncertainty arises from multiple sources and in ascertaining theeffects of uncertainty it is useful and important to consider the different types of error that contribute to
the uncertainty for a given quantity of interest. One useful classification concerns the mechanism bywhich errors occur and involves whether or not errors are independent (on some scale) of the true or
observed value of the quantity of interest. This leads to a distinction between (a) “classicalmeasurement” errors (for which the error is independent of true value) and (b) “assignment” or“Berkson” errors (for which the error is independent of the observed or assigned value). Anotherclassification concerns whether or not the errors are independent between individuals. Errors that are
dependent between individuals are called “shared” errors while those that are independent are called“unshared” errors. Both shared and unshared errors can arise as a result of either measurement or
assignment error.
A7.
Measurement (classical) error: If a quantity is measured with an imprecise measuring device
then we have:observed value = true value + measurement error(A.1)

where “measurement error” is a random variable that is uncorrelated 2 with the “true value”. An
important feature of the classical error* model is that the (population) variance of the observed values,
2
2
2
2
2
s=
s true+ s merr, where σ trueis the variance of the true (unobserved) values and σ merris theobs
measurement error variance. Thus, in the case of measurement error the variance of the observed values
exceeds that of the true values. In linear regression models in which the dependent variable hasclassical error, slope estimates based on observed values are biased towards zero because interindividual variability of true values is overestimated.
A8.
Assignment (Berkson) error is typically the result of some form of assignment in which
individuals in a group are assigned a nominal representative surrogate value. Ideally the assigned value
is equal to the true mean value for that group (in which case the assignment is said to be unbiased).
Thus, using the terminology from [S6]:2Errors that are uncorrelated on one scale may be correlated on another scale. The text for this discussion focuses on additive
measurement error (such as those described in this paragraph), but for many situations errors are multiplicative, i.e. observed
value = (true value) × (multiplicative measurement error). In this case the errors are additive (and uncorrelated) on the log scale,that is log(observed value) = log(true value) + log(multiplicative measurement error), even though the additive errors (i.e.
observed value – true value) are correlated with the true values.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 117

true value = assigned value + individual peculiarity(A.2)

where “individual peculiarity”, which refers to the assignment error, is a random variable that is
statistically independent of the assigned value and depends on (generally unknown) characteristics ofan individual that affect their true value. In other words, assignment errors describe random interindividual variability of true values about a single value assigned to every individual belonging to a
distinct group. The value assigned to each individual in the group is assumed to be the true mean value
for that group. (For the case of additive assignment errors the “true mean” refers to the arithmetic mean,
while for multiplicative assignment errors the “true mean” refers to the geometric mean.) Incorrect
specification of the group mean will introduce shared error (discussed below) and can lead to bias inquantities estimated using the incorrectly assigned values. In contrast to the situation with measurement
error, with assignment errors the variance of the assigned values ( σ av2 ) will be less than that of the true
2
2
2
2
2
= av2 + ip2 or σσσ=variance of values since σσσtrue
avtrue − ip , where σ ip is the variance of the individual

peculiarity in the values about a given assigned value.
A9.
In the presence of unbiased additive assignment error (i.e. when the expected value of theindividual peculiarity is zero), risk estimates derived from a model that is linear in the true values (e.g.
dose) that is fit using the assigned values will provide unbiased estimates of the slope of the regression
on the true values. On the other hand, in the presence of unbiased multiplicative assignment error there
will be a small systematic upward bias in the slope estimate. The magnitude of this bias is a function of
the variance of the individual peculiarity factors.
A10.
Assignment errors are quite common in radiation dose estimation. Examples include:(a) situations in which there is a single dose monitoring device at some workplace and all people whowork in this location are assigned a dose based on the value recorded by this device, or (b), as is thecase for the DS02 dosimetry used to compute doses for survivors who were in typical houses at the timeof the atomic bombings, limited information on the nature of the house and the survivor’s location
within the house is used to pick one of a small number of representative house models for which
distance-dependent dose adjustment factors have been computed; the assigned value of these factors isused to convert estimated free-in-air kerma to an estimated shielded kerma for the survivor’s location.
A11.
Figure A-I contains plots that illustrate the impacts of random measurement (top row) andrandom assignment (bottom row) errors on linear dose–response parameter estimates in the presence ofmultiplicative (left column) or additive (right column) dose uncertainties. The parameters for the fitted
dose–response functions (solid lines) were estimated using the responses at the observed doses (largesolid points). The plots also include the responses at the true doses (smaller open points) and thecorresponding regression for the true doses (dashed lines). As can be seen, there is some downward bias
in the regression estimate in the presence of either multiplicative or additive errors in the measured
doses. However for additive random errors in individual assigned doses the fitted regressions are quite
similar to those one would obtain if the true doses were available. There is a suggestion of small
upward bias in the slope in the case of multiplicative assignment errors, which is as one would expect.

118 UNSCEAR 2012 REPORT

Figure A-I. Plots illustrating the effect of different types of random “dose” uncertainty on estimatesof the parameters of a linear dose–response function
The plots in the top row involve dose measurement errors while the plots in the bottom row involve errors resulting from theassignment of representative doses to individuals (assignment errors). Each plot includes both the measured or assigned
doses (large closed points) and the true doses (small open circles). The solid lines indicate the fitted value of the linear
regression of the response on the measured or assigned dose, while the dashed lines are the fitted value of the linear
regression on the true dose. The measured and assigned doses for the plots in the left hand column were generated with theassumption of multiplicative dose errors in which the magnitude of the error is on average about 40% of the true value. The
observed doses for the plots in the right column were generated using normal additive uncertainties (mean 0 and variance 1)

A12.
Shared errors are errors that are correlated between “individuals”. In the presence of sharederror, the expected value of the difference between the observed or estimated value of the quantity ofinterest and its true value need not, and indeed generally is not, equal to 0. Thus shared error can lead tobias or systematic uncertainty. Shared errors can arise for many reasons. For example, improper
calibration of a measuring device can result in measurements (for example, of doses) that differ in asystematic manner from the true value of the quantity of interest. Shared errors also arise when thequantity of interest is described as a function of some parameters and observed data and either theparameters or the functional form are mis-specified.
A13.
Examples of shared errors include assignment of an incorrect mean dose to a group of people
and use of incorrect parameters in a dose estimation model (for example, mis-specification of the yieldor hypocentre location for the atomic bombings).
A14.
Unshared errors are uncorrelated between individuals on an appropriate scale and for the
purposes of this discussion, can be taken to have a mean of zero. Unshared errors might be the result ofimprecise measurement of some quantity of interest (for example, dose) or because of the assignment of

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 119

representative values to groups of similar individuals. In the latter case, all uncertainty is due to random
inter-individual variability of true values about the assigned value (that is, this situation is identical towhat is referred to in paragraph A.8 as assignment error).
A15.
Unshared errors can arise when quantities of interest are based on individual measurements orobservations (for example, a reading from a personal dosimeter or statements about whether or not an
individual was actually exposed or whether or not they consumed contaminated food products at thetime of exposure and if so, how much).
A16.
Hofer [H16, H18] has noted that it can also be useful to classify uncertainties as either“aleatory” (Type A)*, or “epistemic” (Type B)*. Aleatory uncertainties* are those that reflect statisticalvariability in repeated observations or between different individuals in a population, whereas epistemic
uncertainties* are related to the state of knowledge or degree of belief about the unknown value ofsome specific quantity of interest. Random variability of repeated measurements or random variabilityof unknown true doses among unspecified persons are aleatory (Type A) uncertainties, while
uncertainty about the true dose to specific individuals or in the value of the excess cancer incidence
associated with a given radiation exposure in a population of interest is an epistemic (Type B)
uncertainty.
A17.
The terms “Type A evaluation of uncertainty” and “Type B evaluation of uncertainty” are used
to describe key concepts in the Guide to Uncertainty in Measurements (GUM) [J8, J10, J11], which is aformal Bayesian approach to the characterization of measurement uncertainty widely used in the fieldof metrology. The GUM defines Type A evaluation of uncertainty as an assessment of uncertainty inmeasurements that is based on the statistical analysis of a series of observations. In contrast, Type B
evaluation of uncertainty refers to non-statistical evaluation of measurement uncertainties (e.g. based onearlier measurements and evaluations or other information). These definitions differ from those of
Hofer. Unless noted otherwise, throughout this document “Type A” and “Type B” are used to refer toclassification of uncertainties in the sense of Hofer.
A18.
Uncertainties on estimates of risk from radiation exposure are a consequence of “complex
uncertainties” resulting from a mixture of shared and unshared errors of various types. Some of these
uncertainties are a consequence of individual variability (aleatory uncertainty) while others reflect
limited knowledge of mechanisms by which specific radiation-induced health effects occur (epistemic
uncertainty).

B. Approaches to statistical inference
A19.
As noted above, characterization of uncertainty involves describing the distribution of
uncertainty in a quantity of interest. Examples of quantities of interest that are relevant to this annex
include:(a) Estimates of dose from external exposures for members of a cohort of occupationally-exposed
workers based on measurements from personal dosimeters;(b) Organ dose estimates arising from internal exposures to inhaled or ingested radionuclides formembers of a worker population derived from a limited number of in vivo measurements (forexample, from a single urine bioassay), data on occupational history, and computer models of
nuclide transport and metabolism;

120 UNSCEAR 2012 REPORT(c) The magnitude and shape of the radiation dose–response and how this relationship varies withtime, gender, age and other factors, based on the follow-up of cancer mortality or incidence in a
specific cohort from a well-defined exposed population;(d) An estimate of the assigned share* (probability of causation)* for a cancer that has occurred ina person with a prior radiation exposure based on a (possibly uncertain) exposure history andestimates of risk from radiation exposure derived from observations on some other exposed
population;(e) Estimates of the cancer risk that might be expected to arise as a consequence of routine
ongoing childhood CT exposures in a large population.
A20.
Statistical inference plays a key role in estimating, describing and quantifying the uncertainties
in quantities such as those listed above. Statistical inference is used to combine data (observations),
models, and, in some cases, informed but uncertain judgements, to help reach conclusions about
quantities of interest.
A21.
There are two principal approaches to making statistical inference: the frequentist approachand the Bayesian approach. These two approaches will be briefly outlined here with an emphasis on the
key contrasting features of these two approaches.
A22.
The text in this section is intended solely to introduce key aspects of statistical inference that
underlie material described later. Fuller descriptions of these concepts are given in numerous statisticaltextbooks. Cox and Hinkley [C17] provide a good discussion of frequentist methods. Gelman et al.
[G3] provide a clear presentation of modern applied Bayesian methods, Bernardo and Smith [B6] andJaynes [J7] provide a general discussion of the ideas underlying Bayesian statistics, and Greenland[G17] discusses the application of Bayesian methods in epidemiology.
A23.
The key aspect of statistical inference is the use of data in order to arrive at conclusions
concerning values of quantities of interest. In general, data do not permit exact calculation of thesequantities. Rather, the observations can be considered as realizations of random variables from aprobability density function (pdf) that describes the distribution of these random variables given thetrue but unknown values of various parameters and, in many cases, the possibly uncertain values ofvarious explanatory variables (for example, radiation dose, age, time, and exposure to other risk
factors). In general the parameters of the pdf are defined in terms of a model (), and the quantities ofinterest are functions of model parameters (β) and explanatory variables (Z). The pdf can be represented
as f (data | , β , Z ) , which one reads as the probability density for the data given a model and its
parameters 3 and the values of any explanatory variables. This probability density, which when viewed
as a function of the parameters given the data, is called the likelihood function (L) and plays a central
role in both frequentist and Bayesian inference.*
3
While it may seem that introducing models here unnecessarily complicates the presentation, it is important to stress that thenature of the parameters are almost always determined by a model. For example in a study of the effect of radiation exposure on
cancer incidence one might usefully consider models that describe the data in very different ways (for example, excess relativerisk (ERR) models, excess absolute rates (EAR), or two-stage clonal expansion (TSCE) models). On the other hand, in manycases, such as investigation of the shape of the radiation dose response for the ERR, one model (for example, linear in dose)might involve only a subset of the parameters in another model (linear–quadratic in dose). Models of this latter type are said to benested, whereas the former type of models (ERR, EAR, and TSCE models) are non-nested.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 121

1.

Frequentist approach

A24.
In the frequentist approach to inference the observed data are viewed as one of many
hypothetical realizations of the data given the unique true values of imperfectly known parameterswhich are not considered to be random variables [I1, J8, J10, N6, N9, N11]. The pdf is interpreted as ameasure of the relative frequency of the observed data in this set of hypothetical realizations. Since theparameters are viewed as unique values, it does not make sense to make probability statements about
their values.
A25.
Frequentist inference is typically based solely on the pdf (likelihood) of the data. The
probabilities in frequentist inference (P values for hypothesis tests, confidence intervals) are concernedwith the truth of statements about some parameter(s) (or functions of the parameters) given the actual
values of the parameters.
A26.
Parameter estimation. Although other approaches are possible, parameter estimates are often
determined by choosing values that maximize the likelihood function for the observed data andexplanatory variables. Parameter estimates determined in this way are called maximum likelihood
estimates (MLEs).
A27.
MLEs have a number of desirable properties. In some simple situations, the expected value ofthe MLE (that is, the arithmetic mean from many hypothetical realizations of the data) is close or equal
to the true value of the quantity of interest. More generally, under certain conditions, the expected valueof the MLE will approach the true value of the quantity of interest as the amount of data collected
increases; however, the properties of the MLE may be affected adversely if many parameters are
estimated simultaneously. Further details can be found elsewhere (for example, [B1]).
A28.
The likelihood can be used to provide estimates of the variance (one measure of theuncertainty) of the parameter MLEs, which, in frequentist inference, is the variance of the parameter
estimates from many hypothetical realizations of the data given the true model parameters. The mostcommon way to do this involves an assumption that, given the true parameters, the distribution of theparameter estimates can be described by a normal distribution. Variance estimates obtained in this way
are called Wald estimates. Wald estimates can be used to approximate the variance of functions of theparameters. Alternatively one can view the logarithm of the likelihood as a function of the parameter(s)of interest and examine the shape of this function as the parameter(s) of interest are varied and the valueof the function is maximized with respect to all other parameters. When the (log-)likelihood is viewed
as a function of the parameters of interest maximized with respect to any other parameters it is called
the (log-)profile likelihood.
A29.
Hypothesis tests. Frequentist hypothesis testing involves the specification of null andalternative hypotheses concerning the model parameters and defining a function of the data and therelevant parameters (a test statistic) for which it is possible to evaluate (at least to a good
approximation) the distribution over multiple hypothetical realizations of the data given the null
hypothesis. This distribution is then used to determine the probability that one would obtain a value ofthe test statistic that is at least as extreme as that seen for the observed data if the null hypothesis were
true. The null hypothesis is said to be rejected if this probability is small (typically less than 0.05). This
probability is called a P value. A typical null hypothesis in estimation of the risk from radiation
exposure would be that cancer rates do not vary with dose while the alternative hypothesis would bethat the rates do depend on radiation dose.
A30.
Tests of the hypothesis that the true value of a parameter is zero are often based on the ratio ofa parameter estimate and the Wald estimate of its standard deviation, which is assumed to follow a122 UNSCEAR 2012 REPORT

normal distribution. Wald tests are widely used, but may be misleading when the data are limited orwhen the distribution of the parameter estimates is not symmetric. Generally somewhat more reliable
tests can be obtained by looking at the difference between the maximized value of the log-profile
likelihood function and the value of this function when the parameters of interest take on their values
determined by a null hypothesis. Minus twice this difference, is called the likelihood ratio test (LRT).
Under certain conditions when working with models in which the parameters in the model
corresponding to the null hypothesis are a subset of or impose some constraints on the parameters under
the alternative hypothesis, the LRT has a chi-squared distribution with degrees of freedom equal to thedifference in the number of parameters for the null and alternative models.
A31.
When comparing non-nested models (i.e. models in which the parameters in the null model are
not simply a subset of the parameters of the alternative model) there are no simple methods for
hypothesis testing. In recent years a number of measures, called information criteria, have beendeveloped to help quantify and compare the information content in alternative models. These criteria
generally involve functions of the log-likelihood and the number of free parameters in the model. Oneof the simplest and most widely used is the Akaike information criteria (AIC) [A4] which is defined as
AIC =− 2 ln( L) +2 p , where ln(L) is the natural logarithm of the maximized likelihood for the model ofinterest and p is the number of free parameters in the model. The AIC and other information criteria
play a central role in multi-model inference [B25] which is useful for addressing uncertainty in model
specification. Multi-model inference is discussed in appendix B of this report.
A32.
Confidence intervals and confidence regions. Parameter estimates and hypothesis test results
do not provide information on uncertainty. In frequentist inference the uncertainties in specificparameter estimates are usually described using confidence intervals with some defined level ofcoverage, typically 95%. When parameter estimates are highly correlated (as might be the case, forexample, for the coefficients of dose and dose-squared in a linear–quadratic dose–response model fit tocohort survival data) it can be informative to consider the joint confidence region for all of theparameters of interest. (In general it is challenging to compute confidence regions for two parameters,
and almost always impractical to compute or summarize confidence regions for three or moreparameters).
A33.
Given the nature of frequentist inference, a confidence interval does not provide informationon the probability that the true value of the parameter of interest is contained within the interval.
Rather, the proper interpretation of a 95% confidence interval is that in repeated hypotheticalrealizations of the data, 95% of these confidence intervals would encompass the true value of theparameter of interest.
A34.
Confidence intervals are most commonly determined using the point estimate of the parameterof interest together with the (estimated) variance (covariance matrix) of the parameter estimates.
However, it is often better to define confidence intervals directly in terms of LRT. This is done bydetermining those values of the parameter(s) such that the LRT has the desired level of significance(e.g. P = 0.025 for a two-sided 95% confidence interval for a single parameter).

2.

Bayesian approach

A35.
The Bayesian approach makes use of a broader conceptualization of probability than is used in
the frequentist approach. In the Bayesian approach probabilities are interpreted as a measure of one’s
state of knowledge or degree of belief concerning the true values of imperfectly known quantities ofinterest (which often correspond to parameters in frequentist inference). Given this interpretation it

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 123

makes sense to make probability statements about possible true values of some unknown quantities
given the available information and to define a probability density function that describes one’s current
state of knowledge or degree of belief. Furthermore, as outlined below, one can use Bayes’ theorem, tocombine information based on the current state of knowledge with new information (for example, withnew data from an experiment or study) to update the pdf describing the current state of knowledge andthis updated pdf can be used to make probability statements about the true values of unknown quantities
of interest.
A36.
The Bayesian approach starts from a particular probability density function (pdf), called a“prior distribution”, which summarizes the state of knowledge or degree of belief about values of theparameters of interest in the absence of the data under analysis. The prior distribution depends on themodel and, possibly, the values of some explanatory variables or other information ( Z ). The model canbe viewed in a general sense as a summary of existing knowledge, including knowledge obtained fromother studies, about the quantity (quantities) of interest. This prior distribution can be used to define a
pdf (prior density) that can be written as f prior ( β | , Z ) . This prior density is then combined with a pdf
for the data, f (data | , β , Z ) . In the Bayesian framework, this pdf is interpreted not in terms offrequencies from multiple realizations, but rather as a summary of the betting odds that would be placedon the data realization for given true values of the parameters, quantities of interest and explanatory
variables. Bayes’ Theorem can then be used to combine these two pdfs to provide a posterior density
for the parameters given the model and data, f post ( β | data, , Z ) . The relationship between theposterior density, the prior density and the likelihood can be written as:

f post ( β | data, , Z ) =f (data | , β , Z ) f prior ( β | , Z )f (data | Z )(A.3)

The denominator in this equation is the marginal density of the parameters given the explanatory
variables and is obtained as a weighted sum (integral) of the likelihood over all values of the parameterswith weights defined by the prior density. The posterior density reflects a combination of both one’s
prior knowledge and information gained from the current data. One could generalize the above
formulation to allow, for example, for uncertainties about the nature of the model, in which case thedata may change one’s view of the nature of the model.
A37.
The posterior distribution forms the basis of inference under the Bayesian approach. Until
recently the application of Bayesian methods has been hampered by the difficulties in evaluating theposterior density for all except the simplest problems. However, in recent years, the applicability ofBayesian methods has been revolutionized by the development of Markov Chain Monte Carlo(MCMC) methods and associated computational software, which avoid the need to calculate theposterior distributions using analytical methods [G12]. MCMC methods use a Monte Carlo (simulation)
approach to evaluate the often difficult integrals and hence the posterior distribution, as well as thequantities described below. One particularly popular MCMC method is Gibbs sampling [G4] underwhich—rather than sampling from the joint distribution of all of the relevant variables—sampling is
conducted from the distribution of each variable in turn, conditional on the values specified for theother variables. It is generally easier to simulate from each of these conditional distributions rather thanfrom the joint distribution, particularly if the conditional distributions have a simple form (for example,
log-normal).
A38.
In spite of the advances made in recent years in developing MCMC methods, some caution
may be required in interpreting the results obtained in this way, owing to problems with convergencethat might occasionally arise [G17]. Various tests of convergence have been proposed and these areparticularly important in situations where there are multiple peaks in the distribution(s) from which124 UNSCEAR 2012 REPORT

sampling is taking place. The number of computer simulation runs until the Markov Chain converges
can typically be in the range from thousands to tens of thousands or more [G12].
A39.
An especially attractive feature of MCMC methods is that they summarize the generally nonstandard posterior distributions that arise for almost all interesting problems by samples from these
distributions. These samples can easily be used to obtain information on the marginal posterior
distribution for specific parameters or for functions of the model parameters that are of particularinterest.
A40.
Detailed discussion of MCMC methods is beyond the scope of this report. For more details,
see for example Gilks et al. [G12] and Gelman et al. [G3] and the references therein. There are freely
available, flexible and powerful software packages (e.g. [L33]) that implement MCMC methods.
A41.
Parameter estimation. It is common to use the expected value (arithmetic mean) of themarginal posterior distribution to provide a “best estimate” of the value of a parameter or for a quantityof interest defined as a function of the model parameters. An alternative that is sometimes used is themode of the posterior distribution, that is, the most likely value of the parameter according to theposterior distribution.
A42.
Hypothesis tests. Rather than testing a null hypothesis (based on a simple model) against analternative hypothesis (based on a more complex model that includes the null model as a special case),
the Bayesian approach focuses on the calculation of betting odds in favour of each of possibly many
hypotheses. This allows one to directly compare betting odds for multiple hypotheses (including
comparisons involving non-nested models). This contrasts markedly with frequentist methods which
focus on the probability of seeing the observed data if some null hypothesis is true, but provide no
information on the odds in favour of any specific hypothesis. Thus, unlike in the frequentist approach,the Bayesian approach does not give special status to any specific hypothesis (that is, there is no needfor the concept of a null hypothesis).
A43.
Credible intervals and regions. Bayesian credible 4 intervals (in the case of a single quantity ofinterest) or regions (for several quantities of interest) are defined so that, given the data and the priorinformation, the true values of the quantities of interest fall within a particular interval or range with a
specified probability. The subjective probability that a single parameter value falls outside a (say) 95%
Bayesian credible interval is 5%. Unlike frequentist confidence intervals, Bayesian credible intervals
are based on probability statements about the true value of a quantity (or quantities) of interest.
Credible intervals and regions can be determined directly from the marginal posterior distribution of thequantity (or quantities) of interest.

3.

Comparison of frequentist and Bayesian approaches

A44.
In spite of the fundamentally different conceptual basis for these two approaches, Bayesianand frequentist methods often lead to similar conclusions. This is especially likely to be the case when
the implementation of these methods is well-informed by the scientific context [G17] or when the data
are sufficiently strong to outweigh the choice of the prior distribution.
A45.
When good prior information is available, the Bayesian approach provides a natural method
for combining one’s current state of knowledge or degree of belief with information obtained from thedata. Of course when the data are sparse prior information becomes increasingly important. However,4

In the metrology and some other areas [J8, J10, J11], credible intervals are called “coverage intervals”.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 125

when the data are limited and prior information is lacking, then the way in which the prior distribution
is specified might have a notable impact on the posterior distribution. Indeed, if a “flat” priordistribution (that is, one with a constant pdf) were assigned to a variable that can only take values
greater than zero, then the pdf for the logarithm of this variable would not be flat. Hence it is notpossible in general to have a totally uninformative prior distribution; the posterior distribution couldchange according to which prior distribution is selected, particularly if the data are not strong enough tooutweigh the influence of the prior distribution. Nevertheless, in this situation, inferences would be
limited irrespective of whether a Bayesian or a frequentist approach is adopted.
A46.
Statistical inference is central to the estimation of risks from radiation exposure and to theassessment of both the uncertainty in these risk estimates and the additional uncertainties that arise as
the existing, but necessarily limited, knowledge of radiation-induced health effects is used to address
societal needs and concerns. Both frequentist and Bayesian approaches to inference are useful for these
efforts. Frequentist methods have generally served well in estimating radiation-induced health effects inspecific exposed populations, such as the atomic bombing survivors. However, with increasingly
complex issues, such as those related to the interpretation of site-specific cancer statistics estimatedfrom limited data [P15] or efforts to make use of information on uncertainty in doses estimated bycomplex Monte Carlo systems for simulating doses, Bayesian methods are likely to become
increasingly useful and important. Similarly, as current, uncertain risk estimates are used to address
important societal questions, the need to allow for uncertainties in existing knowledge and makeinformed but qualified judgements about how to apply these risk estimates is likely to increase theimportance of Bayesian methods in the quantification of uncertainty.

C. Quantifying uncertainty
A47.
The Committee recommends that uncertainty in the measurements, variables, and models thatare used to estimate exposures, doses and risks—both for specific individuals and for groups—beexpressed in terms of probability density functions that represent the degree of belief about true valuesof imperfectly known quantities. In this document, the term “probability density function” will be used
to represent the uncertainty about a true value of a fixed quantity (that is, a single value) within thecontext of the assessment of dose and risk for a specific situation. The term “frequency distribution”
will be used to describe the inter-individual variability of true values or the variability of measurements
or observations.
A48.
In the case where there is uncertainty about the form of a frequency distribution that describes
the variability, other probability density functions may be specified that represent alternative (possiblytrue) values for the mean, spread, shape or other aspects of the true but unknown frequency distribution.
This gives rise to alternative realizations of the uncertain frequency distributions, each having a uniquemean, variance, and shape [I1, N6, N9, N10, N11]. If the form of these frequency distributions is itself
uncertain, then this may be addressed—to some extent at least—by placing probability density
functions on the mean, variance and shape parameters of those frequency distributions. In a Bayesiancontext, this is known as a hierarchical Bayes approach [G17].
A49.
Probability density functions representing uncertainty in models used to estimate dose and risk
may be obtained from statistical analysis of repeated measurements (the frequentist approach) or fromsubjective representation of the full state of knowledge derived from evaluation of all evidence
available about each fixed but uncertain quantity and the model used to evaluate dose and risk (theBayesian approach) [I1, J8, J9, J10, J11, N6, N9, N11].

126 UNSCEAR 2012 REPORT

1.

When sufficient data are available

A50.
When an estimate of uncertainty about the true value of a quantity is obtained from a large
number of repeated observations (or measurements) taken from a randomized design, the shape of thefrequency distribution of values likely conforms to the laws of nature. Normal and log-normal
distributions are commonly used in statistical analysis of the variability of data obtained from arandomized design. These and other probability density functions resulting from statistical analysis of
the variability in data are discussed in numerous statistical textbooks and references on quantitative
uncertainty analysis [I1, J8, J9, J10, J11, N6, N9, N11].

2.

When data are sparse

A51.
When uncertainty is defined as a probability density function of possibly true values for aunique quantity that is imperfectly known and for which directly relevant data are limited, thedistribution can be of any form that subjectively describes the present state of knowledge or degree ofbelief for that quantity [N6, N9, N11]. Commonly used probability density functions representing
possibly true values for unique quantities that are imperfectly known include the normal and lognormal, but also the uniform, triangular, log-uniform and log-triangular, beta, Weibull, gamma, andmany other continuous or discrete distributions, including mixtures or hybrids of different distributions[J8, J10, J11, N9].
A52.
When judgement and past experience are the primary basis for proposing a probability density
function representing uncertainty, it is not unusual for the analyst to propose a piece-wise uniform or
piece-wise log-uniform distribution. In a piece-wise uniform distribution, equal probability density is
assigned to all values falling within specified intervals, but different subjective weights are assigned toeach interval to reflect differences in degrees of plausibility associated with each interval [J8, J10, J11,
K6, N6, N9]. The subjective weights will sum to unity for each distribution.
A53.
Sometimes it becomes necessary to describe probability density functions that are a mixture(hybrid) of a continuous and a discrete distribution. Such is the case when there is evidence supportingthe chance that the true value of a model parameter could be zero, and a chance that the parameter
would take on positive (non-zero) values. For example, hybrid probability density functions have often
been used to describe the state of knowledge or degree of belief associated with the modifying factor
representing differences in risk for exposure to different energies and types of radiation, as comparedwith exposure to high-energy gamma radiation [K6].

D. The distinction between variability and uncertainty
A54.
The terms variability and uncertainty are widely used throughout the literature on quantitative
uncertainty analysis. Sometimes these two terms are used interchangeably, and sometimes they are usedas separate components of an uncertainty analysis of a quantity of interest. This section will attempt toclarify the distinction in meaning of these two terms.
A55.
Variability is the term used to describe the variation or dispersion of values resulting from(a) repeated measurements for a quantity of interest, (b) a group of single measurements orobservations taken of a set of multiple quantities of interest (such as single “best estimate” doses madefor each of a larger number of people who make up a cohort in an epidemiological study), or (c) theANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 127

variation or dispersion of true values (such as the variation or dispersion of true individual doses in acohort). To a certain extent variability can be explained through the use of explanatory variables thatindicate why values differ. However, to the extent that variability cannot be explained, variability is
assumed to occur from natural stochastic processes. Distributions used to represent stochastic
variability among a set of true but unknown values are referred to in this report as “frequency
distributions.” The distributions are contrasted with “probability density functions” that represent thestate of knowledge or degree of belief about a quantity of interest that is a single (true) value.
A56.
Uncertainty refers to both (a) the variation in values of quantities due to unexplained
stochastic processes (as described in the previous paragraph) and (b) the state of knowledge or degreeof belief about imperfectly known fixed quantities. As noted earlier in this document, using theterminology of Hofer [H16, H18], uncertainty that reflects unexplained stochastic variability of true
values among a group or population of unspecified individuals is referred to as “aleatory” or “Type A”
uncertainty while the state of knowledge or degree of belief about possibly true values for a quantity forwhich there is only a fixed (single) true value is referred to as “epistemic”, or “Type B” uncertainty.
A57.
If the variability of true values can be specified by the use of a mathematical model with asystem of explanatory variables, and if all other remaining sources of uncertainty are due to
unexplained random variability of true values about the estimated value, the system will involve only
aleatory uncertainty. This uncertainty arises from the assignment of fitted values to represent the true
values, under the condition that the assigned value is unbiased, i.e. equal to the expected value for eachsubgroup sharing the same attributes identified by the explanatory variables. If the observed, measured,or estimated variability of values is composed of (a) variability explained by a model and its system of
explanatory variables, (b) unexplained variability of true values of quantities, and (c) randommeasurement error, then both assignment and classical measurement errors are present. Uncertainty inthe assigned value applied to a group of individuals or to the standard deviation describing interindividual variability of true values within that group is a form of systematic error that is shared by all
members of the group.
A58.
Complex uncertainties are composed of mixtures of systematic and random errors, including
uncertainties that are shared and unshared among individuals in a cohort. Complex random
uncertainties are composed of mixtures of assignment and measurement errors. When assigned values
are based on an imprecise measurement or an uncertain fixed quantity that is shared by one or more
subgroups, there will be the potential for systematic bias in the estimate of central or expected values.
A59.
The role of the assessment objective in determining the need to distinguish variability anduncertainty. The objective of the assessment determines whether or not it is necessary to distinguishbetween inter-individual variability of true values versus uncertainty about quantities that are fixed.
When the assessment objective itself is a fixed true quantity, information about variability of true
values and uncertainty about fixed true quantities may be combined into a single subjective probability
density function representing the state of knowledge or degree of belief about possibly true values forthe quantity of interest [I1, J8, J9, J10, J11, N6, N9, N11]. However, when the assessment objective isthe estimation of variability of true values, such as the inter-individual variability of true exposures ordose, estimates of the inter-individual variability of true values must be processed separately from theuncertainty about quantities that are imperfectly known but shared among members of a subgroup orgroups of individuals. Separate processing of information about variability of true values anduncertainty about shared quantities is necessary to avoid substantial overestimation of the amount ofvariability of true values and to address uncertainty about quantities such as the mean dose and dose
variance for the cohort [I1, N6, N9, N11].

128 UNSCEAR 2012 REPORT

E. Accounting for dependences among uncertain model
inputs and assumptions
A60.
In the case where the assessment quantity is a single unique value, all uncertain terms aredescribed as either discrete or continuous probability density functions of possibly true values. In sodoing, it is important to account for dependences or correlations between the probability density
functions specified for each uncertain parameter with models used to estimate exposure, dose, or risk. Ifsuch dependences are ignored, the probability density function of the final result may be too broad(uncertainty is over-expressed) or too narrow (producing a statement of overconfidence).
A61.
Dependences will usually have a noticeable effect on the probability density function of the
final result when they occur among components of the model that contribute most to the overall
uncertainty in the final result; and on the other hand, accounting for dependences among uncertain
model components or parameters that are associated with low sensitivity and/or small uncertainty willusually not contribute substantially to the overall uncertainty of the final result [I1, N6]. An exception
to this general rule is when extreme values in the tails of the probability density function of the final
result are used for decision-making. These extremes would lie beyond the limits of a 90% or 95%
credible interval. In these situations, the upper extremes are likely to be affected by even relatively
weak dependences among uncertain inputs and model assumptions [I1, N6].

F. Uncertainty propagation and sensitivity analysis
A62.
Uncertainty propagation is the process by which all components contributing to uncertainty inthe estimate of the quantity of interest are combined into an overall statement of uncertainty about thatquantity. Uncertainty propagation can account for most known sources of uncertainty, including
uncertainty in measurements, and uncertainty in model coefficients and explanatory variables. Current
approaches of uncertainty propagation are limited in taking into account uncertainties due toassumptions made in the analysis of the data (model uncertainty). Other approaches to deal with model
uncertainty are described in appendix B.
A63.
In the case where the uncertainty in model inputs is described by probability density functionsof possibly true values, the model result (the estimate of the quantity of interest) will itself be described
as a probability density function of possibly true values. From this distribution of possibly true values, acentral value (usually the arithmetic mean, median or mode) and a 90% or 95% credible interval (alsocalled credibility interval, subjective confidence interval, coverage interval, or uncertainty interval) canbe obtained [I1, N6, N10, N11].
A64.
In the rare case where the quantity of interest can be estimated using very simple equations,
uncertainty propagation can be carried out using closed-form algebraic solutions. This is the case forsimple models composed predominantly of a multiplicative series of uncertain terms, in which the
product of the series of terms is represented by a log-normal distribution, or when normal distributions
are assumed for the uncertain input to models composed of a summation of terms [I1, N6, N9, N10,
N11]. A variety of closed-form algebraic solutions to the uncertainty propagation of simple
combinations of uncertain terms are discussed in other references [J8, J10, N9]. When the quantity ofinterest is estimated using more complex equations, or when the probability density functions assigned
to uncertain model inputs are neither normal nor log-normal, Monte Carlo uncertainty propagation ispreferred to closed-form algebraic solutions.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 129

1.

Monte Carlo uncertainty propagation

A65.
The method most commonly used for uncertainty propagation in equations and models used
for dose and risk assessment is a computer-based numerical algorithm known as Monte Carlosimulation [I1, J11, N6]. This method is constrained neither by the complexity or structural form of theequations used for dose and risk assessment, nor by the shape and dependencies among probability
density functions representing uncertainty in model inputs or outputs. Uncertain model results are
expressed as numerous alternative realizations of possibly true values (as in the case of an assessmentof dose or risk to an individual) or possibly true sets of cohort doses (as in the case where a twodimensional Monte Carlo dose reconstruction is used to support an epidemiological study and where
true random inter-individual variability is separated from uncertain degrees of systematic bias).
A66.
Monte Carlo uncertainty propagation may be based on computer algorithms representing
simple random sampling of values from probability density functions describing uncertain model inputs
to produce random results of dose or risk. Monte Carlo uncertainty propagation may also be based on
stratified sampling strategies, the most common being various forms of Latin hypercube sampling [I1,
N9, N11]. Latin hypercube sampling is often preferred because stable results are produced with lower
sample sizes than with simple random sampling. Monte Carlo uncertainty propagation can address
dependences between uncertain model inputs and equations as statistical or functional relationships [I1,J10, J11, N9].
A67.
One-dimensional Monte Carlo uncertainty propagation. When the assessment end point is aquantity with a single true but imperfectly known value, such as the dose or risk to a specific person, alluncertainties are of Type B. A one-dimensional Monte Carlo uncertainty propagation combines all
known sources of input uncertainty (expressed as probability density functions that are either
continuous or discrete) to produce a probability density function of model results (i.e. values for theassessment end point). This probability density function of model results is made up of numerous
alternative realizations of possibly true values for the single true but uncertain value for the assessment
end point (figure A-II). One-dimensional Monte Carlo uncertainty propagation combines all known
sources of uncertainty, such as variability in repeated measurements and lack of knowledge about thevalues of fixed quantities for which directly relevant data are sparse or missing. Uncertainties resulting
from the use of competing plausible models can also be addressed within one-dimensional Monte Carlo
uncertainty propagation [I1, N6, N9, N10, N11].
A68.
Two-dimensional Monte Carlo uncertainty propagation. The separation of inter-individual
variability of true values from uncertainty about fixed true values of a quantity is often necessary when
the assessment end point or quantity of interest is the exposure of or dose to a group or population ofindividuals. In this case, a two-dimensional Monte Carlo (2D MC) uncertainty propagation is often apreferred option. A 2D MC uncertainty propagation may be necessary when dose reconstruction for
individuals in an epidemiological cohort is carried out using mathematical models instead of direct
measurements.
A69.
When models are used as surrogates for direct measurements of the quantity of interest, theresults for each individual may be composed of varying amounts of systematic error shared by some ormost of the individuals in the cohort. A 2D MC approach allows for sets of possibly true fixed values
that are shared or alternatively unique to each individual to be simulated in one dimension andalternative realizations of possibly true sets representing individual variability of the quantity of interestin the second dimension. Each realization of a set representing inter-individual variability of true doseis conditioned on a unique set of possibly true fixed values (see example in figure A-III), which is
explained in detail below.

130 UNSCEAR 2012 REPORT

A70.
In 2D MC uncertainty propagation, each set of inter-individual variability of possibly true
values for the quantity of interest is partially determined by fixed values of explanatory variables, suchas residence history, diet, age, sex, lifestyle, occupation, and shielding. These fixed values are unique toeach person or subgroup of persons. These values change only from one realization to the next. Anotherportion of inter-individual variability is due to stochastic variability of true dose (aleatory uncertainty).
A71.
When producing alternative sets representing inter-individual variability of true values, it isessential to remove the effect of random classical measurement errors and avoid overestimating theamount of variability of true values [H18].

Figure A-II.

One-dimensional Monte Carlo uncertainty propagation

Uncertain model inputs P1, …, Pn are specified as probability density functions representing the analyst’s state of knowledge
or degree of belief for each uncertain input parameter P. Single values are sampled at random from each probability density
function for P1 to Pn to produce a single realization of the model result. This process is repeated many times, producing
numerous alternative realizations of possibly true values for the model result (a quantity for which there is only one true but
unknown value)ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 131

Figure A-III. Multiple realizations of the distribution of possible true doses in the selected cohort
obtained using two-dimensional Monte Carlo uncertainty propagation
Each realization is a representation of one possibly true set of inter-individual variability of doses in the cohort, while thedifferences between realizations are interpreted as Type B uncertainty [N6]. Estimates of inter-individual variability of true
values include the effect of stochastic inter-individual variability (Type A uncertainty)

2. Example of two-dimensional Monte Carlo uncertainty propagation to
separate inter-individual variability of true values from uncertainty in fixed
quantities
A72.
This section illustrates the basic elements of a two-dimensional Monte Carlo (2D MC)
uncertainty propagation for an idealized case in which inter-individual variability of the quantity ofinterest, R, is a function of three parameters X, Y, and Z
𝑅𝑅 = 𝑓𝑓(𝑋𝑋, 𝑌𝑌, 𝑍𝑍)

To be specific, R = XYZ may be the dose to the heart, X the conversion factor from the dose measured
in front of the breast at the place of the dosimeter, Y the calibration factor of the same dosimeter usedby all study participants, and Z the dose in front of the breast, which is based on a measurement foreach of the participants.
A73.
In this example, X is a frequency distribution representing stochastic variability of true valuesof the calibration factor among each individual (Type A uncertainty). Parameter Y is an uncertain fixed
quantity that is shared among all individuals, and it is assigned a probability density function of
possibly true fixed values (Type B uncertainty that is shared). Parameter Z is unique to each individual,
thus probability density functions that represent uncertainty in the true unknown value of Z are assigned
separately to each individual (unshared type B uncertainty).

132 UNSCEAR 2012 REPORTA74.
The shape of X is assumed to be log-normal, but because the centre and spread of this frequency
distribution are uncertain, probability density functions of possibly true fixed values (Type B uncertainty)
are assigned to the uncertain geometric mean (GM) and geometric standard deviation (GSD). The
probability density functions assigned to GMx and GSDx represent the analyst’s state of knowledge or
degree of belief about the true fixed but uncertain GM and GSD of X (Type B uncertainty).

X = log-normal

(

GMx =

)

, GSDx=One alternative realization of GMx and GSDx produces an alternative realization of the true frequency
distribution of X from which values of x are sampled at random and assigned to each individual. For
each realization, a unique value (gmX) is drawn at random from the probability density function
assigned to GMX and a unique value (gsdX) is drawn at random from the distribution assigned to GSDX.
The values of gmx and gsdx sampled for each realization define a unique frequency distribution of X.

Realization 1

Realization m

Realization 2...
X1 = log-normal(gm1, gsd1)

X2 = log-normal(gm2, gsd2)

Xm = log-normal(gmm, gsdm)

From each unique frequency distribution of X obtained for a given realization j, a single value is drawn
at random for each of n individuals (x1j, x2j, …, xnj).
A75.
Y is a fixed but uncertain parameter whose true value is the same for all individuals in the
population or subgroup (the subjective probability density function that is assigned to Y represents
alternative realizations of a true value that is shared among all individuals).

Y=

For each realization j, a unique value of yj is drawn from its subjective probability density function andis shared among all individuals.
A76.
Z is a fixed but uncertain parameter defined separately for each individual (i = 1 to n) in the
population or subgroup.

Z=

●●●

Individual 1

Individual 2

Individual nANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 133

For each realization, a unique value of zi is drawn from the subjective probability density function
assigned for each individual; thus, each person is assigned a unique value of zi, which changes fromrealization to realization.
A77.
The combination of values of x, y and z assigned to each individual produces a unique value ofr per individual. This unique value of r represents one possibly true value. The set of all individual
values of r for this realization represents one possibly true set R for the group of individuals. For eachrealization j, each individual value of ri is partially explained by a unique value of y applied to allindividuals, individual-specific values of z, and by randomly sampled values of xi that vary fromindividual to individual. Each realization produces a unique set of results (R) representing a possibly
true outcome of inter-individual variability. Each unique set of results (R) will have its own uniquevalue of mean, variance, shape, and minimum and maximum.

Result for each individual (i) and realization (j)ri,j = f(xi,j, yj, zi,j)Realization 1

Realization 2

Individual 1

r1,1 = f(x1,1, y1, z1,1)

r1,2 = f(x1,2, y2, z1,2)…

r1,n = f(x1,m, ym, z1,m)Individual 2.
.
.
Individual n

r2,1 = f(x2,1, y1, z2,1).
.
.
rn,1 = f(xn,1, y1, zn,1)

r2,2 = f(x2,2, y2, z2,2).
.
.
rn,2 = f(xn,2, y2, zn,2)…

r2,n = f(x2,m, ym, z2,m).
.
.
rm,n = f(xn,m, ym, zn,m)R1

R2

Realization m…

Rm134 UNSCEAR 2012 REPORT

3.

Sensitivity analysis

A78.
An analysis of the effect on a model output of changes made to values of model input(including model coefficients and explanatory variables), is often referred to as a “sensitivity analysis”.
Sensitivity analysis can help determine which parameters or processes have the greatest impact on amodel result or on the uncertainty in that result [I1, N6, N9, N11].
A79.
Sensitivity analyses may be conducted at two levels, (a) local and (b) global. Local sensitivity
expresses the impact of a parameter on a model result when the parameter is varied only in the region
very near a specific value. Global sensitivity expresses the impact of a parameter when it is varied
across the full range of possible values. An output variable may have a high local sensitivity to aparameter, but because of low parameter uncertainty, global sensitivity would be small. Likewise, an
output variable may have a low local sensitivity to a parameter, but because of very large parameter
uncertainty, global sensitivity would be large.
A80.
Global sensitivity can be estimated using many different calculational and computational
strategies. Some methods require computationally intensive sampling designs [I1, N9]. Global
sensitivity analysis is used to evaluate the contribution of uncertain model input to the uncertainty in themodel result produced by Monte Carlo uncertainty propagation [I1]. Such methods include statisticalregression analysis of the rank order of uncertain model inputs versus model outputs and/or visualinspection of scatter plots of values obtained from probability density functions of model inputs andmodel results. Other sampling strategies for conducting a sensitivity analysis of the results of Monte
Carlo uncertainty propagation are discussed in references [N6, N9].

II. EPIDEMIOLOGICAL CONCEPTS
A81.
Epidemiology is the study of the distribution and determinants of disease in humanpopulations. In this context “disease” could refer to a specific condition, e.g. breast cancer or
myocardial infarction or to a grouping of conditions such as death from any cause. Epidemiologicalstudies are primarily concerned with describing incidence rates (new cases arising per unit time in the
population of interest), however there is also interest in other descriptions of disease occurrence
including cumulative incidence (the proportion of the population that contracts the disease in somewell-defined time period), and prevalence (the proportion of the population with the disease at a
specified point in time). Some epidemiological studies, such as clinical and field trials, are experimental
studies in which the exposed population is chosen and the assignment of exposures (“treatments”) is
controlled by the investigator. However, most epidemiological studies, especially those concerned withthe health effects of radiation exposure, are generally, observational (i.e. non-experimental) studies inwhich the occurrence and magnitude of the exposures of interest and the choice of the exposed
populations are not controlled by the investigators. While the ultimate goal of epidemiological researchoften concerns the identification of causal factors, observational epidemiological studies candemonstrate associations between disease occurrence and factors of interest, but cannot provecausation. However, Hill [H14] proposed a set of criteria that are often used to guide conclusions aboutcausality based on epidemiological data (see annex A of this report, and for example the discussion in
the preamble to the IARC monograph on carcinogenic risks of ionizing radiation to humans [I3]).
Causal inference is an important subject that is beyond the scope of this appendix. See reference [R4]for a discussion of causation and causal inference. If some variable is associated with a change indisease risks then that variable is called a risk factor. When an association has been observed, it may be

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 135

possible, given suitable data, to use epidemiological data to describe the nature and magnitude of theassociation (e.g. to describe the magnitude and shape of a dose–response relationship) and to describe
how the magnitude of the association is affected by other factors (effect modification).* It can also be
possible to consider the nature of the joint effect* (interaction) of two or more risk factors on theoccurrence of a disease of interest. Since most epidemiological studies are observational in nature, themagnitude of effects of interest might be distorted if one fails to adjust for a risk factor that is also
correlated with the exposure of interest. This effect is called confounding and the risk factor can becalled a confounding factor or confounder. Unfortunately, the term confounding factor is often used todescribe what is really a potential confounding factor.
A82.
Studies of the effects of radiation exposure on the risk of health effects in humans are virtually
all observational studies in which the subjects and nature of the exposures are determined by factorsthat are not under the control of the investigators. Findings of statistical significance on the basis of ahypothesis test in a specific observational study must be interpreted with some caution [S17, Y3].
A83.
This section briefly describes several of the most important types of observational
epidemiological study designs, comment on the strengths and limitations of these designs, and notesome of the methods used to analyse data from the different types of studies. The focus here concerns
the two major types of epidemiological approaches, namely cohort and case–control studies. However,geographical correlation studies (often called “ecological studies”) are also briefly discussed here.
Annex A of the UNSCEAR 2006 Report [U12] contains a discussion of these concepts. For a morethorough description of epidemiology and epidemiological study designs and statistical methods see,for example [C11, J13, R7].

A. Cohort studies
A84.
Cohort or follow-up studies involve the identification of a disease-free population whose
members have different degrees of exposure to the factor of interest (e.g. radiation) and whose health isobserved over time to determine when cohort members develop the disease(s) of interest. An essential
characteristic of a cohort study is that the probability of inclusion in the cohort is independent ofdisease status. However, it is almost always the case that the selection probability will depend on thelevel of exposure. For example, the Life Span Study cohort of atomic bombing survivors was definedusing records from Japan’s 1950 national census and some related local censuses. As originally defined,
the cohort was limited to Japanese citizens who were living in or near Hiroshima or Nagasaki at thetime of the census (a) who were not military personnel and (b) for whom the family registry was in oneof the two cities. The cohort was defined on the basis of a core group who were determined to havebeen within 2 km of the hypocentres at the times of the bombings and who suffered acute radiationinduced health effects. This core group was augmented with three groups of the same size that werematched to the core group on age, sex, and city at the times of the bombings. These three groups were:(a) people who were exposed within 2 km of the hypocentre but did not report suffering from acuteradiation-induced health effects; (b) people who were between 2.5 km and 10 km from the hypocentres
at the times of the bombings; and (c) people who were not in the cities (that is, who were more than
10 km from the hypocentres at the times of the bombings). Over time, as methods to estimate individual
doses became available, the cohort was expanded to include almost all civilian Japanese citizen
respondents to the 1950 census and who were within 2.5 km of the hypocentres regardless of the family
registry location (see references [B4, P9] for additional details).

136 UNSCEAR 2012 REPORT

A85.
The strength of cohort studies arises from the fact that disease rates of interest can becomputed directly from the follow-up data. Rates for cohort members with different levels of exposure
can be compared to detect and characterize the nature of the association between the potential risk
factor(s) of interest and the occurrence of the disease. Provided that it is possible to obtain complete
data on the occurrence of specific outcomes, a cohort study can be used to look at the relationshipbetween exposure and the occurrence of several different outcomes. The primary disadvantages ofcohort studies relate to the cost and length of follow-up required to obtain the disease data and the
difficulties (including cost) in obtaining detailed information on covariates of interest (including dose
estimates, the factor(s) of primary interest) for all cohort members.
A86.
The basic data for each individual in a cohort study include entry and exit (event occurrence or
end of follow-up) times, some measures of exposure (e.g. radiation dose, which may be time dependent,
and work history), basic characteristics such as sex, date of birth, ethnicity, and other risk
factors/potential confounding factors (e.g. smoking history or family history of cancer).
A87.
Analysis of data from cohort studies typically focuses on disease rates (hazard rates* orfunctions) though it is possible to look at other outcomes, such as life expectancy and cumulative
incidence (e.g. lifetime risk). Cohort data are often analysed using log-linear proportional hazards
models fitted directly to the individual survival data using semi-parametric partial-likelihood methods
such as Cox regression modelling [C16]. In Cox regression modelling, the focus is on rate ratios(relative risks) with no direct methods to characterize rate differences (excess absolute rates). An
important alternative to Cox regression, which is widely used in studies of radiation dose response, isPoisson regression in which one directly models the full hazard rate function [C11, F9, P10]. In order to
use Poisson regression models one must restructure the cohort data as a stratified person-year (rate)table. The stratification typically includes time (with the potential for multiple time scales, e.g. attained
age and calendar time), basic data (such as sex, race, and region), exposure (dose, age at first exposure,time since exposure), and other risk factors (e.g. smoking history, alcohol consumption, and family
history of cancer). Some stratification factors can be time-dependent (e.g. lagged cumulative dose, timesince exposure, duration of smoking, or time since smoking cessation). Poisson regression is attractive
for the analyses of cohort studies, because it allows (but does not require) one to model the full hazard
including the time dependence (e.g. on attained age) of the baseline rates and the effects of interest. The
effects of interest may be described in terms of rate ratios (RR), (the ratio of the rates in groups withdifferent exposures) the excess relative risk (ERR) (which is the proportional increase in the risk in one
group—or at a given dose—relative to that in another group—usually those with no exposure—and isequal to the RR minus one), or the rate difference (or excess absolute rate, EAR) models for the
exposure associated hazard. The risk models may consider effect modifiers (factors, such as attained
age, age at exposure, and sex, that modify the exposure-associated risk). The approach iscomputationally more efficient than Cox regression modelling, especially when the risk models include
time-dependent covariates. ERR and EAR models are particularly useful when considering dose–
response functions and the joint effect of two or more continuous risk factors (e.g. radiation andsmoking). Maximum likelihood methods based on individual data are alternative ways to analyse
cohort data, which avoid the potential loss of information by using only grouped data in Poisson
regression [E3, K1].
A88.
As noted above, cost is often a limiting factor in the conduct of cohort studies. Since follow-up
is essential to cohort studies, those costs are inherent to the conduct of a cohort study. However, in
recent years several cohort-based designs have been developed that seek to reduce the (often nontrivial) costs associated with the collection of covariate information (including dose estimation) bylimiting the need to collect this information to a subset of the full cohort. These designs include nested
case–control and case–cohort designs.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 137

A89.
In a nested case–control study, one includes all of the cases in the cohort and a sample of noncases, typically matched to individual cases on various factors such as sex, vital status and age at thetime of diagnosis of the case. The advantage of this type of study is that detailed information on
exposure and other risk factors needs to be obtained only for the cases and their matched controls,
which almost always comprise only a small fraction of the total cohort. Nested case–control study data
are typically analysed using the same methods (conditional logistic regression) that are used formatched case–control studies (see below). These analyses lead to estimates of the (excess) relative risk.
A nested case–control study is limited to a specific outcome, which distinguishes “cases” from“controls”. The advantage of a nested case–control study to a (non-nested) case–control study (see next
section) is that data of the cohort study can be used, and only data on additional risk factors need to becollected.
A90.
As in a nested case–control study, a case–cohort study includes all cases identified in thecohort. However rather than matching non-cases (controls), one selects a subsample of the cohort witha known (possibly stratified) sampling fraction and obtains detailed exposure and risk factor data for allof the cases and all members of the subcohort. Analysis involves a slight modification of standard Cox
regression methods [L7] with an adjustment to adjust for the fact that the analysis is using only a subsetof the full cohort with oversampling of cases. Although some work has been done on the analysis ofcase–cohort data using Poisson regression methods, there are not yet any tools or practical methods forcarrying out such analyses. Case–cohort studies have an advantage over nested case–control studies inthat one can use the same subcohort to analyse the effects of exposure on various outcomes. It has
recently been recognized that case-cohort studies are a special case of multi-stage sampling designs[B22] that permit more effective use of available data from the full cohort.

B. Case–control studies
A91.
Case–control studies involve the identification of individuals with a specific outcome ofinterest (cases) and a sample of individuals (controls) from the same population who could havebecome a case but did not. Case–control studies are best suited for the study of a relatively rare disease(e.g. with prevalence of less than 10%). Analyses involve comparing exposure to a risk factor ofinterest in the cases and the controls. Case–control studies result in estimates of the odds-ratio for
exposure in cases and controls. If the exposures are numerically continuous (e.g. as is usually the casewith radiation dose), the odds ratio can be expressed as a function of exposure. Odds ratio estimatesfrom a well-designed case–control study are approximations to the relative risks that one estimates incohort studies. This approximation is generally quite good for rare diseases.
A92.
The primary advantages of case–control studies are that they involve many fewer study
subjects than cohort studies and they do not require long-term follow-up. Thus they can be considerably
less costly than cohort studies and can often be completed in much less time than cohort studies.
A93.
The primary challenge in the design of case–control studies is to ensure that one can obtain
useful estimates of the odds ratio. The key issues in designing a good case–control study are(a) inclusion of all cases in a population of interest; and (b) selection of controls from the same
population; that is, people who could have developed the outcome (“disease”) of interest and who, hadthey developed the disease, would have been identified and selected as a case. It is also important thatthe nature and quality of the information on the exposure(s) of interest be the same for cases andcontrols. Case–control studies often involve matching on some factors, other than the exposure(s) of

138 UNSCEAR 2012 REPORTinterest and that are known to affect rates (such as sex, race, or being at risk at the age of identificationof the corresponding case).
A94.
Data from case–control studies are analysed using logistic regression if there is no matching,and conditional logistic regression when there is matching. These methods are discussed in detail inreference [B21]. The results are estimates of the odds ratio as a function of exposure and, as noted
above, the odds ratio is approximately equal to the relative risk one could estimate from a cohort study
in the same population. It is not possible, without additional—and often unavailable—information on
population rates for the outcome of interest, to estimate excess rates from case–control data.
A95.
As noted above, case–control studies are generally much less costly and can usually be carriedout more rapidly than cohort studies. They are ideally suited to the investigation of a rare outcome.
Perhaps the biggest challenge in conducting a case–control study is to obtain comparable exposure
information for cases and controls. This is an especially important issue when the characterization of
exposure might be different for cases and controls. For example, being a case might prompt one tobecome more aware of the details of their past exposure or, if cases are deceased or otherwise
unavailable to provide information on exposure, information might be more likely to come fromproxies rather than the study subjects themselves and this could affect the quality and comparability ofthe exposure assessment. While it is possible to examine the (joint) effects of different exposures in acase–control study, in contrast to cohort studies, as noted above, the analysis must focus on a single
pre-determined outcome that differentiates cases from controls.

C. Geographical correlation studies
A96.
Cohort and case–control studies involve the direct observation of outcomes, exposures, andother characteristics in individuals. However in some situations, outcome and exposure data are only
available at the population level. For example, one might have only summary information on disease
rates or risks in some populations of interest together with information on exposure status (yes/no,
proportion exposed, or population mean dose) for these populations. These data are then used toinvestigate the association between the summary measures of outcome and exposure across groups.
Results from geographical correlation (sometimes called “ecological studies”) should be interpreted
cautiously, because they are based on proxy summary measures of exposure, which may attenuate therelationship between exposure and the rate (and estimated risk) of the outcome of interest, and because
it is generally much more difficult (if not impossible) to control for confounding than in studies basedon individual observations.
A97.
Issues related to problems of confounding in geographical correlation studies are highlighted
in the discussion [L28, P19] of a study of United States county-level lung cancer mortality rates andaverage radon levels in homes [C14]. Despite their limitations, under some circumstances geographicalcorrelation studies can provide useful descriptive information on health risks when the exposure data
are based on relevant direct measurements, or there is good individual data on important potentiallyconfounding risk factors. Examples of useful geographical correlation studies include (a) an analysis of
thyroid cancer risks in Ukraine and Belarus following the Chernobyl accident [J2] in which theassigned doses were based on large numbers of age-, village-, and sex-dependent doses and (b) an
analysis of lung cancer and residential radon risks in a large United States cohort with individual
smoking data and region-dependent radon measurements [T11].

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 139

APPENDIX B. SOURCES OF UNCERTAINTY IN
RADIOEPIDEMIOLOGICAL STUDIESI.

UNCERTAINTIES IN HEALTH EFFECT INFORMATION ............................................................ 139
A. Selection bias ............................................................................................................................. 139
B. Information bias ........................................................................................................................ 141
C. Confounding .............................................................................................................................. 143
D. Changes in information over time...................................................................................... 143

II. UNCERTAINTIES IN EXPOSURE AND DOSE ASSESSMENT .................................................. 144
A. Sources of uncertainty in exposure and dose estimation.......................................... 144
B. Reconstruction of external exposure in specific studies ............................................ 158
C. Reconstruction of internal exposure to radon and its progeny inspecific studies........................................................................................................................... 168
D. Reconstruction of internal exposure from other pathways in specificstudies........................................................................................................................................... 172
E. Summary...................................................................................................................................... 178
III. UNCERTAINTIES IN RISK ASSESSMENT ...................................................................................... 183
A. Impact of uncertainty in health effect information on risk estimatesand statistical power of epidemiological studies ......................................................... 183
B. Impact of exposure uncertainty on risk estimates ....................................................... 186
C. Impact of model uncertainties............................................................................................. 200

I. UNCERTAINTIES IN HEALTH EFFECT INFORMATION
A. Selection bias
B1.
A concern that may arise in epidemiology is whether the persons included in the study are
representative of the population of interest. In principle, this ought not to be a problem if the study
population coincides with this target population; for example, if—in an occupational study—all of the140 UNSCEAR 2012 REPORT

relevant workers are included. However, whilst this approach might be possible in some cohort studies,
there are other study designs such as case–control studies and case–cohort studies that include samplesof persons selected, respectively, from the target population or the cohort. If participation were
determined purely on the basis of random sampling from the relevant population, then this approach
ought not to lead to bias. However, non-random failure to participate may lead to bias, as the following
examples will illustrate:(a) In a cohort study of occupationally-exposed workers, it may not be possible to include all of
the workers in the target population because identifying details or information on their radiation
exposure is missing. If such information were missing at random, then this ought not to lead tobias, although the reduction in the study population would diminish the statistical power, albeit bya small amount if the level of dropout were low. However, if the health of those workers withmissing information tended to differ from that of included workers with similar distributions forfactors such as age and sex, then comparisons of disease mortality or morbidity between
occupationally-exposed workers and a reference population would be affected. Since recordkeeping might sometimes be poorer for workers employed for a very short time than for workers
employed for a longer period and because some studies (for example, [G6])—although not all (forexample, [C5])—have suggested that workers employed for a very short time might have higher
mortality rates, studies of occupationally-exposed workers often define the target population as
those employed (or monitored for radiation exposure) for at least six months [M21] or a year [V3];(b) Persons eligible for participation in an epidemiological study (or persons acting on theirbehalf) may choose not to take part. For example, in some cohort studies, such as the United
Kingdom’s National Registry for Radiation Workers (NRRW) [M21], eligible occupationallyexposed workers are given the opportunity to opt out of the study. Provided that—as in thisstudy—the level of dropout is very low (about 1% in the NRRW) and the characteristics of thosechoosing not to take part (for example, in terms of age and dose distributions) do not differ greatly
from those of participating workers, then prospective opting out is unlikely to bias the study.
However, if the level of dropout is high—for example, if participation is based on opting into thestudy rather than opting out—or if participation is influenced by whether or not the person has
developed the disease(s) under study, then the results of the study may be unreliable. An example
of problems with retrospective decisions on study participation arises in case–control studies,
where information is sought on persons with the disease(s) of interest (i.e. the cases) and a sample
of non-diseased controls. For non-fatal disease or for disease/mortality in childhood, a case or thecase’s parents may be more motivated to take part in the study than a healthy adult or the parents ofa healthy child. In this situation, participation may be high among potential cases but low among
potential controls. Conversely, in a case–control study of mortality, it may be difficult to obtainagreements to include dead cases but easier to enrol live controls. Furthermore, the decision on
participation in retrospective studies might be influenced by the level of exposure received. In
particular, a person with a non-fatal disease and a relatively high exposure may be more motivatedto take part than a healthy person with the same level of exposure.
B2.
When the selection of study subjects results in the exclusion of a substantial proportion ofeligible persons—and particularly if this proportion differs notably between persons with the disease orcondition under investigation and those without this disease or condition—then the potential for bias
may be considerable.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 141

B. Information bias
B3.
Errors in the information collected in an epidemiological study either on the disease underinvestigation or on the exposures received by the study population can affect inferences. The impact of
uncertainties in exposure and dose assessment is considered in a later section. Here the focus will be on
errors in information on disease.
B4.
Previous UNSCEAR reports [U11, U12] have given examples of the ways in which errors canarise when assessing disease. “Follow-up bias” can arise if, unbeknown to the investigator, some of thestudy subjects have left the area under investigation. This may occur if data on mortality or cancer
incidence are collected by linking records to regional mortality or cancer registers, but information is
not available on whether persons have migrated from the regions covered by these registries. A specificexample concerns studies of cancer incidence among the survivors of the atomic bombings in Japan[P14], where information on cancer is available for residents of Hiroshima city and Nagasaki prefecture
but not for those survivors who had moved to other parts of Japan. In contrast, information on mortality
is available for the whole of Japan. Unless a person was removed from the follow-up at the time of
migration from the study area, then he or she would appear “immortal” unless information on later
disease or death for that person was collected. This in turn would tend to biased estimates of diseaserisks towards zero [U12]. In the case of studies of cancer incidence among the survivors, theinvestigators have adjusted the numbers of person-years to reflect rates of immigration from andemigration to the catchment areas for the cancer registries [P14]. Although information on thesepatterns is not available for all members of the Life Span Study (LSS) cohort, it is available for a
subgroup of these survivors (within the Adult Health Study, AHS) and this was used to make theaforementioned adjustments. Although the person-years calculated in this way would not be exactly thesame as that obtained had follow-up information been available for the full cohort, the differences areunlikely to be great.
B5.
The ascertainment of disease is often not exact and varies according to the disease in question
and whether the focus is on disease incidence or mortality. For example, it is not always easy toestablish the underlying cause of death, and the diagnostic tools and criteria available to assess cancer
incidence mean that cancer registration data are often preferred to mortality data in epidemiologicalstudies of cancer. For reasons such as this, random or systematic misclassification of disease may arise,
which would tend to bias estimates of disease risks towards zero. An example of systematic errors is thefinding, from an analysis of death certificate diagnoses among autopsy cases in the LSS cohort studied
by the Radiation Effects Research Foundation in Hiroshima and Nagasaki, that cases who had died athome and who were later confirmed at autopsy to have died of lung cancer, frequently had originallyreceived diagnoses of pneumonia as recorded on their death certificates.
B6.
Annex A of the UNSCEAR 2006 Report [U12] gave some examples of ascertainment bias.
The detection of thyroid and non-melanoma skin cancers in the LSS cohort tends to be more complete
for survivors with higher rather than lower doses, because many of the people with higher doses arealso in the AHS and hence received biennial medical examinations. In contrast, the follow-up for these
diseases was not so intensive for cohort members not in the AHS. Consequently, the study investigators
included adjustments in their analyses for participation in the AHS, in order to avoid the overestimation of risks that would have arisen otherwise [P14]. Ascertainment bias might also arise if
comparisons are made between a working population that receives frequent medical examinations and ageneral population that is not subject to the same degree of surveillance; for example, as previously
highlighted by the UNSCEAR 2006 Report [U12] in connection with a study of leukaemia incidence
among Chernobyl recovery operation workers [I22]. In this circumstance, it is better to focus on comparisons
between workers rather than on comparisons with a population followed in a different manner; for example,

142 UNSCEAR 2012 REPORT

as in a study conducted within the aforementioned cohort of Chernobyl recovery operation workers andwhich—unlike the earlier study—did not find a raised incidence of leukaemia [I23].
B7.
It is better to ascertain information on disease from registers of disease or mortality, rather thanfrom the study subjects or from relatives or friends. In a similar way that—as mentioned earlier—somepersons might be more inclined to take part in a study if they have developed the condition underinvestigation, someone might be better able to recall a past medical event (or mistake this for somethingelse) if they suspect a link to a past exposure. The same point would apply if a proxy were asked about
the past health of another person. In such studies, checks with disease information collected fromobjective sources for a subgroup of individuals are valuable to assess the possible impact of any recall
bias. For example, in a study of United States radiologic technologists, Sigurdson et al. [S18] assessed
the accuracy of the technologists’ personal reports of cancer diagnosis by comparing these reports withinformation obtained from medical and pathology records. This showed good agreement for somecancers, such as breast, but less so for some others. Consequently, for cancer sites with a highmetastatic potential (cancers of the liver, bone or joints, soft tissue and brain) and for uterine cervicalcancer (owing to the large numbers recorded with carcinoma in situ), Sigurdson et al. included in theircalculations of Standardized Incidence Ratios only those self-reported cancer cases that had beenvalidated with medical records [S18].
B8.
Self-reported disease status can often be misleading, especially in situations where there has
been a great deal of publicity about cancer risk associated with a controversial exposure, such as toradioactive fallout from nuclear weapons testing. A rather extreme example of information reporting
bias is an analysis of cancer incidence data in a cohort of 4,125 members of Mormon families living inthree counties in south-western Utah in the United States, plus a relative few in nearby areas in Nevada
and Arizona during 1951–1962, as identified from telephone books in selected communities [J15].
“Family” as defined in the study included all persons related by blood or marriage, and the survey, bytrained volunteers from the surveyed towns, was filled out by the surveyor and the head of the family
working together. Response items included church membership, health effects felt immediately after
fallout (such as skin burns, eye burns, hair loss, change in hair colour, nausea, and diarrhoea), anddiagnoses of cancer among family members. Respondents reported a total of 288 cancers among 4,125
family members for the combined periods 1958–1966 (chosen to detect leukaemia) and 1972–1980 (forsolid cancers), which is 60% higher than the 179 expected according to published cancer incidence
rates for all Utah Mormons. This ratio is comparable to that observed in survivors of the atomic
bombings in Japan who received over 1 Gy. Rate ratios were extremely high for certain cancers: 5-foldfor leukaemia, 8-fold for thyroid cancer, 2-fold for breast and brain cancer, 3-fold for melanoma, and11-fold for bone cancer. Among those who were reported to have suffered from acute health effects
from exposure to fallout, the rate ratios were 45 for leukaemia, 11 for breast cancer, and 5 for all
cancers, numbers that are considerably higher than those calculated for atomic bombing survivors withnear-lethal doses exceeding 4 Gy.
B9.
A partial replication based on Utah county mortality statistics for 1950–1980, was conductedwith the rationale that increases in cancer incidence of the magnitudes reported in the interview study[J15] would surely be reflected in mortality statistics for the three Utah counties covered. This study
found a significant deficit of overall cancer mortality relative to the rest of Utah. However, the study
did find statistically significant evidence of an excess of leukaemia mortality, including 9 childhood
leukaemia deaths, in the three counties. The leukaemia mortality finding was consistent withconventional estimates of radiation-related risk, and far smaller than the 5-fold increase reported in theinterview study [M1].

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 143

C. Confounding
B10.
“Confounding factors”, which are correlated both with the disease under study and with an
exposure of interest, are discussed in paragraph 8 of UNSCEAR 2006 Report, volume I, annex A[U12]. In a simple example presented as an illustration, incidence of thyroid cancer among patientsadministered 131I for diagnostic purposes is slightly elevated; the excess incidence was likely related to
the fact that diagnostic screening was motivated by concerns about possible existing thyroid cancer [H1].
It is noted that confounding usually is dealt with at the analysis stage, either by incorporating such factors
into the regression model or by stratifying the data according to levels of the confounding factor.
B11.
It was also noted that cigarette smoking is one of the most serious confounding factors thathave to be dealt with in epidemiological studies, especially those dealing with smoking-related diseases[U12]. A recent analysis by Furukawa et al. [F11] found that models assuming generalized interactionsof smoking and radiation fit markedly better than simple multiplicative or additive interaction models.
The joint effect appeared to be super-multiplicative for light/moderate smokers (that is, excess relative
risks were greater than those estimated by a multiplicative interaction model), involving a rapid
increase in excess risk with smoking intensity up to 10 cigarettes per day, but additive or sub-additivefor heavy smokers smoking a pack or more per day. The estimated sex-averaged excess relative risk
(ERR) per unit dose at age 70 after radiation exposure at age 30 was 0.59 (95% CI: 0.31, 1.00) Gy−1 fornon-smokers, about 1.6 (95% CI: 0.73, 2.4) Gy−1 for those who smoked 10 cigarettes (one half pack)per day, but only about 0.1 (95% CI: −0.15, 0.37) Gy−1 for those smoking one pack per day. The impactof smoking on estimates of lung cancer risk from indoor exposure to radon is discussed in appendix Dof this annex.
B12.
Cigarette smoking is also a confounding factor for lung cancer risk associated with exposure toinhaled radon and radon progeny in underground mines and in dwellings, and individual smoking
histories must be taken into account in dose–response analyses. However, a recent pooled analysis ofthree European case–control studies of uranium miners [L12] of the effects of radon exposure on lungcancer risk including adjustment for smoking found little indication that smoking acted as aconfounding factor of the radon risk estimates. The BEIR VI Committee [N18] evaluated the joint
effect of radon and smoking on lung cancer risk in six cohorts of underground miners for whichsmoking data were available. The modelling of joint effects was handicapped by the small number ofminers who had never smoked and by limited quantitative information on tobacco smoking; however,the BEIR VI Committee assigned a twofold greater lifetime radon-related ERR for never-smokers
compared to that for ever-smokers. The nature of the joint effect of radiation exposure and smoking
was also considered in the pooled European miner study mentioned above [L12]. In this analysis it wasreported that the data favoured a sub-multiplicative interaction between radon exposure and smoking.
B13.
Geographical correlation studies of lung cancer risk based on area-wide estimates of radon andcigarette smoking levels in different geographical areas, which lack individual information on smoking
levels and radon exposure, are particularly vulnerable to bias, as discussed in chapter III of annex A to
the UNSCEAR 2006 Report [U12].

D. Changes in information over time
B14.
Site-specific and age-specific population cancer incidence rates are subject to secular changes,
in part because of lifestyle trends involving risk factors such as smoking, diet, and reproductive history,
but also because of increased surveillance and improved diagnostic methods. Examples of the latterinclude mammography screening for female breast cancer and ultrasound screening for thyroid cancer,

144 UNSCEAR 2012 REPORT

which are widely used to diagnose existing cancers early so that treatment may be more successful.
Collateral effects include shifting of cancer incidence rates in public health statistics toward younger
ages, and diagnosis of indolent cancers that in the absence of screening might never have become
clinically significant [N17].

II. UNCERTAINTIES IN EXPOSURE AND DOSE ASSESSMENT
B15.
Uncertainties in exposure and dose may influence interpretation of the epidemiological dose
response. Uncertainties in individual dose estimation may affect the evaluation of the statisticalsignificance of the dose response, the shape and steepness of slope, and the width of the confidence
interval.
B16.
The degree to which dose uncertainties affect interpretation of the dose response depend onwhether the random errors are due to measurement or assignment error and the nature of any sharederrors. In many instances, the uncertainties in dose estimates used to support an epidemiological study
may be complex mixtures of multiple sources of systematic and random errors. Methods for evaluating
the effect of dose uncertainties on the dose response, including a review of epidemiological studies thathave explicitly considered the effect of dose uncertainties, are discussed in section III.B of thisappendix.
B17.
In general, the radiation dose to specific organs and tissues of the human body cannot bemeasured directly. Some form of mathematical modelling is required to estimate the dose to specificorgans or tissues after measurements are taken from dosimeter readings or bioassay, or are made ofradionuclide concentrations in air, water, food, or soil in the location where the individual may havebeen exposed.
B18.
Uncertainty in dose estimation can be expected to increase according to the extent to whichmathematical models are used to compensate for an absence of direct measurements of exposure orradionuclide concentrations in the human body or in specific media of the workplace or theenvironment. The further away from the human receptor that models must be employed to estimate
individual exposure and dose, the greater the uncertainty anticipated. These uncertainties may include
complex combinations of random and systematic errors [N9, N10, N11]. The following section
discusses various sources of uncertainty associated with dose estimation.

A. Sources of uncertainty in exposure and dose estimation
1.

Common errors and mistakes

B19.
Common errors and mistakes in dose estimation can arise, for example, with measurements,
laboratory procedures, record keeping, programming, data input, and computation. Such common
sources of errors can invalidate the overall interpretation of a dose response. Thus, it is essential thatthese common sources of errors be identified and corrected prior to using dose estimates for
epidemiological evaluation.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 145

B20.
When individual organ doses are estimated with computer models that account for multiple
exposure events, numerous contributing pathways of exposure, and time-varying residence and dietaryhistories for thousands of subjects, rigorous quality assurance/quality control procedures should be
followed to identify and correct mistakes. These procedures should include cross-comparison of model
inputs, equations, intermediate results and individual dose estimates with independent calculations
performed by different persons using independent computational platforms [L31, S20]. All
discrepancies identified through these procedures should be resolved and corrections made before
estimates of individual doses and their uncertainties are deemed suitable for the evaluation of the dose
response.
B21.
In the subsequent discussions of this section, it is assumed that all exposure and dose estimates
are free of common errors and mistakes. Nevertheless, even after initial dose estimates have been tested
by a quality assurance/quality control protocol, the potential for residual errors and mistakes remains.
This means that uncertainty in dose estimation may extend beyond the credible intervals and probability
density functions specified to represent the states of knowledge about values of dose assigned toindividual members of the cohort.

2.

Interview data

B22.
Often data must be obtained from individual members of an epidemiological study regarding
their personal histories of occupation, residence, diet, and lifestyle. These data can be subject to bothrandom and systematic errors. Systematic errors can be the result of numerous causes, including bias
inherent in the formulation of interview questions and the conduct of the interview itself [H7, R5, R6,
W9]. For epidemiological studies that are of retrospective case–control design, systematic errors areoften due to associated recall bias, such as when individuals recall only times when they consumed
large quantities of a particular food type, but not times when they avoided the food type completely or
when they consumed only smaller portions. Recall bias can also occur when parents or nearest relatives
are asked to estimate quantities of specific foods consumed by subjects when these subjects were
infants and young children. In general, the amount of recall bias will tend to increase the greater thetime between past exposure and the conduct of the interview [R5, R6].
B23.
An important type of recall bias occurs when answers given to a questionnaire are correlatedwith the disease status of the subject. In epidemiological texts, questionnaire information that iscorrelated with the status of the subject with respect to other variables, including disease status, isreferred to as “differential bias.” An example would be subjects with lung cancer who during theirinterview under-report their past history of smoking. Recall bias that is correlated with disease status
can have a profound effect on the dose–response analysis. Differential bias can both exaggerate andsuppress the slope of a dose–response relationship [R6]. Recall bias that is not correlated with the statusof the individual with respect to exposure or disease, is referred to as “non-differential bias.” In general,
but not always, non-differential recall bias will tend to bias the dose response towards the null.
B24.
When data are obtained from individual subjects via an interview and systematic errors such asrecall bias have been corrected or judged to be of negligible importance, remaining errors in individual
responses to questions will tend to have a random error structure that is classical (that is, the variability
in individual responses to interview questions will be greater than the true inter-individual variability oftrue values) [C7]. Removal of recall bias from interview data, however, will be difficult for those
epidemiological studies based on a subject’s memory of past exposures in a retrospective case–control
design [G18, H7, R5].

146 UNSCEAR 2012 REPORT

3.

Uncertainty in estimation of external exposure

B25.
Organ doses due to radiation emitted from sources external to the human body are usuallyestimated from conversion coefficients that are tabulated in terms of kerma in air. The estimates arehence based on values of kerma in air inferred from (a) direct readings of dosimeters worn on theclothing of radiation workers, (b) approximations for individuals without dosimeters made by
extrapolating information from those who wore dosimeters and who were present in the same location
at the same period of time, or from those who wore dosimeters and had similar occupational
assignments, or (c) the measurement or model estimate of the radiation dose rate at the location ofhuman exposure, combined with an estimate of the time over which the individual was exposed and thetype and effectiveness of any shielding present [N9]. In general, for exposure to high-energy photons,
the uncertainty in the estimation of an individuals’ organ dose due to external radiation will be less thanthat in the estimated dose due to internal emitters [N9, N10, N11]. However, depending on the radiation
type, and the number of unknown variables, uncertainty in the estimate of the dose from external
exposure due to low-energy photons (of <0.03 MeV) can be considerable [N9].
B26.
Larger uncertainties will be expected if the kerma in air at the location of exposure is not
obtained from a measured value, but instead is approximated using mathematical models of
atmospheric dispersion and surface deposition to first estimate the concentration of radionuclides in air,on the ground, and on other surfaces at that location, and from these modelled concentrations, tocalculate the corresponding kerma in air and subsequent organ dose [N10].
B27.
Measurement uncertainty. The major sources of measurement uncertainty in estimating doses
from external sources result from imperfect knowledge of the radiation field in which the instrument
was used or the dosimeter exposed, owing to differences in energy and angular response between thecalibration field and the actual field of radiation. Other important sources of measurement uncertainty
include bias in reading and recording the instrument output, finite resolution and sensitivity, inexact
calibration standards, and poor precision. The uncertainty can be expected to be greater if themeasurement was reported as an operational quantity (for example, as personal or ambient dose
equivalent) rather than as a physical quantity (for example, as air kerma or fluence) [N9]. The
directional distribution of the field will also contribute significantly to the uncertainty, because some ofthe dose estimates will be based on isotropic quantities (for example, kerma in air or ambient dose
equivalent) whilst others will be based on strongly directional quantities (for example, personal dose
equivalent). Organ doses in a given field are strongly influenced by the directional distribution of the
field and the orientation of the individual.
B28.
In general, the uncertainty for measurements currently made using most personal dosimetersand survey instruments in gamma radiation fields is within limits set by international and national
standards organizations [N9]. These standards generally require that a measurement be accurate towithin ±30% to ±50% of a true value. However, such a high degree of accuracy was not the case fordosimeter measurements made in the 1950s and 1960s, which are often used for historical dosereconstructions. There may be additional uncertainty associated with changes to the dose quantities thathave been used over extended periods, since it will not always be possible to know what quantity wasused for some dose estimates. The uncertainty in neutron measurements and mixed field doses isgenerally greater than for photon and charged-particle exposures. A detailed discussion of the major
sources of uncertainty for various instrument systems used to assess external exposure is given in [N9]and summarized in table B1.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 147

Table B1. Summary of major sources of uncertainty for various instrument systems [N9]Instrument system

Major sources of uncertainty

AREA MEASUREMENTS OF GAMMA AND BETA RADIATION
Ion chambers

Energy and angular response

GM counters

Energy and angular response

Scintillation detectors

Energy and angular response

Semiconductor detectors

Energy and angular response

Film and TLDs

Energy response, calibration, processing, fading

In situ gamma spectrometry

Calibration, data processing (unfolding spectral data)

AREA MEASUREMENTS OF NEUTRON AND MIXED RADIATION FIELDS
Tissue equivalent proportional counters

Lower limit of detection, energy and angular responses

Multi-detector neutron spectrometers

Data processing (unfolding), calibration (response matrix)

Scintillation detectors for neutron
spectrometry

Data processing, photon–neutron discrimination

Hydrogen and helium proportionalcounters

Pulse height discrimination

Activation detectors

Calibration, energy and angular response, data processing to infer fluence

PERSONAL DOSIMETERS FOR MONITORING GAMMA AND BETA RADIATION
Film dosimeters

Calibration, processing, energy response for beta, X-rays, fading

TLDs

Calibration, processing, energy response, fading

OSLs

Similar to TLD but potential fading more important

Electronic dosimeters

Detector-dependentPERSONAL DOSIMETERS FOR NEUTRON AND MIXED RADIATION FIELDSNTA® film

Fading, energy response, track counting

TLD for neutrons

Neutron–gamma partition, energy response, laboratory processing

Track-etch detectors

Track counting, angular response

Neutron bubble detectors

Response varies with temperature

B29.
Uncertainties in conversion of measured quantities to organ absorbed dose. The true dose totissues and organs cannot be measured directly, but must typically be calculated by using some type ofa model and relevant input data [N9]. Model calculations often require assumptions about conditions
that cannot be known with certainty. The model itself may also contribute uncertainty in that it may not
perfectly represent the actual exposure scenario and physical situation being assessed. The uncertainty
of an estimated dose will be significantly larger than the precision of related measurements because oflack of knowledge about important exposure-related variables. Thus, depending on the circumstances
and the state of knowledge about the conditions of irradiation, the evaluation of total uncertainty
associated with measurements, models, and the assumptions necessary to estimate the absorbed organdose may vary from the relatively simple to a highly complex process. The number and relative
importance of assumptions necessary to estimate the uncertainty in organ dose can be expected to varywith the exposure situation [N9].

148 UNSCEAR 2012 REPORT

B30.
Variations in body size and orientation of the body with respect to the direction of incident
radiation contribute to the overall uncertainty. Even if the reported measurement represents an accurate
estimate of the exposure rate in air, if the actual incident energy and geometry is not specified, the model
estimate of the absorbed organ dose can be highly uncertain, particularly for low-energy penetratingradiations with energy less than 0.03 MeV [N9]. Conversely, even if the model used to convert
measurements to absorbed dose is based on the actual energy and geometry of the assessment scenario, if
the measurement calibration is conducted in an energy field that differs substantially from the actualenergy spectrum, the reported kerma in air can be markedly in error. High uncertainty in the reported
kerma in air will translate directly into high uncertainty in the estimate of absorbed dose in an organ [N9].
B31.
A comprehensive treatise on uncertainties in the measurement and dosimetry of external sourcesof radiation has been recently published [N9]. It includes a comprehensive chapter dedicated to theevaluation of the uncertainty in instruments used to measure external exposure, and it includes, inchapter 4, 13 tables of information summarizing the uncertainty in dose conversion factors obtained frommathematical models used to convert measurements of the kerma in air to absorbed organ dose, forvarious radiation types, energies, organs and tissues, and various irradiation geometries. The analysis isbased on published data for 18 different computational phantoms. Table 4.9 in [N9] shows that for higher
energy photons (>0.1 MeV) and a known irradiation geometry, the uncertainty in the conversion from air
kerma to red bone marrow (RBM) dose is very small, the geometric standard deviation (GSD) varying
from 1.01 to 1.12. This small uncertainty can be contrasted with the case where exposure is to low-energy
photons (<0.03 MeV) with an unknown irradiation geometry (GSDs vary from <2.0 to >10, depending on
the specific situation (tables 4.10 and 4.11)). Tables in [N9] are also given to correlate individual bodymass index with estimated values of absorbed organ dose per unit kerma in air, in order to make more
precise estimates of individual-specific doses from external exposure.
B32.
Table B2, taken directly from [N9], provides estimates of ratios of the maximum to minimum
absorbed doses for example organs and radiation spectra when irradiation geometry is unknown. Thesemaximum-to-minimum dose ratios vary from a low of 1.4 for 18 MV bremsstrahlung irradiating thecolon and RBM to 38.0 for 60 kV X-rays irradiating the thyroid gland. Maximum-to-minimum ratios
for external doses due to deposited radionuclides after the Chernobyl accident or following detonationof a nuclear fission-based weapon vary from 1.5 for the skin to 3.8 for the thyroid gland.
Table B2. Uncertainty arising from unknown irradiation geometry
The table lists ratios of maximal/minimal absorbed dose in different organs for a number of irradiation geometries assumed [N9]Spectrum or source of exposure

Maximal/minimal ratio
Breast

Colon

Lung

Red bonemarrowSkin

Thyroid

60 kV X-rays

30.5

11.6

11.8

6.4

2.3

38.0

90 kV X-rays

21.0

7.5

7.8

5.0

2.1

17.2

120 kV X-rays

16.4

6.2

6.5

4.4

1.9

12.3

Radionuclide deposition from Chernobyl
accident

3.6

2.6

2.8

2.1

1.6

3.8

Fallout from detonation of fission-based
nuclear weapon

3.0

2.1

2.3

1.8

1.5

3.0

Gamma rays (prompt and delayed) fromdetonation of fission-based nuclear weapon)

2.1

1.6

1.7

1.5

1.9

2.0

18 MV bremsstrahlung

2.4

1.4

1.5

1.4

2.1

1.7

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 149

4.

Uncertainty in estimation of internal exposure

B33.
For radionuclides that have entered the body by inhalation, ingestion, skin absorption, or via
wounds, doses must be determined indirectly using appropriate mathematical models that describe the
distribution and delivery of dose over time. Biokinetic models are used to describe the distribution,
retention and excretion of radionuclides and dosimetric models of organ and tissue structures are used
to calculate doses. The most widely used models are those developed by the International Commission
on Radiological Protection (ICRP) for the calculation of effective dose coefficients for protection
purposes [I7, I14]. However, the same models, or adaptations of them, are also often used for scientificpurposes, including the calculation of doses for epidemiological studies [H5, S11, S20, V1]. Dose
calculations may be prospective or retrospective. Prospective calculations for managing planned or
potential exposures include those performed by ICRP to provide dose coefficients (expressed as valuesof equivalent and effective dose per unit intake of activity). Retrospective calculations are made for
epidemiological studies and risk assessments, and also for protection purposes to determine compliancewith occupational and public dose limits and constraints. The steps in the calculation of averageabsorbed organ or tissue doses that are required for epidemiology or risk assessment are shown infigure B-I. The additional steps in the calculation of the protection quantities, equivalent and effective
dose, are also shown. This section reviews some of the important sources of uncertainty in thecalculation of internal exposure, including: uncertainties in the biokinetic and dosimetric models, andmeasurement uncertainty. Other uncertainties not discussed here can include the time of intake, theroute of intake and uncertainty on the isotopic composition of the incorporated material [N11].
Figure B-I. Steps in the calculation of internal absorbed and equivalent organ dose, internal effective
dose and radiological risk

B34.
Measurement to intake. Intakes of radionuclides incurred by individuals or populations are
estimated from measurements. Doses to individuals are often determined from bioassay measurements,
which can include whole or partial body counting or measurements of activity excreted in urine or
faeces. The estimation of the intake from bioassay measurements requires a suitable biokinetic model

150 UNSCEAR 2012 REPORT(discussed below). For populations exposed to radionuclides, intakes may be determined frommeasurements of radionuclides in air, soil, vegetation, food or water, or from an estimation of theamount released by the source, combined with a suitable environmental pathway model to estimate theintake by the population group.
B35.
Intake to dose. This is a two-stage process: first, biokinetic models, which estimate the uptake
and dynamic distribution of radionuclides within the body, are used to calculate the number of nuclear
disintegrations that occur in organs and tissues. Then, a suitable dosimetric model, which relies on
defined spatial relationships between source and target organs, and on the assumed geometries andmasses of these organs, is used to convert the number of disintegrations into the average absorbed dose
received by each tissue and organ (figure B-I).
B36.
Biokinetic models. These are compartment models which follow first-order kinetics and areused to calculate the number of nuclear disintegrations occurring in individual organs and tissues.
Specialized models are used to determine the deposition and clearance of inhaled radionuclides to bloodfrom the lungs [I9], the transit and uptake to blood of ingested radionuclides from the alimentary tract[I13], or the uptake to blood of radionuclides deposited in wound sites [N8]. For radionuclides entering
blood, element-specific models are used to calculate the distribution of radionuclides in systemic
tissues. The most widely used models are those published by the ICRP. These include the Human
Respiratory Tract Model (HRTM) which is used to calculate the deposition and clearance of inhaledradionuclides [I9], and the Human Alimentary Tract Model (HATM), which describes the transit andabsorption of radionuclides in the alimentary tract [I13]. The ICRP also publishes a range of elementspecific models for calculating radioactive disintegrations occurring in systemic tissues afterradionuclides have been taken up to blood from the respiratory or alimentary tracts [I8, I10]. Updated
systemic models, such as those for plutonium [L10], caesium [L9] and polonium [H5, L10], have beendeveloped based on more recent information. Some of these models are considered for potential use by
the ICRP.
B37.
Dosimetric models. These models estimate the fraction of energy absorbed in every target
organ for each disintegration that occurs in a source organ or tissue. The fraction of energy absorbed ina target tissue for a particular source organ/target organ pair and emission type and energy is referred toas the absorbed fraction (AF). For penetrating radiations, AFs have been calculated using Monte Carloradiation transport algorithms and anthropomorphic phantoms developed at Oak Ridge National
Laboratory (ORNL) [C18]. In these, the sizes and positions of the source and target organs are definedby quadratic surfaces in an idealized representation of the human body. More recently, the ORNL type
phantoms have been superseded by voxel phantoms which are based on medical imaging data of real
people and adjusted to the sizes and proportions of reference males and females [I16, L13]. For nonpenetrating radiations, the AF is unity unless the sizes and dimensions of source and target regions
prohibit this assumption. Such a situation occurs for walled tissue structures such as the respiratory andalimentary tracts, or for sources in the skeleton. With the exception of the latter, which is represented
by a simplified energy-independent model, AFs for the target regions in the HRTM and HATM havebeen determined using Monte Carlo radiation transport algorithms and three-dimensional models
representing source and target cell, or tissue geometries [I9, I13]. The dosimetric model for the skeleton
is currently being revised to address a number of simplifications in the ICRP Publication 30 model;
these include accounting for electron escape from the trabecular spongiosa to surrounding cortical boneand variations in absorbed fractions with changes in bone marrow cellularity [B17].
B38.
Various methods have been used to quantify the uncertainties present at each stage of the dose
calculation for internal exposure. The most significant is probably parameter uncertainty analysis,
where uncertainties on parameters are propagated through to the calculation of dose using the MonteANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 151

Carlo method [T10]. Another popular approach is to directly assign a subjective probability statement
to the dose in question [N11].
B39.
When quantifying uncertainty it is important to consider the purpose of the dose assessment.
For estimating the average risk to populations from radionuclide exposures with a linear model,
population mean doses to organs and tissues are of interest. Estimates of these doses are convoluted
with appropriate organ or tissue-specific risk coefficients to obtain estimates of lifetime cancer risk
(cancer risk per unit intake). For example, the United States government publishes lifetime risk
coefficients for exposures to environmental radionuclides [U1]. These coefficients apply to an average
member of the United States public, or more precisely, a “hypothetical population whose survival
functions and cancer mortality rates are based on recent data for the United States” [P1]. In this case, it
is uncertainty on population mean absorbed organ and tissue doses per unit intake that is of interest in
estimation of risk using such risk coefficients.
B40.
When attempting to quantify uncertainty on population mean absorbed organ dose per unit
intake it is important to distinguish between the effects of uncertainty (model parameters that have
fixed but unknown values) and variability (model parameter values that vary between individuals),
since the misclassification of variability as uncertainty will tend to exaggerate the uncertainty on themean dose per unit intake. In contrast, if the purpose of the assessment is to estimate the uncertainty on
the risk to a specific individual resulting from an internal exposure then it is the distribution of all
possible organ doses for the individual in question that is required. Under these circumstances, bothvariable and uncertain model parameters may be expressed as probability density functions and the onedimensional Monte Carlo method described in appendix A can be used to calculate the uncertainty on
dose. However, if additional bioassay data are available, then Bayesian methods may be used to
calculate the conditional distribution of dose given the data. For estimating cancer risk from internal
exposures in an epidemiological study, the effects of uncertainty and variability should be separated toaccount for their differential effects on the estimate of risk. Under these circumstances an appropriate
method, such as the two-dimensional Monte Carlo method described in appendix A can be used.
B41.
Uncertainty in measurements. The type of measurements used for the estimation of internal
exposure differs depending on whether the exposure setting is occupational, medical, or environmental.
Measurements related to internal exposures in the workplace involve direct and indirect bioassay
measurements, workplace measurements in air, water, and on surfaces, and biodosimetry [N11]. The
sources of uncertainty in direct measurements of whole or partial body emission of photons include
calibration uncertainties that involve unknown distributions of radioactivity in the subject, unknown
thicknesses of overlying tissue, and other differences between the subject being measured and thecalibration standard. Uncertainties in bioassay measurements of excreta, sweat, or saliva arise from:sampling, the critical issue of which is the representativeness of the sample; storage conditions, which
include the duration of storage and variable storage conditions; chemical analysis, the main problem
being chemical yield recovery; and counting, for which the critical issue is the calibration of themeasurement system [N11].
B42.
The calibration of direct bioassay measurements requires the use of anthropomorphic
phantoms. Uncertainties may arise because of differences between the amount of shielding provided byoverlying tissue of a real person and that provided by the phantom. This is less of a problem for thedetection of high energy gamma radiation stemming from the decay of uniformly distributed
radionuclides such as 137Cs or 60Co, but much more of a challenge for. the detection of lower energy
photons that are not uniformly distributed [N11].
B43.
Analysis of excreta samples is used to assess intakes of radionuclides that do not emit
energetic photons. It is much more sensitive in detecting radioactivity in a sample, with few of the152 UNSCEAR 2012 REPORT

calibration problems associated with whole body or partial body counting. Radionuclide concentrations
in excreta can vary with time for the same individual and from person to person. This inter- and intraperson variability of samples becomes an additional source of uncertainty, which, along with factors
associated with proper sample collection, will introduce uncertainty that likely exceeds the uncertainty
in the measurement of the sample’s activity alone [N11].
B44.
The term “workplace measurements” is used to refer to measurements of radioactivity ofsamples collected from the work environment. These may include, but are not limited to, workplace air
samples, or smears of workplace surfaces. For radionuclides that emit no penetrating radiations and thathave very low rates of excretion from the body, workplace samples may be the only means available toderive an estimate of intake [N11]. Although the measurement uncertainties may be similar to thoseencountered with excreta sampling, the uncertainty in the estimate of intake may be greater because it is
the worker’s environment, rather than the individual worker, that is being monitored.
B45.
The term “environmental measurements” is used for measurements of radionuclides in samples
taken of air, soil, water, vegetation, and agricultural and non-agricultural food products. Measurement
uncertainties are similar to those for bioassay analyses, but a more important source of uncertainty is
the representativeness of the sample for estimating the actual exposure or intake of a subject in an
epidemiological cohort. When direct measurement of radionuclide concentrations in environmental
media at a specific location is absent or sparse, mathematical models are employed using coefficientsand algorithms to use measurements and observations made at other locations and time periods. The
representativeness of modelled estimates to actual concentrations of radionuclides in the environment isa major source of uncertainty in estimating internal exposure. The uncertainty in the estimation ofenvironmental concentrations in the absence of direct measurements may equal or dominate over theuncertainty in the estimation of the dose per unit intake [A9, A11, N10, N11].
B46.
Uncertainty in intakes. Exposure to internally-emitting radionuclides can be acute or
protracted, and they can be from inhalation, ingestion, skin absorption, uptake from wounds, or fromintravenous injection. In occupational settings, intakes can be derived from bioassay analysis and theuse of biokinetic models. In addition, estimates of intakes can be made from measurements ofradionuclides in the air or the environment.
B47.
An important source of uncertainty in the estimation of dose due to inhalation is knowledge ofthe physico-chemical form of the radionuclide in air. This affects the extent to which the radionuclide isdeposited and retained in the airways of the respiratory tract, and the rate at which the material iscleared to blood or the alimentary tract.
B48.
The magnitude and uncertainty of intakes estimated from bioassay data depend mainly on thesolubility of the inhaled material in the lung. Erroneous assumptions regarding the rate of dissolution
and uptake to blood of inhaled aerosols can lead to significant systematic errors in estimated intakes
and doses, especially those derived from measurements of radionuclides in urine [B12, D5]. This isespecially noteworthy because intake and dose estimates from urine bioassay have been used inepidemiological studies of workers exposed to plutonium and other actinides, including those of the
Sellafield workforce [O3] and workers of the Mayak Production Association [G1, S23]. Over the past
decade, Bayesian methods have proved useful in identifying true values of intakes and calculating
uncertainties on intakes and doses estimated from bioassay data [D4, M14, P16]. The technique has
proved a useful tool for incorporating different forms of prior knowledge regarding the exposure. For
example, the prior can include workplace measurements of intakes, such as air sampler data, together
with plausible ranges of biokinetic parameter values determined from experimental studies.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 153

B49.
When measurements of radionuclides in the air or environment are available, intake frominhalation is determined as the product of the time-integrated radionuclide concentration in air, thebreathing rate of the individual estimated as an average for the time of passage of the radioactive
plume, and any factors accounting for indoor filtration of air compared to outdoors. Rates of inhalation
will vary considerably depending on whether the individual is engaged in light or heavy physicalactivity, or is resting at the time of passage of the plume. To estimate uncertainty in intakes due toinhalation of fallout particles from distant testing of nuclear weapons, the United States National
Cancer Institute assigned a geometric standard deviation of 1.3 to age- and sex-specific geometric meanvalues of inhalation rates [N3]. These log-normal distributions of inhalation rates were to represent
uncertainty mostly due to inter-individual variability in breathing rates among individuals of the sameage and sex.
B50.
Intakes by ingestion are more common in environmental settings where radionuclides released
to air and water lead to subsequent radionuclide concentrations in drinking water and terrestrial andaquatic food sources of importance to the human diet. Intakes by ingestion are less common in
occupational settings. Intakes from ingestion are derived from the product of the measured or estimatedconcentration of the radionuclide in water or food, the estimated consumption rate for drinking waterand specific food types, and factors that account for radionuclide losses due to water filtration, foodpreparation, radiological decay during the delay time between food harvest and consumption, anddietary dilution owing to the intake of water and food materials obtained from sources with noradionuclides [N10, N11].
B51.
Ingestion rates are obtained from dietary surveys of the individuals, their parents or closest
relatives, or from more general dietary surveys of populations composed of individuals of like age andgender. Uncertainties in the estimate of an individual’s intake from ingestion will be a combination of
the uncertainty in all of the factors mentioned above. As mentioned previously (see section II.A.2 ofthis appendix), the uncertainty in information obtained from dietary surveys involving an individuals’
or parent’s memory of past intakes of specific food types will be subject to the systematic error of recall
bias. Because of the multiple sources of uncertainty affecting the overall estimate of uncertainty for theingestion of specific radionuclides, the uncertainty in intake via ingestion may often be as great as or
greater than the uncertainty associated with the estimate of the absorbed organ dose per unit intake via
ingestion [N10].
B52.
In a few circumstances, intakes via ingestion for some members of epidemiological cohorts
have been determined by direct measurement of radionuclides in food and water combined withbioassay measurements. This has been the case for the estimation of 131I and 137Cs intakes during theaftermath of the Chernobyl accident and 90Sr intakes via ingestion of foodstuffs contaminated byreleases to the Techa River [N11].
B53.
Uncertainty in biokinetic models. There are two sources of uncertainty: uncertainty in how
well the structure of the biokinetic model represents the underlying processes that describe the retention
and excretion of the radionuclide in question (“model uncertainty”), and uncertainty in the values of theparameters for a given model structure (“parameter uncertainty”). Because biokinetic models are
generally constructed for representative members of exposed populations, uncertainty in biokinetic
model structure represents a shared error in an epidemiology study. However, uncertainties on
biokinetic model parameter values can be shared or unshared. Parameters that describe individualspecific physiological processes (for example, those describing the systemic retention and excretion ofradionuclides) have shared and unshared components. The uncertainties in mean and standard deviationof the distribution describing variability are shared among individuals, while the samples from these
distributions for a given mean and standard deviation are unshared. Material-specific parameters,

154 UNSCEAR 2012 REPORT

however, such as those describing the deposition and clearance of inhaled materials from the lungs, willusually have shared errors among individuals.
B54.
The extent of the uncertainty in the structure of a biokinetic model is dependent on the qualityof the data that were used to derive it. Direct measurements of radionuclides of interest in humans are
the most representative data in formulating a biokinetic model [L8]. Data expected to be less reliable
include measurements of radionuclides of interest in animals, or measurements of chemical analogues
in humans or animals. Generally, the most complete data pertain to radionuclides that are of the greatest
radiological significance and the best understood biologically. These categories have been used as atool to derive subjective probability statements regarding the uncertainty in the dose per unit intake fora given exposure pathway [N7]. Quantification of model uncertainty is complicated by the fact that it
represents a conceptual uncertainty; however, one approach is to represent model uncertainty in an
uncertainty analysis by assigning discrete probabilities to plausible model structures.
B55.
The uncertainty on parameter values is more easily quantified than model uncertainty. In manycases it is difficult to measure the value of a biokinetic parameter directly. However, where variation in
the parameter value produces an observable change in a bioassay quantity, and suitable data are
available, an empirical distribution can be derived that reproduces the observed variation in thisquantity in the human population [A10, N11]. For example, rates of uptake of plutonium to skeleton
and liver can be varied in the systemic model for plutonium in order to reproduce the observed intersubject variation in uptake by these organs. It is less straightforward, however, to derive empiricaluncertainties for parameters that do not strongly influence bioassay quantities, but may neverthelesssignificantly impact dose estimates. Under such circumstances, much greater reliance is placed on
subjective judgement to assign an uncertainty. The uncertainty assigned to these parameters will
significantly affect the uncertainty in the dose for the organ in question. An illustrative example of thisis long-term binding of inhaled plutonium to bronchial airways of the lung; here, a small bound fraction(in the order of a few per cent) can increase absorbed doses to bronchial cells from inhaled plutoniumby over two orders of magnitude [B12]. However, the inclusion of binding at these levels has anegligible effect on urine bioassay or lung content over time.
B56.
For retrospective assessments, bioassay data will generally provide additional information
about parameter values that will reduce uncertainties on dose estimates. Bayesian methods have proved
useful in this regard by combining existing knowledge with individual-specific data [D4, M20, P18].
B57.
Uncertainty in dosimetric models. Uncertainties in the absorbed fractions (AFs) calculatedusing dosimetric models arise because of uncertainty in the positions of source and target tissues, and in
the geometry and masses of these tissues. However, quantifying uncertainties in AFs is notstraightforward.
B58.
To properly account for uncertainties in AFs for penetrating photon emissions it is necessary to
perform Monte Carlo radiation transport calculations for a set of phantoms that represent particular
combinations of source and target geometries in the uncertainty distribution of interest; such a
calculation is computationally very difficult. The variability in the AF values for 137Cs wasapproximated by Apostoaei and Miller [A10] by quantifying the variation in the ICRP AFs due to thevariability in body mass among adult males and females. Estimation of uncertainty in AFs should
account for the systematic difference that may exist between the idealized (reference) ORNL phantom
and the average individual in the actual population of interest. Voxel-based phantoms offer a means ofassessing the likely differences between doses calculated for reference individuals using the ORNL
phantom and doses to actual or “true” individuals (a set of AFs that represent the mean of the humanpopulation under consideration). Studies show that the biggest discrepancies between the ORNL andvoxel phantoms exist for organ cross irradiation (the source and target organs are different) at low

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 155

photon energies (<100 keV) [Z1]. On the other hand, the differences in the AFs for self-irradiation oforgans (the source and target organ are the same) is small when adjustments have been made for organ
mass. As might be expected, the overall effect on absorbed organ doses is less pronounced: doses
calculated with the ORNL type phantom are lower than those calculated using the voxel type phantoms,
but appear to be typically within 50% [Z1].
B59.
For low-penetrating alpha and beta radiation, significant uncertainties in dosimetry exist where
the dimensions of source and target regions are small and separated by short distances (a few
micrometres). Such situations arise in dosimetric assessments for the respiratory and alimentary tracts
and the skeleton. In the lung, the target cells in the bronchial airways are assumed to be the basal andsecretory cells in the airway wall. In the formulation of lung dose, the dose to the bronchial region is
assigned 33% of the weighted lung dose; however the mass of the bronchial cells constitute around
0.1% of the total lung mass [I9]. Sensitivity analyses of lung doses from radon progeny have confirmedthat the dose received by these cells is indeed sensitive to the spatial relationship that exists between
them and the low-penetrating alpha-emitting radionuclides that are deposited in the mucus layer of the
airway wall [M7]. This sensitivity was comparable to the sensitivity of the lung dose to the assumed
physico-chemical form of the inhaled aerosol [M7]. However, for radionuclides with long half-lives
that are inhaled in a less soluble form, the uncertainty on lung dose is likely to be dominated by a lackof knowledge of the solubility of the material.
B60.
An additional uncertainty is introduced when the location and identity of target cells is poorly
defined. In the current bone dosimetry model, for example, it is assumed that the radiosensitive cells
that give rise to bone tumours reside in a 10 μm layer of tissue adjacent to the endosteum. However,research by Gössner [G14] and Gössner et al. [G15] indicates that the development of bone sarcomas
resulting from irradiation of mesenchymal stem cells is complicated and not dependent on a single celltype. These studies also suggest that the target cells extend at least up to 50 μm from the surface of theendosteum into the active marrow.
B61.
Uncertainties in the dose per unit intake for an unspecified person. For assessing the risk ofinternal exposure for a population group, it is the uncertainty in absorbed organ doses per unit intake foran unspecified, but representative or average person, in the population of interest that is required.
B62.
An extensive discussion of the various sources of uncertainty associated with the estimate ofdose per unit intake for an unspecified person is given in NCRP Report 164 [N11]. This comprehensive
report includes tables of uncertainty estimates for specific radionuclides, exposure conditions andorgans, when person-specific information from direct or indirect bioassays is not available. Table B3
provides estimates of uncertainty in the absorbed dose to the lung per unit exposure to radon (222Rn)
and its decay products [N11]. This average dose to the thoracic region of the respiratory tract accounts
for the uncertainty in sensitivity to radiation of different regions of the thoracic airways and has aplausible range (defined as the ratio of the upper to lower bound estimate) of a factor of 10. However,for exposure to radon and its decay products in particular, there is evidence that most lung cancers
occur in the bronchial and bronchiolar regions (83%) rather than in the alveolar region (16% [S1]),
suggesting that a meaningful quantity for epidemiology or risk assessment could be the absorbed doseto the bronchial and bronchiolar regions, as opposed to the average dose to the entire lung.
B63.
Table B4 (adapted from [N11]) provides central estimates, together with “likely” upper andlower bound estimates of the associated uncertainties on the central values, of absorbed organ doses forselected radionuclides in which intakes are acute or chronic through ingestion or inhalation, and theintake is of a variety of physico-chemical forms. The uncertainty estimates were largely based on
subjective judgements of NCRP. The ratio of upper to lower bound dose estimates varies considerably.
For example, for an acute ingestion of 137Cs incorporated in food (or as a soluble inorganic form) and156 UNSCEAR 2012 REPORT

for absorbed dose to the RBM, the ratio of upper to lower bound dose estimates is a factor of 2. Thisratio increases to a factor of 5 for the colon. Comparable uncertainties are associated with thyroid doses
resulting from chronic intakes of 131I (upper to lower bound dose ratios of 3.4). Higher uncertainties areassociated with ingestion of 106Ru in food (upper to lower bound dose ratios ranging from 25 to 40,
depending on the organ of interest). Larger uncertainties will be present when the physico-chemical
form of the intake is unknown, and if uptake via the alimentary tract is associated with acute, as
opposed to chronic, exposure.
Table B3. Central estimates and plausible ranges of absorbed dose to lung tissues per unit
exposure to radon (222Rn) and its decay products
Estimates are for intake by a typical healthy adult male and can be applied for residential or workplace exposures[I9, N11, N18]

TissueAbsorbed dose per unit exposure to radon (222Rn) and
its decay products (mGy per WLM)

Ratio of upper tolower boundBest estimate

Lower boundUpper boundLung (Dlung)

4.5

1.7

17

10

Bronchial region of lungb (DBB+bb)

5.6

2.6

12.2

5

a

a

Detriment-weighted average dose to lung [N11]. Uncertainty range represents a 90% confidence interval and was obtained by Monte
Carlo methods for uncertainty propagation. The range accounts for uncertainty in weighting the radiosensitivity of the different tissues(bronchi BB, bronchioles bb, alveolar interstitium and thoracic lymph nodes) considered in the ICRP lung model [I9].
b

Dose to the bronchial region (BB+bb) [N18]. Uncertainty range represents a 90% confidence interval.

Table B4. Central estimates and plausible ranges of 50-year committed doses per unit intake of
selected radionuclides
Estimates are for intake by a typical healthy adult male [N11]

IntakeForm

Acute ingestion of131
I

Incorporated infoodChronic ingestionof 131I

TissueBestestimate(Sv/Bq)a

Lower
bound
(Sv/Bq)a

Upper
bound
(Sv/Bq)a

Ratio of upper
to lowerboundbThyroid

4.2 × 10−7

1.8 × 10−7

1.0 × 10−6

5.4

Incorporated infood

Thyroid

4.2 × 10–7

2.3 × 10–7

7.8 × 10−7

3.4

Acute ingestion of137
Cs

Incorporated infood or soluble
inorganic form

Colon

1.3 × 10–8

6.0 × 10–9

3.0 × 10−8

5

Red marrow

1.4 × 10–8

8.0 × 10–9

1.6 × 10−82Ingestion of 106Ru

Incorporated in
food

Colon

5.0 × 10–9

1.0 × 10–9

2.5 × 10–8

25

Kidney3.0 × 10–9

5.0 × 10–10

2.0 × 10–8

40

Liver

1.5 × 10–9

2.5 × 10−10

9.0 × 10–9

36a

The values for 131I, 137Cs, and 106Ru of equivalent dose per unit intake (Sv/Bq) and absorbed dose per unit intake (Gy/Bq) are equal.

b

The ratio of the upper to lower bound approximates a “likely range”, not an absolute minimum or maximum value.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 157

B64.
A limited number of studies describe the application of parameter uncertainty analysis toquantify uncertainties on doses per unit intake, some of which have been reviewed by NCRP [N11].
These studies have focused on radionuclides of high radiological importance that are well understoodbiologically; these including iodine [A10, F8, H3, H23], tritium [H6, M10], caesium [A10] andplutonium and americium [P18]. The studies calculate distributions of absorbed or equivalent organ
doses, or effective dose per unit intake. Some of the analyses acknowledge that the doses should be
regarded as population mean or central values and interpret their results accordingly [A10, H6, P18].
Generally, however, no attempt was made to distinguish variability from uncertainty in the distributions
that were derived for model parameters since many of those studies were not intended for
epidemiological purposes. It is therefore likely that the distributions of doses that were calculated
overestimate the uncertainty in the population mean absorbed organ doses per unit intake. However, it
is possible to infer the uncertainty in the mean values for the exposure pathways that were considered.
Approximate ratios of upper to lower bounds of mean dose per unit intake for adult members of the
public are:(a) Within a factor of 2 for absorbed organ doses resulting from ingestion of 137Cs in food [A10]and absorbed dose to the thyroid from ingestion of soluble forms of 131I [A10, D10, F8, H3];(b) Within a factor of 3 for absorbed organ doses from inhalation or ingestion of tritiated water[H6, M10];(c) Within a factor of 4 for absorbed dose to the thyroid from inhalation of environmental aerosols
bearing 131I [F8, H8];(d) Within a factor of 5 for absorbed organ doses from ingestion of organically bound tritium [H6,M10];(e) Within a factor of 10 for absorbed doses to liver and bone surfaces from ingestion of 239Pu or
241
Am [P18].
B65.
Uncertainties in doses for specific individuals. Uncertainties on absorbed organ doses resulting
from internal exposures to radionuclides have been calculated for individuals in a number of
epidemiological studies. From the standpoint of uncertainties in the internal dosimetry model, theserange from the fairly simple (e.g. thyroid doses resulting from ingestion of iodine) to the complex (e.g.
lung doses resulting from inhalation of plutonium).
B66.
Estimates of dose to the thyroid have been calculated to derive estimates of risk of thyroid
cancer in childhood or adolescence following the Chernobyl accident [D8, D9, S28]. In these studies,
uncertainties on individual thyroid doses were calculated using Monte Carlo techniques and accounted
for uncertainties in the exposure pathway in addition to uncertainty in the dose per unit intake to thethyroid. In both studies uncertainty in the latter was simply taken directly from estimates of thevariation in thyroid dose per unit intake estimated by Apostoaei and Miller [A10] or Dunning and
Schwartz [D10]. Thus it was assumed that the range of thyroid dose per unit intake for the subjects inthe study groups was comparable to those observed in United States subjects of similar ages. In
addition to deriving uncertainties on parameters, Drozdovitch et al. [D8] categorized parameters as
shared or unshared, with a view to preserving this error structure in a Monte Carlo analysis of risk. The
uncertainties on doses calculated by Stepanenko et al. [S28] were included in a risk analysis by
Kopecky et al. [K10]. However, because the uncertainties on thyroid doses were calculated separately foreach individual, shared and unshared parameters were not distinguished in the analysis of risk [K10].
B67.
The study of nuclear workers exposed to plutonium and other actinides is an invaluable tool
for obtaining risk estimates of lung cancer for alpha emitters other than radon progeny. So far, risk

158 UNSCEAR 2012 REPORT

estimates have been derived from point estimates of lung dose that are often estimated from urine or
faecal bioassay [G9, S23]. However, such estimates ignore errors in lung dosimetry. As a consequence,
there has been significant interest in applying Bayesian inference methods to calculate uncertainties inthese estimates. Miller et al. [M15, M16] derived prior distributions of biokinetic model parameterswith a view to applying them in a Bayesian analysis of former workers of the Mayak Production
Association. This distribution was limited to a small set of biokinetic “types”; each type consisted of aset of parameter values associated with a biokinetic model and was derived by fitting the data to one of
41 sets of worker bioassay and autopsy data. However, representing the prior uncertainty on parameters
as a discrete set of sets rather than as continuous distributions may distort the uncertainty on dose andmay also make it difficult to distinguish shared from unshared parameters. In a more recent analysis,
Puncher et al. [P17] derived uncertainties in the ICRP Human Respiratory Tract Model [I9], in the formof a multivariate continuous prior distribution. This was used to calculate uncertainties on lung doses
for 2,056 European nuclear workers in a recent European case–control study of lung cancer risk fromoccupational exposures to actinides [T5]. Although the Bayesian calculation was performed separately
for each worker, the sampling regime was implemented so that parameters identified as being shared or
unshared would be preserved between workers. Effectively what was calculated was a joint posterior
distribution of worker doses conditioned on the matrix of worker bioassay data.

B. Reconstruction of external exposure in specific studies
1. DS02 dosimetry for survivors of the atomic bombings of Hiroshima andNagasaki
B68.
The most recent set of dose estimates for the survivors of the 1945 atomic bombings ofHiroshima and Nagasaki is referred to as DS02 [G23, K4]. Estimates of the external absorbed dose toeach organ for each survivor provide the basic foundation for the most recent updates of risk
coefficients from the Radiation Effects Research Foundation of Japan (RERF). The absorbed dose
estimates from DS02 [G23] provide the basis for the majority of estimates of standardized coefficientsof risk per unit dose, including those published by the United States National Research Council [N19],ICRP [I14] and UNSCEAR [U12]. To date, almost all radiation risk coefficients are derived from theLifespan Study cohort (LSS) of RERF; exceptions are risk coefficients from pooled studies for breast
and thyroid, and for lung cancer due to exposure to radon and its decay products [I14, N19, U13]. A
detailed analysis of uncertainty in the DS02 dose estimates has been conducted by Kaul et al. [K4].
They evaluated uncertainties in each modular component of the individual dose calculation andcompared their calculated total uncertainty estimates with field measurements to test the validity of theresults. The computational process for estimating absorbed doses in DS02 is composed of three
independent elements: (a) propagation of the radiation leakage from the weapon through air to derive
the radiation field above bare, flat ground (referred to as the “flat field”), (b) transmission through andaround structures and terrain to produce a “shielded radiation field”, and (c) transmission into the bodyto compute mean radiation fields and doses in individual organs of each survivor. Calculations aredifferentiated by neutron and gamma-ray components. The dose uncertainties of each computational
element are inferred from input parameters, reaction cross sections, computational methods,
computational statistics, assumptions made in creating the computational description of events and on
expert judgement. Uncertainties are differentiated into two types: “systematic,” describing the
likelihood that doses to all individuals at a given city will increase or decrease together, and “random,”
which affect each individual survivor more or less independently.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 159

B69.
To evaluate the validity of the computed dose uncertainties, comparisons were made between
ensemble uncertainties (computed for individual computational elements and radiation dosecomponents) and field observations, at critical intervals in the computational process for survivor dose
estimation. These comparisons included observed and calculated radiation free-field components; theobservations included thermal- and fast-neutron activation and gamma-ray thermoluminescence. These
comparisons are relevant to the evaluation of systematic uncertainty in DS02. Comparisons were also
made between field observations and calculations of survivor shielding, where the observations
consisted of biodosimetric measurements for individual survivors. These comparisons were relevant forevaluation of the amount of random uncertainty specified in DS02.
B70.
Systematic uncertainty. Sources of systematic uncertainty include the yield of the weapon forprompt and delayed radiation, radiation output (that is, radiation leakage from the weapon, describing
the disassembly of the bomb as it explodes), height of the burst, air density, air moisture, soil moisture,
air transport, nuclear cross sections, fission product radiation uncertainties (including gamma-ray andneutron dose), shielding calculation methodology, and the calculational methodology adopted for
estimating organ dose. The total estimated systematic uncertainty for a representative survivor isexpressed as a coefficient of variation (CV, also called standard error as a percentage of the central
estimate) of 13.6% for the city of Hiroshima and 12.6% for the city of Nagasaki (tables B5 and B6). In
this situation, the CV accounts for one standard error about the estimate of the mean, or 64% of thetotal uncertainty about the mean value.
B71.
Random uncertainty in dose at a known location. The various factors considered in estimating
the random component of total uncertainty are: the distance of the survivor to the hypocentre of thebomb detonation, shielding associated with house modelling, shielding assignment for an individual
survivor, shielding histories associated with the use of the 9-Parameter Shielding Model, the use of avariable phantom model and assumptions about the orientation of each survivor to the influence of
irradiation, survivor coordinates, survivor recall of location and factors affecting shielding, and recall of
posture and orientation (based on re-interviewing 88 survivors of the Nagasaki bombing). The total
random uncertainty in survivor dose estimates range between 20% and 41% (coefficients of variation)
for the Hiroshima bombing and between 25% and 44% for the Nagasaki bombing.
B72.
Total dose uncertainty. The uncertainty for each component of the dose calculation for arepresentative survivor and representative conditions of orientation, shielding and dose at 1,500 m
distance from the hypocentre are given in table B5 for Hiroshima and table B6 for Nagasaki. The total
uncertainty is dominated by the random uncertainty and ranges in terms of the coefficient of variationfrom 24.4% to 43.3% for Hiroshima and 27.9% to 45.3% for Nagasaki. These uncertainties appear tobe substantiated by limited comparisons for a small number of survivors (22) whose gamma kerma
doses could be determined using biodosimetric information [K4].
B73.
Dose uncertainty assumed for LSS risk estimation. In their evaluation of risk coefficients fromthe LSS cohort, Preston et al. [P14] assumed a general dose uncertainty (CV) of 35% for survivor dose
estimates from both the Hiroshima and Nagasaki bombings. This was assumed to be random andassociated with classical measurement error. Pierce et al. [P6] re-evaluated the assumptions used by
Preston et al. [P14] and concluded that the total random uncertainty associated with each individual
survivor dose estimate ought to be more appropriately expanded to 44%. Of this, a CV of 40% is
considered as classical measurement error and a CV of 20% assignment error (referred to in [P6] as“averaging errors”). Of the two types of random errors, classical measurement errors have the mostprofound effect on introducing a bias in the dose–response analysis (see section III.B of this appendix).

160 UNSCEAR 2012 REPORT

Table B5. Representative DS02 random and systematic uncertainties in total marrow dose at
Hiroshima (from [K4])Factors

Absorbed dose uncertainties (CV, %)Total

Methodology
systematic

Yield

5.8

5.8

Neutron output

2.6

2.6

Air density and moisture

2.6

2.6

Air cross sections

3.3

3.3

Hydrodynamic model

5.2

5.2

Fission product source

2.6

2.6

Air transport calculation method

7.6

7.6

Burst height

1.2

1.2

Hypocentre location

1.4

Survivor coordinates

14.2

House materials

5.5

5.5

Shielding assignment

15.6

15.6

(Range)(5.0–35.0)(5.0–35.0)

Shielding calculation method

4.5

Phantom materials andorientation

4.9

4.9

(5.0–10.0)(5.0–10.0)(Range)Methodology
randomInput
random

1.4
14.2

4.5

Organ dose calculation method

3.7

Shielding survivor recall

10.8

10.8

Posture and orientation recall

3.6

3.6

Total

28.5
(Range)3.7

13.6(24.4–43.3)

17.3

18.2

(9.1–36.8)
Total random

25.1(Range)(20.3–41.1)

UNCERTAINTY DUE TO DS02 METHODOLOGY ALONE
Total

22.0
(Range)(16.3–39.3)

Note of survivor specifications: City: Hiroshima; Distance: 1,500 m.
Conditions of shielding: First floor, external structure within 22.5 degrees to hypocentre,
unshielded factor >3, slant penetration from outer surface to survivor 6 metres.
Adult survivor facing hypocentre.
Total dose: 22.7 mGy.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 161

Table B6. Representative DS02 random and systematic uncertainties in total marrow dose at
Nagasaki (from [K4])Factors

Absorbed dose uncertainties (CV, %)Total

Methodology
systematic

Yield

4.5

4.5

Neutron output

3.5

3.5

Air density and moisture

2.2

2.2

Air cross section

3.4

3.4

Hydrodynamic model

4.1

4.1

Fission product source

2.1

2.1

Air transport calculation
method7.5

7.5

Burst height

0.6

0.6

Hypocentre location

2.1

Survivor coordinates

20.3

House materials

5.1

5.1

Shielding assignment

14.5

14.5

(Range)(5.0–35.0)(5.0–35.0)

Shielding calculation method

4.3

Phantom materials andorientation

4.9

4.9

(5.0–10.0)(5.0–10.0)(Range)Methodology
randomInput
random

2.1
20.3

4.3

Organ dose calculation
method

3.9

Shielding survivor recall

10.4

10.4

Posture and orientation recall

3.8

3.8

Total

31.0
(Range)3.9

12.6(27.9–45.3)

16.2

23.2

(9.0–36.8)
Total random(Range)28.3(24.8–43.5)

UNCERTAINTY DUE TO DS02 METHODOLOGY ALONE
Total

20.6
(Range)(15.5–38.9)

Note of survivor specifications: City: Nagasaki; Distance: 1,500 m.
Conditions of shielding: First floor, external structure within 22.5 degrees to hypocentre,
unshielded factor >3, slant penetration from outer surface to survivor 6 metres.
Adult survivor facing hypocentre.
Total dose: 44.3 mGy.

162 UNSCEAR 2012 REPORT

2.

Occupational exposures

B74.
In epidemiological studies of occupationally-exposed people, estimates of absorbed doses toorgans of individual workers are used to evaluate dose–response relationships. Procedures must be
developed that translate dosimetric data recorded for workers—obtained both from current dosimetry
systems designed to estimate the Personal Dose Equivalent (known as Hp(10), the energy absorbed at a
depth of 10 mm in tissue), and from older dosimetry systems for which the dose objective was not soclearly defined—into estimates of the absorbed dose in an organ. While translating historical and more
recent recorded doses into estimates of organ dose, attention is given to account for systematic andrandom sources of uncertainty. The following material reviews cohorts occupationally exposed
primarily to external sources of high-energy gamma radiation. Individuals exposed occupationally tointernal emitters or externally to neutrons or low-energy photons are excluded from consideration.
B75.
Hanford workers. In a study presenting results of dose–response analyses based on estimatedexternal radiation doses for Hanford workers, Gilbert [G8] corrected for bias in recorded doses to
produce estimates of absorbed dose for organs, and they estimated the systematic and random
uncertainty in the correction factors. Sources of uncertainty in the bias correction factors were found toinclude both the random variation of laboratory measurements and the limited ability of the personal
dosimeters worn by workers to respond accurately to all radiation energies, as well as the uncertainty
arising when measured dose is converted to absorbed dose in an organ. Systematic uncertainty about
the overall bias B for specified time periods is represented as a ratio (KS) between the upper 97.5th
percentile of a probability density function for the bias correction factor and the geometric mean value
for B for red bone marrow dose and lung dose. The systematic uncertainty in the bias correction factors
used in this study were assumed to be perfectly correlated among workers [G7].
B76.
The study by Gilbert [G8] of dose–response analyses relied on an earlier study of the same
Hanford cohort which evaluated bias and uncertainty in estimates of external exposure derived frommeasurements using personal dosimeters [G7]. That 1996 study focused on recorded doses as theprimary information for estimating absorbed doses to organs, addressing the extent that uncertainties
for different workers were correlated. This analysis involved categorizing errors as random (reflecting
uncertainties that were independent among individual workers), and systematic or biased (reflecting
uncertainty between the mean of the reported dose and the true mean of the absorbed dose to organs for
an identified subgroup within the exposure period). The authors assume that uncertainty due toindividual sources is described by independent log-normal distributions. Overall uncertainty factors are
obtained through propagation of log-normal distributions of uncertainty through a series ofmultiplicative terms. Data that would allow rigorous determination of uncertainties were not available;thus, the uncertainty factors presented in that paper reflect subjective judgement of the authors.
B77.
The evaluation focused on uncertainty resulting from the fact that dosimeters, especially thoseused in early periods of plant operation, were limited in their ability to respond accurately to allradiation types to which workers were exposed (that is, beta, photon, and neutron) and to radiation
coming from different directions (for example, anterior–posterior or rotational). This specific energy
and geometry dependence of exposure conditions was a major source of both random and systematic
error in the Hanford dose estimates. Because of the different capabilities of dosimeters used in different
time periods, separate evaluations were made for the periods 1944–1956, 1957–1971, 1972–1983, and
1984–1993. It was concluded that systematic uncertainties in different dosimetry systems were unlikely
to be perfectly correlated, and so the overall systematic uncertainty in cumulative doses that include
contributions from more than one of these time periods were likely less than that for uncertainty
contributed by individual exposure periods.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 163

B78.
The estimated doses follow approximate log-normal distributions, characterized by bias
factors B and 95% uncertainty factors KS (quantifying the systematic uncertainty regarding how well thebias factors are known) and KR (quantifying the inter-individual variability of true dose among workers,
given a possibly true value for B that is without systematic uncertainty). The recorded doses weretranslated into estimates of deep dose and estimates of absorbed dose to the red bone marrow and lung(see table B7). KR represents only aleatory uncertainty or assignment error. Classical error resulting
from variability of laboratory methods was not considered, because it was only a minor contributor to
the total uncertainty of most members of the cohort, especially for those who experienced multiple
exposure events over a period of several years.
Table B7. Overall bias and uncertainties in recorded doses of monitored workers as estimates ofdeep dose, red bone marrow dose, and lung dose [G7, G8]
Source of uncertainty

1944–1956

1957–1971

1972–1983

1984–1989

DEEP DOSE
Overall bias (B)a

1.27

1.02

1.12

1.01

1.2

1.1

1.05

1.05

1.4, 1.8

1.3, 1.5

1.2, 1.3

1.2, 1.3

1.8

1.4

1.2

1.2

Systematic uncertainty (KS)a
From energy and geometry
From other sourcesbRandom uncertainty (KR)c

From energy and geometry

RED BONE MARROW DOSE
Overall bias (B)a

1.75

1.41

1.54

1.40

Systematic uncertainty (KS)a
From energy and geometry

1.3

1.2

1.1

1.1

b

From other sources

1.5, 1.8

1.3, 1.6

1.3, 1.4

1.3, 1.4dOverall uncertainty

1.6–1.9

1.4–1.7

1.3–1.4

1.3–1.4

1.9

1.6

1.4

1.4

1.33

1.07

1.17

1.06

1.2

1.1

1.05

1.05

Random uncertainty (KR)cFrom energy and geometry

LUNG DOSE
Overall bias (B)a
Systematic uncertainty (KS)a

From energy and geometryb

From other sources

1.5, 1.8

1.3, 1.6

1.3, 1.4

1.3, 1.4

Overall uncertaintyd

1.6–1.9

1.3–1.6

1.3–1.4

1.3–1.4

1.6

1.4

1.2

1.2

Random uncertainty (KR)cFrom energy and geometryaValues of B and KS define a log-normal distribution representing systematic uncertainty in the central estimate of bias correction that isshared by all members of an exposure period subgroup. B is the geometric mean of the bias correction factor and KS is the ratio of theupper 97.5th percentile to the geometric mean. KS is often referred to as a “95% uncertainty factor,” because when it is divided into thegeometric mean and then multiplied by the geometric mean, it defines a 95% uncertainty interval for a log-normal distribution.
b

The first entry is uncertainty for the anterior–posterior geometry; the second entry is uncertainty for the rotational geometry.

c

The selection of a possibly true value for systematic uncertainty in bias correction combined with KR define the inter-individual
variability of true doses for each person in the exposure period subgroup.
dOverall systematic uncertainty reported in [G8].

164 UNSCEAR 2012 REPORT

B79.
A 15-country study of radiation workers. In order to derive direct estimates of risk of cancer
due to chronic exposure to radiation, a 15-country collaborative study of radiation workers in the
nuclear industry was conducted, using a common core protocol. An investigation of shared errors in
dosimetry was established as part of the study and reported in Thierry-Chef et al. [T2]. One of the main
objectives of this investigation was to identify and quantify bias and uncertainties in available recorded
dose estimates. Bias correction factors (with their uncertainties) specific for individual recorded doses
for each facility and calendar-year period were estimated to correct absorbed doses for organs thatwould be, on average, unbiased estimates of each subject’s organ dose of interest.
B80.
Because historical practices for measuring lower-energy photons (<100 keV), very-highenergy photons (>3,000 keV), neutrons, and internal contamination by fission and activation products
were less reliable than those for measuring high-energy photons, those workers who had the potential
for substantial doses from these radiation types were excluded from the investigation. In addition,
independent, unshared (classical) errors due to sampling variation in measurements inherent to different
types of dosimeters were not evaluated.
B81.
The identified sources of errors in doses associated with high-energy photon irradiation were:
exposure conditions in the workplace, dosimetry technology, calibration practices, and administrative
practices for recording doses in files. Methods were developed to enable the comparison of recorded doses
through time and among different facilities and to quantify identified bias and uncertainties in historical
recorded worker doses. Table B8 lists the characteristics of the sources of uncertainty considered by [T2]and identifies which were considered in the quantification of systematic sources of uncertainty.
B82.
Thierry-Chef et al. [T2] determined a bias factor B (geometric mean) and its uncertainty
factor K (= GSD1.96, where GSD is the geometric standard deviation) to estimate a 95% uncertainty
range assuming a log-normal distribution. Doses to colon, lung, and active bone marrow were estimatedby dividing the individual recorded doses by a random value selected from the log-normal distributionof the bias factor (as defined by Bi and the uncertainty factor K for a given organ i, see table B9). Oncea random value of the bias correction factor is applied for each facility and year, that sampled value isapplied for each subject with a recorded dose who worked at the facility and in that year and who was
exposed to high-energy photons. The error structure is assumed to be 100% due to assignment (that is,inter-individual variability of true dose varies stochastically and independently about an unbiased meanvalue that is applied for each cohort subgroup).
B83.
Although uncertainties in bias correction factors across different facilities are neither perfectly
correlated nor independent. Since common assumptions were used to develop the bias correction
factors [G10], the effect of partial correlations in the uncertainty of individual bias correction was notconsidered.
B84.
Oak Ridge National Laboratory workers. An illustrative case study by Stayner et al. [S25]developed a method to account for shared errors in exposures within a dosimetry system for a cohort ofnuclear workers at the Oak Ridge National Laboratory, United States. Data from this study facility,
comprising annual records of external radiation doses from personal dosimeters for all workers, ispublicly available from the United States DOE “Comprehensive Epidemiologic Data Resource: A
digital collection of public use data sets (CEDR)” website (https://www.orau.gov/cedr/). The ORNL
cohort included 5,345 workers, and, following the protocol for the 15-country study [T2], workers who
received substantial doses from neutrons and from internal exposures were excluded from the analysis.
The bias factors and uncertainties developed for the ORNL facility in the 15-country study were used inMonte Carlo simulations, repeated 10,000 times for each individual in the cohort, to randomly select a
set of bias factors from the log-normal distribution for each time period, defined by β and κ intable B10. The bias factors (B) were then used to estimate annual ‘corrected’ doses for each worker inANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 165

the study, by dividing their annual recorded doses by the appropriate sampled bias factor. Workers wereassigned the same correction factor for each year of the period, thus sharing a common assignment
error and preserving the correlation structure in the errors in doses between individuals in the sampling
process. Uncertainty due to classical measurement error was not addressed. Inter-individual variabilityof recorded dose was assumed to be equal to inter-individual variability of true dose once the recorded
dose was divided by the sampled value of B to correct for systematic errors.
Table B8. Characteristic source of errors in dose estimates for the 15-country study of radiation
workers [T2]
Sources of errors

Uncertainties
in estimatedbias factors

Uncertainties resulting
from variation in thecorrect bias factors
among workersa

Potential impact
on the dose
estimates

Considered inthequantificationof errors

CONDITIONS OF EXPOSURE
EnergySharedAssignment

Major

Yes

Geometry

SharedAssignment

Major

Yes

Other environmental factors(heat, humidity, light)

SharedAssignment

Negligible

No

DOSIMETRY TECHNOLOGY
Response to energy

SharedAssignment

Major

Yes

Response to geometry

SharedAssignment

Major

Yes

Laboratory practices (dosimeter
processing and reading)

UnsharedClassical

Minor

No

CALIBRATION PRACTICES
Dosimetric quantity

SharedAssignment

Major

Yes

Radiation source used forcalibration

SharedAssignment

Major

Yes

Backscatter factor

SharedAssignment

Major

Yes

Factors affecting sources

SharedAssignment

Minor

Yes

ADMINISTRATIVE PRACTICESaFrequency of monitoring

SharedAssignment

Generally minor

No

Criteria for monitoring

SharedAssignment

Generally minor

No

Rules for below threshold doses
and for missing doses

SharedAssignment

Generally minor

No

With the exception of laboratory practices, the errors in the estimated bias factors from each of the sources are shared among

workers within a group defined by time period and facility and are due to assignment.

166 UNSCEAR 2012 REPORT

Table B9. Final estimated biases and uncertainties in dose estimates for radiation workers inselected facilities in France and United States [T2]
Facility

Start

End

Lung
Blung

Red bone marrow
Klung

Colon

BRBM

KRBM

BcolonKcolonFRANCE
1

2

3

4

1950

1956

1.62

1.51

1.94

1.33

1.72

1.69

1957

1960

1.01

1.28

1.21

1.31

1.07

1.22

1961

1966

1.01

1.17

1.21

1.21

1.07

1.07

1967

1984

1.00

1.17

1.19

1.30

1.06

1.07

1985

1994

1.02

1.20

1.22

1.30

1.08

1.07

1995

1995

1.04

1.20

1.25

1.28

1.10

1.08

1968

1978

1.13

1.32

1.36

1.33

1.20

1.26

1979

1995

1.13

1.22

1.36

1.25

1.20

1.15

1955

1960

1.01

1.28

1.21

1.31

1.07

1.22

1961

1964

1.01

1.17

1.21

1.21

1.07

1.07

1965

1995

1.03

1.22

1.36

1.25

1.20

1.15

1968

1982

1.16

1.21

1.38

1.38

1.23

1.29

1982

1982

1.11

1.18

1.33

1.20

1.18

1.28

1983

1997

1.05

1.17

1.26

1.19

1.11

1.18

UNITED STATES
5

1943

1952

1.93

1.41

2.31

1.72

2.05

1.99

1953

1979

1.13

1.22

1.36

1.25

1.20

1.15

1980

1997

1.08

1.23

1.29

1.31

1.13

1.20

B = bias factor (geometric mean).
K = uncertainty (geometric standard deviation1.96).

Table B10. Parameters of the log-normal distribution for bias factors developed for ORNL workers[S25]
Year(s)aParameters of the distribution for the bias factor
Geometric mean (β)

Uncertainty factor (κ)a

1943

2.048

1.601

1944–1952

1.353

1.698

1953–1979

1.201

2.464

1980–1997

1.137

1.708

κ = the ratio between the upper 97.5th percentile and the geometric mean of a log-normal distribution for the bias correction
factor; the ratio represents systematic uncertainty.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 167

3.

Medical cohorts

B85.
Thyroid cancer following scalp irradiation. A reanalysis accounting for uncertainty indosimetry. In the 1940s and 1950s, scalp irradiation was used as a medical treatment for over 20,000
children in Israel who had ringworm, or tinea capitis, in order to induce epilation. Follow-up studies
showed that this radiation exposure was associated with thyroid malignancies, but the individual doses
to the thyroid gland estimated in these studies contained probable errors. Schafer et al. [S5] and Lubin
et al. [L29] have developed methods to account for the uncertainties in the dose estimates forindividuals in this cohort.
B86.
Schafer et al. [S5] developed a variant of the multiplicative assignment error model to refine
the uncertainties in dose estimates used in the dose–response estimation. Starting from a large data set
with health outcomes and imprecisely-determined doses from the tinea capitis cohort, they incorporated
data from a separate study of anthropomorphic phantoms exposed to X-rays under similar conditions toformulate and characterize a model for estimating dose. This approach results in assignment error due
to using the expected dose from a regression model as a surrogate for the individual’s true dose. Schafer
et al. [S5] distinguished between classical measurement errors and assignment errors in their approach,as well as noting that the classical errors in dose estimates for different individuals are correlated.
B87.
Schafer et al. developed a model for the distribution of dose on a single course of treatment
which included error terms for: (a) intra-individual effects, reflecting the different thyroid doses thatwould occur if a child were irradiated twice under identical conditions, (from movement during
treatment or differences in positioning the body), (b) between-individual effects, reflecting the different
doses for different children due to differences in head size and shape, and (c) random errors due to thedifferences between prescribed and actual skin exposure. These error terms were represented as thestandard deviation of logarithms of dose, with the mean of the logarithm of dose assumed to be zero(that is, the uncertainty in dose be unbiased). All three sources of uncertainty are assumed to be
associated with 100% assignment error.
B88.
The variance of logarithms of the uncertainty variables was considered to be known;
moreover, the analysis was conducted with several combinations of values varied within speculated
ranges. Values for intra-individual variation of true dose, inter-individual variation of true dose, andrandom errors due to differences between prescribed and actual skin exposure were assigned standard
deviations of logarithms of 0.17, 0.49 and 0.15. The analysis was repeated varying the values of thestandard deviation of logarithms to (0.17, 0.25, 0.25) and to (0.5, 0.5, 0.5), respectively.
B89.
In analysing the same Israeli tinea capitis cohort, Lubin et al. [L29] present an alternative
method to account for uncertainties in dose. They base their analysis on an externally-estimated doseprediction equation that used results from studies of anthropomorphic phantoms. As with the paper by
Schafer et al. [S5], Lubin et al. adjusted for uncertainties inherent in the prediction* of true dose basedon studies of phantoms, for random differences in sizes of children of a given age, and for random
movements by children during treatment. Additional accommodation was made for uncertainties
associated with missing data for ages at subsequent exposure for those receiving multiple treatments.
When the prediction equation for individual dose includes uncertainty arising from estimation of theequation parameters, this type of uncertainty also represents a shared error common for all subjects. A
second source of uncertainty results from the random deviation of the (log) dose prediction for eachsubject from the (log) true dose and is called (multiplicative) assignment error [L29].
B90.
As was the case with [S5], the intra-individual variability of true dose was estimated as astandard deviation of logarithms of 0.17, based on 13 degrees of freedom, from the data of Modan et al.
[M17], in which a phantom was repeatedly repositioned and re-irradiated. The inter-individual

168 UNSCEAR 2012 REPORT

variability of true dose was estimated as a standard deviation of logarithms of 0.49. Additional random
uncertainty associated with the difference between actual skin exposure and the amount prescribed by asingle X-ray machine was estimated as the standard deviation of logarithms of 0.25. All remaining
sources of random uncertainty, such as machine power output, the time the machine was on, andtreatment records, were assumed to be minimal. The result was that expected values for true doses werelarger than original mean estimates. For example, person-year weighted means for original doses andexpected true doses were 94 mGy and 108 mGy, respectively, for treated patients; 101 mGy and
116 mGy for thyroid cancer cases; and 102 mGy and 115 mGy for benign tumour cases. Mean expectedtrue doses are higher than the mean original doses for each category of number of treatments. While theassessment includes most major sources of uncertainty, not all sources of uncertainty are accounted for
explicitly. The extent to which the study does not correctly account for random processes generating
missing data, or ignores systematic influences, is unknown; however, the authors conclude that any
residual random or systematic errors are likely small. Furthermore, the extent of classical error
associated with the parameters that define the relationship between added filtration and dose wasdetermined to be small relative to random prediction error from phantom studies.

C. Reconstruction of internal exposure to radon and its
progeny in specific studies
1.

Occupational exposure (miner data)

B91.
Colorado Plateau uranium miners. Review of the literature on occupational exposure to radonand radon decay products reveals few epidemiological studies in which exposure uncertainty has beenaccounted for explicitly. An exception is the paper by Stram et al. [S31], who re-evaluated estimates ofindividual exposure rates for each of the 3,347 uranium miners of the Colorado Plateau cohort who
were exposed for one or more years over the period of 1950 to 1969. Mine–year exposure rateestimation involved averaging measured exposure rates (in working level months, WLM) for eachmine–year for which there were measurements, followed by extrapolating those average measured
exposure rates to years and mines for which there were no measurements. Measured and extrapolatedmine–year estimates were then combined with each miner’s history of employment in the industry to
produce monthly exposure-rate estimates for each member of the cohort. A crucial aspect of thisprocedure is the extrapolation of measured exposure rates to years and mines without measurements,
taking into account proximity in both time and location.
B92.
The authors re-examined the interpolation scheme originally used to create estimates of
exposure histories for each of the miners, and computed revised exposure estimates for the large
majority of miners in the cohort. Their measurement error correction method was based on thecalculation of imputations of mine–year exposure rates for each mine and year of interest. A multi-level
analysis of variance model for true average exposure rate as a function of year, mine, locality, anddistrict, was combined with a multiplicative measurement error model for the errors in the actual
measurements of exposure rate in that mine–year (if any were taken). Imputations for each mine–year
for which at least one cohort member was represented were calculated as the expectation of the trueaverage exposure rate, conditioned on all measurement data specific to a given mine, year, and locality
within a given mine district. In the Colorado Plateau miner cohort, errors in exposure estimates comefrom at least four important sources: (a) from the interpolation process used to estimate dose rates inmines without measurements; (b) from sampling error in the years with measurements owing to the fact

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 169

that the mines were not monitored continuously; (c) from within-mine differences in miners’ true
exposures from the average estimated for that mine–year; and (d) inadequacies in each miner’s work
history data. Of these four sources of uncertainty, differences in each miner’s true exposure from theaverage estimated for that mine–year was ignored, assuming that if the estimated average is unbiased
then all remaining uncertainty is due to assignment error.
B93.
A coefficient of variation (CV) of approximately 50% appears to reasonably characterize thevariability of measurements within a given mine–year. However, uncertainty about an imputed average
exposure to radon (expressed in working level months, WLM) for a given mine–year is a function of
how many measurements were taken in the same mine in other years, and in other mines in the same
locality or district both in the same year and in other years. For example, in 1950, two years prior to any
available measurements, the average imputed value of 74 WLM for exposure rates in a typical mine has
a 95% CI ranging from 0.3 WLM to 541 WLM. By contrast, a single imputation of a typical true dosein a mine–year with measurements available was approximately equal to 8.7 WLM with a 95% CI from
5.5 WLM to 13.1 WLM. For years with a single interpolation based only on early exposure-rate
estimates obtained from the United States Public Health Service, a typical average mine–year of
13 WLM would have a 95% CI extending from 0.7 WLM to 66 WLM. Further information regarding
the calculation of exposure imputations supporting this analysis is available in a supporting technicalreport [S30].
B94.
French miner cohorts. The uranium industry in France developed in the aftermath of theSecond World War. Prospecting for uranium began in 1946. The last uranium mine in France closed in
1999. The French cohort of uranium miners serves as an important source of information about the riskof lung cancer associated with exposure to low levels of radon and its decay products [A6]. It is
recognized that all studies of miner exposure to radon decay products are associated with uncertainty,
the nature of which varies with the measurement method. To address uncertainty in the estimate ofradon exposure (expressed in Working Level Months, WLM), Allodji et al. [A6] (a) reviewed theuranium extraction process, mining conditions and changes in radiation monitoring methods over time,(b) estimated the overall magnitude of uncertainty in exposure estimates, and (c) characterized thestructure of uncertainty in terms of its nature and shape of the uncertainty distribution. This work is apreliminary step towards taking uncertainty into account in the risk models for this cohort and inassessing their impact on the exposure–risk relationship.
B95.
The overall size of the uncertainty in the exposure to radon decay products was evaluatedusing the root sum square (RSS) method. This method is derived by analogy to the statistical
calculation that would be used to estimate the variance of a product of independent random variables.
The size of each individual source of relative uncertainty was estimated, and the size of the combined
relative uncertainty was then calculated as the square root of the sum of the squares of each individual
relative uncertainty. In this work, all uncertainties were determined as Type B (characterizing
uncertainty about unknown fixed values of the quantity of interest using methods other than a statisticalsummary of the variability of direct measurements). All sources of uncertainty were separated into two
categories: random unshared uncertainties and systematic (shared) bias. It is recognized that random
uncertainty can be composed of combinations of assignment errors and classical measurement errors.
Measurements were not available for the years 1946−1955, and exposures were retrospectively
reconstructed by an expert group. However, because of the likelihood of significant correlations among
the sources of uncertainty, it was not possible to determine all of the characteristics of uncertainty for thisearly period. For this reason, the analysis of uncertainty was restricted to the period of 1956−1999 [A6].
B96.
Six primary sources contributed to the overall uncertainty in exposure to radon decay products
in French uranium mines: (a) natural variations of airborne gas concentrations; (b) precision of themeasurement device; (c) approximation of the equilibrium factor to estimate the proportion of radon

170 UNSCEAR 2012 REPORT

decay products to radon gas in air; (d) human error; (e) estimation of working time; and (f) recordkeeping and data transcription. The combined relative uncertainty (expressed as a relative standard
error) ranged from 46.8% during the period of 1956−1974 to 10.1% during the period of 1983−1999.
Uncertainty in the natural variation of radon gas concentrations, precision of the measuring devices, andequilibrium factor dominated the overall uncertainty from 1956 to 1982. For the time period of 1983 to
1999, only the uncertainty in the precision of measuring device dominated the overall uncertainty in theestimate of radon exposure because of an improved system of continuous monitoring of each individual
miner. These results do not address the issue that shared errors can lead to a bias in the central estimatesof exposure. Prior to 1983, the overall annual mean exposures ranged from 21.3 to 1.4 WLM from 1956
to 1982. From 1983 to 1999, the annual mean exposure was 0.4 WLM. From 1956 to 1982, the overall
uncertainty was assumed to be 100% assignment error. From 1983 to 1999, the uncertainty was
assumed to be composed of 100% classical measurement error. The presence of shared sources of
uncertainty, and how this potential source affected possible bias in the estimates of the overall meanannual exposure was not addressed.

2.

Residential exposure to radon

B97.
Residential radon exposure in south-west England. In a 1998 case–control study of lungcancer in south-west England, Darby et al. [D1] used measured radon concentrations at the addresses
where subjects had lived for 30 years, in a period ending five years before the study. For each residence
in which measurements had been taken, an average annual radon concentration in indoor air was
estimated. Each subject’s time-weighted average indoor radon concentration was calculated over the
30-year period of interest, the weights being equal to the number of years living at each address. Whenthe measured radon concentration at a specific address of a subject was available, its value was used.
For estimating missing values of radon concentrations, a method of analysis was developed that
accounted for uncertainty due to measurement error associated with the estimate. The mean timeweighted average radon concentrations, adjusted for uncertainties, are the average values for the
subjects in question. For each subject, this quantity is the expected value of the true time-weighted
average radon concentration given the observed value, conditional on current residence. All remaining
uncertainties are assumed to be due to assignment.
B98.
Residential radon exposure and lung cancer—a collaborative analysis of 13 epidemiologicalstudies in Europe. In a 2006 collaborative analysis by Darby et al. [D3], data from studies of residential
radon exposure from 13 European countries were assembled in a uniform manner in order to investigate
any association between radon exposure and lung cancer. The major source of uncertainty in exposure
originated from variability associated with repeated measurements in the same dwelling. Analyses werefirst carried out using the observed radon concentration without making any adjustment for the effect ofrandom uncertainties in the assessment. The major analyses were then repeated with an approximate
adjustment to take these uncertainties into account. Long-term measurements (of at least two months)of radon gas concentrations in the residences were made, which were expected to be representative ofthe levels experienced by the study subjects during the time in which they lived there. A weighted
average was calculated to give a single representative value for each dwelling. A time-weighted
average (TWA) of the observed radon concentrations was calculated for each subject. In order tocorrect for the biases caused by both assignment and classical error, it was assumed that the “true”
radon concentrations had a log-normal distribution. It was also assumed that, on a log scale, thevariability associated with repeated measurements in the same dwelling was normally distributed about
the true radon concentration for that dwelling. The TWA of the radon concentrations were corrected byassuming that every measured or estimated radon concentration was equal to the expected value of thecorresponding distribution of the true radon concentrations given the observed value, using theANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 171

distribution for the logarithm of the true radon concentration. These corrected values were used toderive the mean corrected radon concentrations for groups of persons. The main analyses were thenrepeated. Using the corrected TWA of the radon concentrations rather than the observed ones in aregression calibration assumes that any remaining error is 100% due to assignment.
B99.
Residential radon exposure in a high-exposure area of Gansu Province, China. In a 2002
case–control study of lung cancer in a predominantly rural area of China with low mobility and highradon levels, Wang et al. [W5] identified three important sources of error in assessing radon exposure:(a) detector measurement error; (b) use of contemporary measurements to estimate radon levels
throughout the house and in prior years; and (c) missing radon values. The authors restricted data to
subjects for whom data were nearly complete in order to reduce the effect of missing radon values, thus
minimizing assignment error. Classical error from the estimation of radon levels was the predominant
form of uncertainty affecting the study. A sub-study, in which six alpha-track detectors were placed for
one year in each room of 55 houses over three consecutive years, was conducted to provide data toadjust for exposure variability. Uncertainties were assumed to have resulted from random variations inradon concentrations within houses and over time, and residential mobility was assumed to be unrelated
to radon level. Use of a component of variance analysis estimated a GSD of about 1.5 for the error
distribution. A Monte Carlo approach was used to evaluate error, in which a randomly-sampled value
was chosen for each subject’s house in order to compute a “true” time-weighted average radon
concentration. Later measurements of Yamada et al. in the same homes in Gansu, with a discriminatoryradon detector measured both radon (222Rn) and thoron (220Rn) [Y1]. Thoron was a significant fractionof the total measurement signal, suggesting additional bias and uncertainties in the exposure estimates.
B100. Adjusting lung cancer risks for temporal and spatial variations in radon concentration in
dwellings in Gansu Province, China. In a 2005 re-analysis of the Wang et al. [W5] study of residential
radon exposure in Gansu Province, China, Lubin et al. [L31] used a three-year sub-study to model the
temporal and spatial variations in radon levels. Their error model specified random variation about atrue mean radon concentration (Bq m−3) for each dwelling type and random variation common to all
homes. Bootstrap sampling accounted for the usual sampling variability of the data, the uncertainty inestimating mean and variance from the control data, and the imputation of gaps in the exposure–timewindow. Regression calibration shrank exposures toward the mean of the true distribution and reduced
the range of exposures. The study’s estimate of uncertainties in adjusted mean radon concentration was
expressed as a GSD of 1.50, corresponding to a CV of 0.43 (95% CI: 0.40, 0.46).
B101. Residential radon exposure assessment in Sweden. In a re-analysis of an epidemiological studyof residential radon exposure and lung cancer in Sweden, Lagarde et al. [L1] attempted to refine thequantification of random error in the exposure assessment. Radon measurements were made in 8,992
dwellings over a period of 3 months during the heating season. In the original study [P2], information
on imprecision in exposure assessment [B3] was used to evaluate possible bias in risk estimates related
to random error in the retrospective assessment of time-weighted average radon concentrations.
Simulated “true” exposures and corresponding “estimated” exposures were modelled, using the squareof the correlation coefficient (R2) between the “true” and “estimated” exposures, to show a measure of
the discrepancy between “true” and “estimated” exposures related to the sources of errors modelled in
the simulations. A coefficient of variation (CV) of 35% was used in the original study to represent the
combined error due to radon measurement and extrapolation to a long-term average concentration, in
accordance with the findings of Bäverstam and Swedjemark [B3]. However, subsequent simulations in
the re-analysis, which reflected more of the error conditions from the original study, showed a CV of
53%. A value for R2 of 0.55 as observed in the simulations involving multiple error components wasthen chosen to reflect the more appropriate size of the CV and used in the re-analysis of the data [L1].
Some underestimation of error is still expected because uncertainties associated with choices forplacement of detectors in rooms and incorrect address information were not taken into account.

172 UNSCEAR 2012 REPORT

Individual “corrected” exposures were based on the use of imputed values of the expectation of the truetime-weighted average exposure as a surrogate for the observed time-weighted average. Once corrected
exposures were obtained, all remaining uncertainty was assumed to be 100% assignment error.

D. Reconstruction of internal exposure from other pathways
in specific studies
1.

HanfordB102. The Hanford Nuclear Site in south-eastern Washington State, United States, was established in1943 to produce plutonium for atomic weapons. From 1944 through 1957, approximately 27 PBq of 131I
were released to the atmosphere [K8]. The potential impact of these releases on children off-site
consuming milk containing 131I was addressed by the Hanford Thyroid Disease Study (HTDS) [D6].
Individual dose estimates were made for 3,191 participants who made up a retrospective cohort study[D6, K8, K9].
B103. Individual doses were calculated for HTDS using the computer program, Calculation ofIndividual Doses from Environmental Radionuclides (CIDER), developed by the Hanford
Environmental Dose Reconstruction Project [F1]. CIDER provided 100 alternative sets of 3,191 dose
realizations, an early version of a two-dimensional Monte Carlo uncertainty propagation. The CIDER
uncertainty analysis addressed both inter-individual variability of possibly true doses and uncertainty inindividual doses.
B104. Point estimates of individual doses, composed of the median of the 100 Monte Carlo dose
realizations for each individual were used for the primary dose–response analysis performed by HTDS.
Individual median doses ranged from 0.0029 mGy to 2,823 mGy. The arithmetic mean of all individual
median dose estimates was 174 mGy, with a standard deviation of 224 mGy. These statistics provide anindication of inter-individual variability of dose. They do not address uncertainty in dose estimation.
B105. The uncertainty of each individual’s dose estimate was characterized as the ratio of theindividual’s upper 95th percentile to the 50th percentile (median) of the 100 alternative dose
realizations produced by CIDER for each person. These uncertainty ratios ranged from 1.8 to 13.7. Of
these individual dose uncertainty ratios, 80% ranged from 2.7 to 5.3. The GSD (exponential of thestandard deviation of log-transformed values) of the uncertainty in the individual dose estimate ranged
from 1.56 to 5.42. A total of 890 participants had dose estimates with uncertainties expressed by GSDsof less than 2.0.
B106. The primary dose–response analysis was based on the individual median dose. All uncertainty
was assumed to be due to stochastic inter-individual variability of true dose. Thus the dose uncertainty
was assumed to be associated with pure assignment error. It was further assumed that there were noimportant systematic sources of bias [D6, H19, K8].
B107. Hoffman et al. [H19] reviewed the dose estimates of HTDS and concluded that the dose
uncertainties were likely larger and more complex than originally estimated and reported. HTDS
individual dose uncertainties were composed of mixtures of shared and unshared assignment errors,classical errors, and uncertain degrees of systematic bias in the estimate of the centre and spread of

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 173

model coefficients used to simulate stochastic inter-individual variability of true dose. For example, thecentral value of the transfer coefficient for 131I in the milk of commercial dairy cows may have been
overestimated by as much as a factor of five, resulting in a systematic bias towards large overestimationof the thyroid dose for individuals consuming dairy milk from commercial sources. Data obtained frompersonal interviews of a subject’s parent or other relative were assumed to be without random orsystematic error, even though information was obtained from memory recall of events that occurred
more than four decades previously. Assumptions about dietary sources, dairy management practices,and participant and residence histories were assumed to be known without error. Concomitant exposure
to significant amounts of 131I from 1950s fallout from the Nevada Test Site was treated as a general
confounding variable, but these additional exposures were not included in estimating individual doses.
Hoffman et al. [H19] concluded that underestimation of the magnitude and complexity of dose
uncertainty affected the overall interpretation of the HTDS findings, namely increasing the magnitudeof uncertainty on risk estimates and decreasing the power of the study to detect a statistically significant
dose response for thyroid cancer and other thyroid neoplasms.

2.

Weapons fallout studies

B108. Exposure to fallout from detonation of nuclear weapons at the Nevada Test Site. Nuclear
weapons were tested above ground at the Nevada Test Site (NTS) from 1951 to 1958. Additional
releases continued on occasion through 1968 as the result of venting from underground tests. In the
1980s, individual thyroid doses and uncertainties were estimated for a retrospective study cohort of
2,473 subjects who were children at the time of exposure [K5, S29]. In a recent effort to restore thedatabases and computer codes used to estimate doses reconstructed in the 1980s, various deficiencies
were found in the estimated doses owing to improperly operating computer codes, corruption of
secondary data files, and lack of quality control procedures [S20]. From 2001 through 2004, thedosimetry system was restored and corrected, and individual doses were recalculated for 2,497 subjects.
Although the arithmetic means of all individual mean dose estimates were not changed significantly,
many individual mean doses were revised by more than an order of magnitude [S20].
B109. As the result of this revised dose reconstruction with improved quality control procedures,individual mean doses varied from 0.0011 mGy to 1,400 mGy. The arithmetic mean of individual meandose estimates was 120 mGy with a standard deviation of 167 mGy, indicating inter-individual
variability of thyroid doses among individuals in the cohort.
B110. Uncertainty in individual doses was represented by the GSD, which ranged from about 1.5 to
8.5, with 90% of the cohort GSDs ranging from about 2.0 to 4.0. Assuming a log-normal distribution ofindividual dose estimates, these GSDs would translate into a ratio between the upper 95th percentile ofindividual dose to the median of individual dose ranging from about 1.9 to 34, with 90% of the cohort
ranging from 3.1 to 9.8. These uncertainties were estimated using algebraic solutions to the propagationof uncertain terms in multiplicative and additive series [S20].
B111. The initial dose–response analysis performed by Lyon et al. [L34] used regression calibrationand point estimates of individual doses based on the individual mean dose, assuming 100% unsharedassignment error. Subsequent analysis by Li et al. [L14] evaluated the uncertainty in dose accounting
for mixtures of shared and unshared assignment errors and classical errors. Individuals were classified
into 40 strata depending on the type of exposure, the location of exposure, and the source of milk
consumed. Ranges of 50% to 70% were set for the shared assignment correlation of Washington county
residents who consumed milk from local commercial sources, 40% to 60% for local backyard sourcesof milk, and roughly 20% to 40% for other sources of exposure. For residents from other Utah counties,174 UNSCEAR 2012 REPORT

lower ranges of shared assignment correlations were specified. It was also estimated that 30% to 50%of the total uncertainty assigned to each individual’s dose was composed of random classicalmeasurement error. Mixtures of assignment and classical uncertainty were accounted for explicitly inthe dose–response analyses performed by Li et al. [L14] (see section III.B of this appendix).

3.

Other environmental exposures

B112. Chernobyl accident cohorts. In a study supporting the Kopecky et al. [K10] case–control
epidemiological study of childhood thyroid cancer in Bryansk oblast after the Chernobyl accident,
Stepanenko et al. [S28] estimated individual thyroid doses for 26 cases and 50 controls, all of whomwere children born before 26 April 1986 and diagnosed with thyroid cancer before October 1997. The
children were all present in one of the most contaminated areas of the oblast on 26 April 1986. In themonths May–June 1986, thousands of measurements were taken of the radiation emitted from the necksof residents of the contaminated areas, in order to estimate the 131I activities in their thyroids. These
direct measurements served as the basis for thyroid dose estimates for samples of the population, butsuch data were not available for all affected individuals. Because the epidemiological study requiredthat thyroid doses should be estimated using the same method for all study subjects, a semi-empiricalmodel was selected that could be applied uniformly to all cases and controls. Using this method,modelled doses for all study subjects were calibrated using direct measurements available for sample
individuals. Uncertainty in individual thyroid doses comes from a variety of sources: the unknown
coefficients of empirical regression models (derived using data from settlements in reference
territories), the isotopic ratios (131I to 137Cs, which ranged from 10 to 45 with an average of 24, and
GSD of approximately 1.4), and the 137Cs deposition densities (measured in nine locations, with
substantial variation among the average doses for the same settlement contamination level). The
uncertainty in individual thyroid doses was estimated using a Monte Carlo calculation procedure, withuncertainty distributions of all of the variables in the thyroid dose calculations sampled repeatedly andused to compute 10,000 estimates of the thyroid dose for each person. The distributions of individual
dose estimates were typically log-normal, and the overall uncertainties were characterized by the GSDsof the log-normal distributions of dose estimates. The GSD representing the uncertainty characteristicof reference individual thyroid dose estimates ranged from 3.0 to 3.9, depending on the type and sourceof milk consumed and the time interval between consumption and cessation of 131I uptake [S25]. The
mean ratio of the thyroid doses between those estimated using the semi-empirical model and thoseestimated using direct thyroid measurements was 1.2 ± 0.99 (sample standard deviation); the geometricmean ratio was 0.77 (GSD = 2.9); the distribution of model-to-measurement ratios was approximately
log-normal. The investigators found no evidence of a systematic bias in the individual dose estimates.
All sources of uncertainty in this study are assumed to be random classical measurement error, although
it is recognized that uncertainties are likely complex, composed of classical and assignment error. To
the extent that uncertainties are shared, systematic uncertainty affecting multiple groups of individuals
simultaneously remains to be investigated.
B113. Supporting an epidemiological study for Astakhova et al. [A14], Gavrilin et al. [G1] conducted
an extensive evaluation of thyroid dose for individuals, considering the contribution of 131I, short-lived
radioiodines (132I, 133I, and 135I) and short-lived radiotelluriums (131mTe and 132Te). The model was
based on three “reliability groups” originally developed by Gavrilin et al. [G2], in which doses were(a) derived from direct measurement of the thyroid gland; (b) derived by affinity (for example, whenmilk consumption accounted for most of the thyroid doses in a village, it was assumed that the 131I
concentrations in milk were relatively uniform throughout the village and therefore that the thyroid
doses for individuals of a given age was a linear function of their milk consumption; for every village
with a sufficient number of residents with measured thyroid doses, individual thyroid-doseANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 175

distributions—“passport doses”—were determined for several age groups and levels of milk
consumption); or (c) empirically derived (“inferred” from measurement of 137Cs deposition). The
overall method selected for individual dose assignment was the “inferred” methodology, as this method
was available for all cases and controls. This “inferred” method was used in estimating doses due to131I, making use of the observed relationships between the 137Cs deposition density and the mean adultthyroid doses derived for the people with direct thyroid measurements in the areas considered.
Although this method provides dose estimates that are more uncertain than other methods, only theplace of residence of the subjects within a few weeks of the accident and the 137Cs deposition density atthose locations were available for all subjects. Overall uncertainties attached to the estimates arecharacterized by GSDs of 2.2 to 2.8 if the milk consumption rate is relatively well known, and 2.5 to
3.1 if the milk consumption rate is unknown. For a number of cases and controls, “measured” and“passport (derived by affinity)” doses could be compared to the “inferred” doses. The results of thiscomparison are illustrated in figure B-II.
B114. In a supporting study for the International Agency for Research on Cancer (IARC) a
population-based case–control study described by Cardis et al. [C2], Drozdovitch et al. [D9]reconstructed thyroid doses for young people aged 0–18 who resided in the areas of Belarus and Russia
that were heavily contaminated after the Chernobyl accident. They estimated doses derived (a) frominternal ingestion of 131I; (b) from the short-lived radioisotopes of iodine, 132I, 133I, and 135I and of
tellurium, 131mTe and 132Te; (c) from internal exposure to long-lived radionuclides such as 134Cs and137
Cs; and (d) from the external irradiation of the thyroid resulting from deposition of radionuclides on
the ground. In general, the fraction of the thyroid dose due to exposure to the short-lived iodine andtellurium isotopes, from external exposure, or from radiocaesium ingestion, was found to be nearly 1%
for each pathway mode. Because a single uniform method for the dose reconstruction was required for
all individuals in the study, Drozdovitch et al. [D9] conducted an inter-comparison evaluation of four
dosimetric models previously developed for use with Chernobyl cohorts who had not had their thyroids
directly measured in order to select the model with which to estimate individual thyroid doses(figure B-III).
B115. An uncertainty analysis was performed on the estimates of thyroid dose due to 131I intake, as
this was the dominant pathway for thyroid exposure for the majority of study subjects [D8]. A Monte
Carlo method was used to obtain the stochastic distribution of individual dose estimates for each study
subject, simulating 1,000 possible dose realizations for each person in each trial, with a probability
density function assigned to each uncertain model parameter. The values of some model parameters
were common to groups of subjects (shared), for which inter-individual correlations were also definedto account for the shared errors. For other uncertain subject-related model parameters, the values wereindependent from subject to subject (unshared), and different levels of uncertainty were associated withthese unshared errors. Characteristics of the distributions were evaluated using a maximal-likelihood
method, and a mean or median of distribution and CV or GSD were used to describe the parameters.
Around 70 parameters were used in the dose reconstruction and considered in the uncertainty analysis.
The GSD of the thyroid doses varies from 1.7 to 3.7 among study subjects with a mean GSD over all
subjects of 2.3 (figure B-IV). The extent to which shared uncertainties are associated with uniqueconditions of systematic error and to which random uncertainties can be separated into classical andassignment errors is a subject that requires further investigation.

176 UNSCEAR 2012 REPORT

Figure B-II. Comparison of the “inferred” thyroid dose estimates and (a) the “measured” thyroid dose
estimates for the 12 cases with direct thyroid measurements, (b) the “passport” thyroid dose estimatesavailable for 51 cases, and (c) the “passport” thyroid dose estimates available for 58 controls
The error bars represent 95% confidence intervals (adapted from [G1])ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 177

Figure B-III. Comparison of estimates of individual thyroid doses due to 131I for 81 study subjects
calculated using the model with doses derived from direct thyroid measurements
The error bars represent 95% confidence intervals (adapted from [D9])Figure B-IV. Distributions of the geometric standard deviation (GSD) of the estimates of individual
thyroid dose due to 131I for the subjects of the case–control study (adapted from [D9])178 UNSCEAR 2012 REPORT

E. Summary
B116. A summary of the uncertainties in the estimation of absorbed dose to organs is given intable B11 for external exposure, table B12 for internal exposure to radon and its progeny, and table B13
for internal exposure to other radionuclides. To enable a comparison of dose uncertainties in tabularform, all reported uncertainties in specific studies (with the exception of table B12) were converted to a
95% uncertainty factor, assuming an underlying log-normal distribution. For example, where
uncertainties are reported as a geometric standard deviation (GSD), the 95% uncertainty factor (UF95) is
calculated as
UF95 = GSD1.96(B.1)

In the case where uncertainties are reported as a coefficient of variation (CV), the 95% uncertainty
factor is calculated as=
UF95 exp 1.96 ln ( 1 + CV 2 ) 



(B.2)

For occupational exposures based on recorded doses, the recorded dose is divided by a bias correction
factor to obtain an estimate of the absorbed dose to a specific organ. The 95% uncertainty factor or thebias correction factor represents systematic uncertainty that is applied to the correction of eachindividual’s recorded dose. Additional uncertainty associated with the inter-individual variability oftrue dose is assumed to be associated with 100% assignment error. The uncertainty associated withinter-individual variability of true dose in occupational exposures is only quantified in the study of
Hanford workers [G7, G8]. Among the studies of external exposure reviewed, only Pierce et al. [P6]make an explicit distinction between the amount of total uncertainty that is composed of assignment
error and the amount of total uncertainty that is classical.
B117. For the studies on internal exposure (table B13), the 95% uncertainty factor refers to theuncertainty associated with dose estimation for specific organs of particular or representative
individuals. The uncertainty factors for estimation of internal exposure (which range from 2.21 to 66.3)
are markedly higher than the uncertainty factors for external exposure given in table B11 (which range
from 1.07 to 2.61). Among the studies on internal exposure, only the study by Li et al. [L14] made an
explicit distinction between the amount of total uncertainty that is shared and unshared assignment error
and the amount that is classical.
B118. For the radon exposure studies summarized in table B12, all studies that address exposure
uncertainties use a form of a regression model to impute an expected value of a true time-weighted
average radon exposure for groups of individuals occupying the same mine or residential dwelling,respectively, conditioned on information obtained from measurements and data about occupation orresidence history of study participants. This imputed expected value of a true time-weighted averageradon exposure is used as a surrogate for observed or measured values of time-weighted averaged
exposure assigned to the individual. All remaining uncertainty is associated with inter-individual
variability of true exposure rates, and thus the remaining uncertainty is assumed to be composed of
assignment error. Uncertainty associated with the imputed true time-weighted average value of radon
exposure varies as a function of the number of measurements and other information available for agiven mine or dwelling, and with the data available about the working or residence history of eachstudy participant.

Table B11. Epidemiological studies of external exposure that discuss uncertainties
Name of study

Size of uncertainty
Bias correction factoraAccounts for

95% uncertainty factorbsystematic error?

assignment error?

classical error?

DS02
Kaul et al. 2005 [K4]

n/a

c, d

Hiroshima 1.6–2.25
Nagasaki 1.71–2.33i

Yes -Total randome -Hiroshima 1.3
Nagasaki 1.28

Hiroshima 1.48–2.17
Nagasaki 1.61–2.26

Preston et al. 2007 [P14] c, f

n/a

1.95

No

Pierce et al. 2008 [P6]

n/a

2.28

No

c, f

No

Yes
95% uncertainty factor
Assignment error: 1.47
Classical error: 2.13

OCCUPATIONAL EXPOSURES

Gilbert 1998 [G8]Yes

Red bone marrow

1.40–1.75

1.3–1.9gLung

1.06–1.33

1.3–1.9

g

j

j

Yes

No

1.4–1.9

1.2–1.6 hh15-country study
Thierry-Chef et al. 2007 [T2]
Red bone marrow

1.19–2.31

1.19–1.72

Lung k

1.00–1.93

1.17–1.41 g

Colon k1.06–2.05

1.07–1.99 g

k

Yes

Yes

No

Yes

Yes

No

g

ORNL workers
1.14–2.05

Stayner et al. 2007 [S25](specific organs not given)j

1.60–2.46 g

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 179

Hanford workers

Size of uncertainty
Bias correction factora

Accounts for

95% uncertainty factorb

systematic error?

assignment error?

classical error?

No

Yes

No

No

Yes

No

MEDICAL COHORTS
Israeli tinea capitis
Schafer et al. 2001 [S5]lWithin-person variation of true dose

n/a

1.40

Between–person variation of true dose

n/a

2.61

Differences between prescribed and actual
skin exposure

n/a

1.34

Lubin et al. 2004 [L29]l
Within-person variation of true dose

n/a

1.40

Between–person variation of true dose

n/a

2.61

Differences between prescribed and actual
skin exposure

n/a

1.63

a

Bias correction factor is divided into recorded dose to estimate absorbed dose to a specific organ.

b

Ratio of 97.5th percentile to the 50th percentile.

c

95% uncertainty factors derived from coefficient of variation (%), assuming a log-normal distribution.

d

Total marrow dose for representative individuals, for both Hiroshima and Nagasaki.

eAssignment vs. classical errors are not specifically identified within the general uncertainty category designated as random uncertainty.

f

Hiroshima and Nagasaki bombing survivors are assigned the same dose uncertainty.

g

Systematic uncertainty about a central estimate (geometric mean) of the bias correction factor.

h95% uncertainty factors that account for random inter-individual variability of true dose.

i

Total systematic and total random uncertainty for a representative individual located at 1,500 m from the hypocentre.

jBias correction factor and its uncertainties are dependent on the time period of exposure.

kBias correction factor and its uncertainties are dependent on the specific facility and the time period of exposure.

lClassical error assumed to be inconsequential.

180 UNSCEAR 2012 REPORTName of study

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 181

Table B12. Epidemiological studies of radon exposures that discuss uncertainties
Name of study

Remarks
MINER COHORTS
Colorado Plateau

Stram et al. 1999 [S31]

Typical variability of measurements (CV = 50%) within a mine-year
Uncertainty about imputed average radon exposure for a given mine-year varies
considerably depending on the number of measurements available in the same andnearby mines for the same and other mine-years
Imputation of monthly average values of radon exposure for each miner assumes all
remaining uncertainty is 100% assignment error

RESIDENTIAL COHORTS
South-west England
Darby et al. 1998 [D1]The mean time-weighted average radon concentrations, adjusted for uncertainties, isused as the expected value of the true time-weighted average radon concentration
given the observed value, conditional on each subject’s residence history. Allremaining uncertainty is assumed to be 100% assignment error

European collaborative study
Darby et al. 2006 [D3]

To correct for biases caused by assignment and classical error, it was assumed that the“true” radon concentrations had a log-normal distribution and that the variability of
repeated measurements was log-normally distributed about the true radon
concentration for each building. Corrected time-weighted average concentrations
were substituted for observed values for each subject, assuming all remaining
uncertainty was 100% assignment error

Gansu Province, China
Wang et al. 2002 [W5]and Lubin et al. 2005
[L31]

The estimate of uncertainties in adjusted mean radon concentration was expressed as
GSD equal to 1.5
All remaining uncertainty assumed to be 100% assignment error once corrected meanradon concentrations were assigned to each subject, conditional on dwelling type,location, and residence history

SwedenLagarde et al. 1997 [L1]

Simulated “true” and corresponding “estimated” exposures were modelled andshowed CV of 53% representing the combined error from radon measurements andextrapolation to a long-term average concentration in homes
Once the adjusted expected value of a time-weighted average exposure is obtainedfor each study participant, all remaining uncertainty is assumed to be 100%
assignment error, although additional sources of uncertainty due to placement ofdetectors and the presence of errors in addresses were not addressedName of study

Size of uncertainty
Bias correction factor a

Accounts for

95% uncertainty factor b

systematic error?

assignment error?

classical error?

HANFORD
Davis et al. 2004 [D6] and Kopecky et al. 2004 [K8]n/a2.39–24.5c

NoAll uncertainty assumed to be 100% assignment

WEAPONS FALLOUT STUDIES
Nevada Test Site
Simon et al. 2006 [S20] and Lyon et al. 2006 [L34]n/a2.21–66.3d

No

All uncertainty in [L34] assumed to be 100% assignment

Li et al. 2007 [L14]n/aTotal individual dose
uncertainty same as in
[S20]

No

Assumed 20–70% of total
uncertainty was sharedassignment errore

Assumed 30–50% of total
uncertainty was classicale

CHERNOBYL ACCIDENT
Kopecky et al. 2006 [K10] andStepanenko et al. 2004 [S28]n/a8.6–14.4f

No

Milk consumption rate relatively well known

n/a

4.69–7.52

Milk consumption unknown

n/a

6.03–9.18h

n/a

2.83–13.0i

Gavrilin et al. 2004 [G1]Drozdovitch et al. 2010 [D9]aBias correction factor is divided into recorded dose to estimate absorbed dose to a specific organ.

b

Ratio of 97.5th percentile to the 50th percentile.

c

Obtained from individual dose GSDs ranging from 1.56–5.42.
Obtained from individual dose GSDs ranging from 1.5–8.5.

e

The degree of shared assignment versus classical measurement error depends on location and individual diet.

fUncertainties characteristic of reference individuals, depending on diet, milk source, and duration of 131I uptake.

g

Obtained from individual dose GSDs ranging from 2.2–2.8.
Obtained from individual dose GSDs ranging from 2.5–3.1.

i

Obtained from individual dose GSDs ranging from 1.7–3.7.

No

No

No

No

No

No

g

d

h

All uncertainty in [K10] assumed to be 100% classical182 UNSCEAR 2012 REPORT

Table B13. Epidemiological studies of internal exposure that discuss uncertainties

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 183

III. UNCERTAINTIES IN RISK ASSESSMENT

A. Impact of uncertainty in health effect information on risk
estimates and statistical power of epidemiological studies
1.

Impact of uncertainty in health effect information on risk estimates

B119. Section I summarizes four types of uncertainty in health effect information, namely, selection
bias, information bias, confounding and changes in information over time. These uncertainties may leadto systematic errors in the estimates of risks from radiation exposure and/or affect the precision of theserisk estimates. Section I provides examples of how each of these types of uncertainty may affect therisk estimates.
B120. As mentioned in annex A (section I.D) of the UNSCEAR 2006 Report [U12], statisticalmethods have been developed to deal with multiple sources of bias, such as those listed above (forexample, [G16]). However, concerns have been raised about the methodological basis for suchapproaches (see discussion in [G16]). To date, these methods have been used infrequently inepidemiological analyses.

2.

Statistical power and aggregation of epidemiological studies

B121. Low statistical power, associated with studies of small sample size and/or low radiation doses,
typically will result in non-significant results whether or not there is a true underlying association
between radiation dose and the disease of interest. Such a finding, in isolation, has very little
informational value, since the same result is to be expected under the null hypothesis of no associationor the alternative hypothesis of a positive association. However, the statistical inference process, inorder to allow for the possibility of a statistically significant finding under the alternative hypothesis,
requires the possibility of an occasional statistically significant finding when there is no association
between exposure and disease occurrence as the price of being able to detect a true association. At the
5% significance level, for example, over the long term it can be expected that one in twenty wellconducted studies will reject the null hypothesis, regardless of whether or not there is a true underlying
association. Moreover, if a study of low statistical power results in a significant finding, then bydefinition the point estimate of risk likely will be exaggerated [L3]. In such cases the confidence
intervals on the risk estimate are likely to be very wide (although by definition the limits will notinclude zero). Thus, the body of evidence regarding radiation-related risk relies heavily on a
combination of studies of high statistical power and replications of study findings in different exposed
populations.
B122. Aggregating findings from different studies that address the same topic increase the statisticalpower and ought to give more precise estimates of risk. Furthermore, as described below, this approach

184 UNSCEAR 2012 REPORT

may provide insights into how the risks of radiation exposure vary according to possible modifying
factors such as age, time and smoking status. However, care is required to ensure that the process ofdata aggregation does not lead to invalid findings.
B123. Meta-analyses of published findings. An approach that is sometimes adopted involves
combining published findings from several studies. For example, estimates of relative risks or absolute
rates for specific exposure categories or estimated linear or log-linear trends in relative risks or absolute
rates with some measure of radiation exposure—together with the corresponding confidence
intervals—may have been cited in the publications giving the results from these studies. It may then be
possible for each exposure category to calculate average values of the risks, weighted according to thereciprocals of the corresponding variances. Alternatively, an overall estimate of the trend in risk could
be calculated, either as a weighted average of the estimated trends from each study or via weighted
regression of the average risks for each exposure category. For example, in examining the risk of lungcancer following exposure to radon in homes, Lubin and Boice [L27] fitted—for each of eightstudies—a weighted linear regression model to the published estimates of the logarithm of the relativerisk for each exposure category. A weighted average of the estimated trends from each study was thencalculated.
B124. In principle, conducting a meta-analysis is fairly straightforward, provided that the necessary
information has been published. However, this condition is not always met, because, for example,
different exposure categories might be used in different studies, the measures of risk used might vary or
the confidence intervals or standard errors might not be given for all of the relevant quantities. A further
concern is whether the variations between studies, either in the control for confounding or in modifying
factors that influence the risks from radiation exposure, could lead to incompatibility in the results
across the studies. A statistical approach that is often used in meta-analyses is a “random-effects”
model. Unlike a “fixed-effects” model, where the underlying risk is assumed to be constant acrossstudies, the random-effects model assumes that the underlying study-specific risks vary between studies
according to, say, a normal or a log-normal distribution. In this instance, it is possible to calculate an
overall risk estimate and confidence interval using an approach that takes account not only of
uncertainties within the studies, but also between the studies. Lubin and Boice [L27] describe theapplication of this technique to the aforementioned analysis of radon exposure and lung cancer.
Typically, the confidence interval for the overall risk estimate is wider under a random-effects model
than under a fixed-effects model, particularly if there is strong evidence of heterogeneity in the findings
between the studies.
B125. While the random-effects model provides a statistical means of allowing for differences
between studies, care is required in its use. Without a clear understanding as to why risk estimatesmight vary between studies, the computation of an overall estimate may have little meaning.
Furthermore, if it is clear from the description of the individual studies that some studies were muchbetter conducted and/or made better allowance for confounding than other studies, then it isquestionable as to whether the findings from all of these studies should be combined. Rather, there
would be a case for combining those studies that are judged—based on criteria defined a priori—to bemethodologically superior.
B126. If the impact of modifying factors could differ between studies, then it would be better tocombine studies with similar values for these factors, rather than to combine all studies. For example, itwould be more sensible—at least in the first instance—to look at studies of childhood exposure
separately from those of exposure in adulthood. A more sophisticated approach is taking into accountdifferences in modifying factors by scaling the results to a comparable quantity before combining themin a meta-analysis (see, e.g. [J5]).

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 185

B127. Combined analyses using original data. On occasion, investigators who have been studying
the same topic in, say, different countries or regions may collaborate in a combined analysis of theirindividual-level data. For example, combined analyses of radon exposure in homes and lung cancer
have been conducted in Europe [D2, D3], North America [K14, K15] and China [L30]; these analyses
are discussed further in appendix D. This approach has several advantages over meta-analyses ofpublished findings:(a) By bringing together their data, the investigators ought to be able to recognize any differencesin the way in which the data had been collected or in which exposures had been assessed. Thisought to inform decisions about how the data might be combined. For example, data from cohort
studies and those from case–control studies might be pooled separately in the first instance,
because of the differing potential for bias between study designs. Alternatively, analyses may be
restricted to persons with a specific form of radiation exposure (for example, by excluding persons
with high-LET irradiation in an analysis of low-LET irradiation). More generally, since a
combined analysis is easier to perform if the individual studies are of a similar design, aprospective approach whereby studies are constructed around a common protocol may be moreadvantageous than a retrospective pooling exercise. This approach was advocated for aninternational study of cohorts of occupationally-exposed workers in the nuclear industry [C1] andfor case–control studies of lung cancer and residential radon exposure [S2];(b) In contrast to meta-analyses, it is possible in a combined analysis of original data to use thesame approach to analyse all of the data; for example, in using common exposure categories and inapplying the same form of adjustment for confounding factors. This should enhance thecompatibility of the findings across studies. In the case of radon exposure in homes and lungcancer, a key advantage of the combined analyses was the ability to adjust for smoking (the leading
cause of lung cancer) in a uniform way across studies, whereas the published findings fromindividual studies had used differing adjustments. It is notable that whereas the earlier metaanalysis of Lubin and Boice [L27] found statistically significant heterogeneity between studies in
the radon-related lung cancer risk, this was not the case for the combined analyses in Europe [D2,
D3], North America [K14, K15] and China [L30] which used individual-level data;(c) In general, the published findings are not sufficiently detailed to allow for a full examination
in a meta-analysis of how risks might be modified by factors such as age, time and smoking. In
contrast, this topic can be addressed using the original data from the studies. For example, Darby etal. [D2, D3] were able to look at how radon-related risks varied between continuing smokers, exsmokers and never-smokers. Furthermore, the sensitivity of the findings, for example, to the formof adjustment made for confounding or the exposure metric used, may be addressed using theoriginal data but not through the published findings.
B128. Thus, in addition to increasing statistical precision, combined analyses may be able to resolve
apparently conflicting results from different studies. By aligning the studies in a parallel fashion andanalysing them using a common approach, it may be possible to explain such differences on the basisof, for example, different categorizations of the exposure data. Although there is a greater opportunity
to address this topic in combined analyses of original data than in meta-analyses, it is important in bothtypes of analysis to consider the compatibility of data from different studies before combining findings
across studies. If there is statistically significant heterogeneity in estimates of risk between studies, thenit is not sufficient simply to report findings based on a random-effects model; rather, careful
examination is required of the possible reasons for this heterogeneity and, based on this, then to decide
whether it is sensible to pool all or even part of the data.

186 UNSCEAR 2012 REPORT

B129. Another difficulty that may affect attempts to pool findings across studies is publication bias,that is, the selective reporting of results depending on whether the outcome was judged to be positive or
negative. However, this tends to arise for small or ad hoc studies, which would carry less weight in apooled analysis if a number of large studies with clear, predefined objectives were included.
Furthermore, in contrast to meta-analyses, it is possible in combined analyses to address a wider rangeof questions than were addressed in the original publications, thereby reducing the impact of any
selective reporting within studies.

B. Impact of exposure uncertainty on risk estimates
B130. The impact of exposure uncertainty on risk estimates was considered briefly in the UNSCEAR
2006 Report (annex A, section I.D) [U12]. Key distinctions were made between the effect of random
errors and systematic errors, and whether or not these errors were differential, that is, related to thedisease outcome.
B131. Systematic errors in exposure assessment could arise, for example, from incorrect calibrationof a dosimetry badge reader or from incorrect assumptions or coefficients in an algorithm to reconstructdoses [U12]. The impact of systematic errors depends on the particular context and it is not possible to
make a general statement on how such errors would bias dose–response relationships. There are some
exceptions to this. For example, if all doses had been underestimated by a given fixed factor and alinear dose response had been used to model the relationship between disease risk and dose, then theeffect of these systematic dose errors would be to overestimate the slope of the dose response by thesame factor.
B132. In practice, the magnitude of systematic errors—expressed either as a proportion or an
absolute value—may vary according to the level of dose, possibly in a complex fashion. Consequently,
the impact of these errors would need to be evaluated on a case-by-case basis. Generally this involves
sensitivity analyses, in which different assumptions are made about the form and magnitude of thesystematic errors. For example, in analysing the United Kingdom National Registry for Radiation
Workers, Muirhead et al. [M21, M22] explored the impact of dose recording practices by conducting
sensitivity analyses that excluded some or all of the correction factors applied to recorded doses.
Here—and in many other examples where investigations of systematic errors indicated little impact on
the dose–response analyses—no adjustments were made to estimates of risks from radiation exposureor their confidence intervals to reflect the possible impact of systematic errors. This contrasts with thesituation regarding random errors where—as will be described below—more sophisticated approaches
have been used to quantify the impact of these errors on dose–response analyses. However, in someanalyses of nuclear industry workers, including of workers at Oak Ridge National Laboratory [S25] andat Hanford [G8] in the United States, account was taken not only of correction factors to allow fordifferences between recorded doses and organ doses, but also for the uncertainty in these correction
factors [T2]. In essence, these analyses took account of shared errors that arose from applying the same
correction factors to doses for groups of people.
B133. Differential measurement errors, such as when greater efforts are made to determine the dosefor persons with the disease of interest than for persons without it, can introduce serious andunpredictable bias. Whilst it may be possible to assess whether risk estimates have been
underestimated—or overestimated—as a consequence of differential errors, quantifying the impact on
dose–response analyses is almost impossible without a detailed understanding of the structure andmagnitude of these errors. Avoiding such errors is a major concern in study design.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 187

B134. Non-differential random measurement errors, which are not influenced by disease status, affectvirtually all quantitative epidemiological studies to some degree and can introduce bias. However, suchbias can often be addressed and corrected in the analysis, based on information about the statisticalstructure of the errors. These errors form the focus of much of the research undertaken into the impact
of exposure uncertainty on risk estimates, as described below.
B135. In epidemiology, measurement errors of true exposure will generally result in a bias of a dose–
response function towards the null [C7, H18, S6, U12]. Thus, what appears to be a source of randommeasurement error will actually lead to a systematic bias towards overestimation of the statistical powerof an epidemiological study and an underestimation of risk [C7, H16, H17, H18, S6]. An example ofmeasurement error occurs when individual dosimeter readings are used to estimate individual doses to
occupationally-exposed workers over a certain period; the error reflects a (random) lack of precision ineach of the individual measuring devices. Here, assuming a multiplicative error model for dose and alinear dose–response model, the effect of error in the estimated dose is to flatten the fitted dose
response gradually with increasing dose, creating an apparent negative curvature and a bias toward
reduced slope [C7]. Similarly, if the true dose–response relationship were linear–quadratic with positive
curvature, the fitted curve might show a reduced, zero, or even negative curvature. Another example iswith the reconstructed gamma-ray doses from the atomic bombings of Hiroshima and Nagasaki, whichwere affected by uncertainties about the locations of individual survivors and the shielding provided tothem by buildings and other structures. In addition to inducing bias, classical error reduces statisticalpower, but bias correction typically does not involve a further decrease in statistical power [S6].
B136. Virtually all epidemiological studies of the radiation dose response for cancer or other disease
outcomes rely on individual dose estimates derived largely from idealized dosimetry systems that werebased on few, if any, direct measurements of the relevant doses. Even in nuclear worker studies forwhich there might be individual film badge readings, numerous models and assumptions must be madeto develop the (organ) dose estimates needed for risk assessment. In studies of environmental exposures(including, for example, survivors of the atomic bombings or populations exposed as a result ofaccidental releases of radioactive material) there are often few, and in many cases no, measurements ofindividual dose.
B137. Traditionally dosimetry systems have provided point estimates of the dose for individual (orrepresentative individual) members of the population of interest. However, as awareness of thepotential effects of uncertainty in individual doses (including biased risk estimates and underestimationof the uncertainty in these estimates) has increased, efforts are being made to provide more informationon the magnitude and nature of the uncertainty in individual dose estimates. When information about
the uncertainty of individual dose (component) estimates is available, it comes in many forms. Some
examples are:(a) A statement that estimated doses have an uncertainty of x %;(b) An uncertainty associated with each individual dose (component);(c) A set of realizations of dose (component) estimates for each person based on a complex
dosimetry system; uncertainties associated with measurements, model parameters, individual
characteristics (such as age or residence location) and other factors affecting dose are described interms of (generally subjective) distributions; and dose realizations are determined using a Monte
Carlo-based system to determine specific values for the parameters associated with an individual
dose (component).

188 UNSCEAR 2012 REPORT

B138. Methods for quantifying the impact on risk estimates of exposure uncertainties will now be
described in more detail, together with summaries of radiation epidemiology studies in which thesemethods have been applied.

1.

Regression calibration

B139. The basic idea of regression calibration is as follows. If the true values of an explanatory
variable (referred to here as “dose”) are unknown, then these values are replaced in a regression
analysis by the expected values of dose given the observed values [C7]. In other words, “observeddose” is replaced in the regression analysis by “E(true dose|observed dose)”. If the expected value ofthe dependent variable in the regression analysis (in this context, a disease rate or an indicator ofwhether or not an individual has the disease under investigation) were to vary as a linear function of“true dose”, then this linear relationship would be preserved—with the same slope—if E(truedose|observed dose) were used instead. In contrast, if the relationship based on “true dose” were nonlinear, then this relationship would not be preserved if E(true dose|observed dose) were substituted into
the regression analysis. However, in practice this approach appears to work well in a range of nonlinear regression models [C7].
B140. A complication is that E(true dose|observed dose) may not be known exactly. For additive
assignment errors as defined in appendix A, the situation is simple, because in this situation E(truedose|assigned dose) is equal to the “assigned dose”. Thus, the regression analysis would proceed basedon the observed doses. However, for measurement errors, the calculation of E(true dose|measured dose)would require knowledge of the distributions of the measurement error and of true dose. If, forexample, these latter two variables are distributed independently as normal, with variances σC2 and σ2
respectively, and if the measurement errors were unshared, then:E(true dose|measured dose) = [σ2 × measured dose + σC2 × E(true dose)] / (σC2 + σ2)(B.3)

which is a weighted average of the measured dose and the expected true dose. Thus, in this situation,measured dose is replaced by a value that is closer to the expected value for true dose. The spread in thevalues of E(true dose|measured dose) is narrower than that in measured dose, by an amount that
depends on the ratio of the variance of the measurement errors to the variance of the true doses. If thisratio were much smaller than 1, then the values used in the regression analysis would be similar to themeasured doses. Conversely, if this ratio were larger than 1, indicating that much of the variation in themeasured doses is due to classical measurement errors, then the values used in the regression analysis
would be “shrunk” towards E(true dose). For linear regression under the assumptions outlined above,
correction for unshared non-differential classical measurement errors would increase the slope of thedose–response curve by a factor of 1+ σC2 /σ2, which corresponds to the ratio of the variance ofmeasured dose to that of true dose. In order to implement this approach, estimates of these twovariances are required.
B141. In practice, the situation may be more complicated. First, if there were assignment errors, butthey were multiplicative rather than additive, that is if
log (true dose) = log (assigned dose) + individual peculiarity,(B.4)

then E(true dose|assigned dose) would not be equal to “assigned dose”. As shown by Schafer and
Gilbert [S6], multiplicative assignment errors would lead to an overestimation of the slope of a linear
dose–response model and would overstate the degree of curvature in a linear–quadratic dose–responseANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 189

model, unless account were taken of these errors. Secondly, if there were multiplicative rather thanadditive classical measurement errors, that is if
log (measured dose) = log (true dose) + measurement error,(B.5)

then E(true dose|measured dose) could not be calculated using the simple expression given in thepreceding paragraph. Unless these errors are taken into account, they may induce downward curvaturein the observed dose–response relationship and understate the evidence for any upward curvature [S6].
Thirdly, if the errors were of a more complex form—for example, containing a mixture of assignmentand classical measurement errors, either or both of which may be multiplicative, and possibly including
shared errors—then it would not be possible to make general statements about the impact of theseerrors and the calculation of E(true dose|observed dose) might be more difficult than in the preceding
situations.
B142. In situations where E(true dose|observed dose) cannot be calculated analytically, an alternative
is to use simulation. This has the advantage that shared errors can be handled automatically as part ofthe simulation process. However, it is important to be aware of the importance of specifying therelevant probability density functions correctly. In particular, Schafer and Gilbert [S6] highlighted thepotential for confusion between the population distribution of “true dose given observed dose” and the
hypothetical distribution of “true dose given observed dose” for a particular individual. Otherwise,
shared errors might not be handled correctly, for example. Furthermore, the parameters used to specify
these distributions are themselves unknown and the use of estimates rather than the true values of theseparameters may have some impact on the effectiveness of regression calibration [S6], although themagnitude of this impact would vary according to the situation under study.
B143. In some instances, regression calibration implies the same—not only in terms of best estimatesof the risks from radiation exposure, but also in terms of measures of uncertainty such as confidence
intervals—as an approach based on the probability density function for the disease outcomesconditional on the observed doses. For example, through the use of maximum likelihood under afrequentist approach or combining the likelihood function with a prior distribution under a Bayesian
approach. This equality will hold if the expected value of the dependent variable (that is, a disease rateor an indicator of whether or not an individual has the disease under investigation) varies as a linear
function of “true dose”. However, if this relationship is non-linear, then regression calibration andmethods based on the likelihood function may give different answers. Consequently, other statisticalmethods have been developed to deal with such situations. These methods and their application inradiation epidemiology are described in subsection 2 below.
B144. The principal applications of regression calibration in radiation epidemiology will now be
described.
B145. Life Span Study. Recent analyses of the Life Span Study (LSS) of Japanese atomic bombing
survivors (e.g. [P14]) have routinely incorporated corrections for additive measurement errors using
regression calibration. The foundation for these corrections was an analysis by Jablon [J1], in which heconcluded that the errors in the dosimetry were most likely to be distributed log-normally, with acoefficient of variation of about 30%. Pierce et al. [P4] examined the impact of such errors on analysesof cancer in the LSS, based on linear dose–response models. Using regression calibration, Pierce et al.
[P4] concluded that risk estimates would be increased by 6% to 17%, once adjustment was made formeasurement errors with a coefficient of variation in the range 30% to 40%. However, the increase wasonly 4% to 11% if, as in some analyses of LSS, survivors with dose estimates above 4 Gy were
excluded from the analysis. Pierce et al. [P4] did not quantify the impact of these errors on the width of
confidence intervals. A later analysis by Pierce et al. [P6] considered both classical and assignment

190 UNSCEAR 2012 REPORT

error models. They presented formulae for E(true dose|observed dose), based on log-normally
distributed classical and assignment errors and applied this approach to data on solid cancer mortality inthe LSS. Having excluded survivors with dose estimates above 4 Gy, allowing for measurement errors
with GSDs in the range 35% to 40% increased estimates of the risk per unit dose by 12% to 14%.
Additional adjustment for assignment errors had little impact on the risk estimate. Pierce et al. [P6] also
found that adjustment for classical errors increased the evidence for curvature in the solid cancer dose–
response, such that the risk per unit dose increased with increasing dose. Again the impact of theseadjustments on the precision of risk estimates was not quantified.
B146. Medical exposures. Lubin et al. [L29] analysed data on thyroid neoplasms in a cohort of
10,834 Israeli patients who were treated with X-rays for tinea capitis, together with unexposedcomparison groups. In so doing, they took account of uncertainties in dose estimates that arose from:(a) modelling of phantom data and extrapolating this to all ages of exposure; (b) applying the prediction
model for a given age, filtration and beam exposure; and (c) adjusting for missing patient information.
First, the relationship between dose to the thyroid and various predictor variables was modelled.
Secondly, because the patient data were complete, missing values of the predictor variables were
imputed based on the data that were available. Having estimated the expected values for true individual
dose given the predictor variables, these expected values were then inserted into the regression model
linking radiation dose to the risk of thyroid neoplasms. The expected true doses were generally larger
than the original doses, particularly for those persons who received only one treatment. In contrast, forpersons with two or more treatments, the ratio of original dose to expected true dose was generally lessthan one, because of the adjustments made for age of exposure and the failure of the original doses toaccount for ages at second or later treatments. The estimated excess relative risk (ERR) of thyroid
cancer per unit absorbed dose, based on a linear dose–response model, was slightly smaller (by 12%)
based on the expected true doses, compared with the original doses, reflecting the tendency for theformer doses to be greater than the latter doses. The impact of using expected true doses on themodifying effects on the ERR per unit dose of factors such as age at exposure and time since exposure
was minimal.
B147. In this study, there were both shared classical measurement errors, associated with theestimation of parameters in the prediction equation, and assignment errors, resulting from random
deviations between the predicted and true doses. Although the confidence intervals for the ERR per unit
dose calculated by Lubin et al. [L29] based on the expected true doses were similar to those based on
the true doses, they cautioned that regression calibration would not have accounted for the variability
arising from measurement errors. However, an earlier analysis of these data using a likelihood-based
approach that took account of measurement errors [S5] suggested that the upper and lower confidence
limits for the ERR per unit dose should be multiplied and divided by a factor of about 1.06,
respectively; this means that the impact on the confidence interval should be small.
B148. Residential radon exposure and lung cancer. In a combined analysis of case–control data from
European studies of radon exposure in homes and lung cancer, Darby et al. [D2, D3] calculated risk
estimates and associated confidence intervals that were adjusted for classical and assignment errors.
Classical errors are particularly important in studies of this topic, because measurements made in thesame dwelling in different years show considerable variability, with a coefficient of variation that may
be of the order of 40% [D2]. Thus, representing the long-term average radon concentration in adwelling by a measurement made in a single year is a major source of uncertainty. This uncertainty islikely to be due not only to the measurement process, but also reflects variation in the true radon
concentration arising from year-on-year changes in weather, changes in the habits of the occupants ofthe dwelling and structural changes to the dwelling. In addition to classical errors, assignment errors
arose through the need to input values for dwellings where no measurement of radon levels could be
made. In these situations, the arithmetic mean of the concentrations measured for controls was used,ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 191

either for all of the controls in the study in question or—for those studies where the mean square errorof prediction was improved by more than 10%—by using solely data for those controls within the same
area [D2].
B149. In order to allow for classical measurement errors, Darby et al. [D2, D3] assumed that withineach geographical district, the “true” (i.e. long-term average) radon concentration followed a lognormal distribution. It was also assumed that the variability associated with repeated measurements ofradon concentrations in the same dwelling followed a log-normal distribution about the true
concentration for that dwelling. For those countries where repeated radon measurements had been
made, these data were used to estimate a country-specific coefficient of variation for the classicalmeasurement errors. For the remaining countries, a coefficient of 40% was assumed, based on the
median of the variances for the logarithm of measured concentrations for those countries where data
were available. Having used regression calibration to replace the measured radon concentrations by
their expected values, the mean radon concentration for the lung cancer cases fell from 104 Bq m−3 to90 Bq m−3, whilst the corresponding values for the controls were 97 Bq m−3 and 86 Bq m−3,
respectively. As expected, regression calibration “shrank” the range of concentrations: for those persons(cases and controls combined) associated a measured concentration of more than 800 Bq m−3, the mean
measured value was 1,204 Bq m−3, whereas the mean corrected value was 678 Bq m−3. Similarly, forthose persons (cases and controls combined) associated with a measured concentration of less than
25 Bq m−3, the mean measured value was 17 Bq m−3, whereas the mean corrected value was 21 Bq m−3.
B150. Based on a linear model, the excess relative risk was estimated to be 0.084 (95% CI: 0.03,
0.16) for 100 Bq m−3 without adjustment for classical measurement errors and 0.16 (95% CI: 0.05,0.30) when adjustment was made for these errors using regression calibration [D2]. Adjustment forthese errors using a more sophisticated approach, namely Monte Carlo integration of the likelihood
gave a very similar result to that from regression calibration, specifically an ERR of 0.16 (95% CI:
0.05, 0.31) for 100 Bq m−3. Analyses of effect modification by sex, age, smoking status and histologicaltype of lung cancer gave similar results with and without correction for classical measurement errors,
although the correction had a proportionately greater impact on the ERR estimate for ex-smokers andlifelong non-smokers than on the corresponding estimate for current smokers. Nevertheless, there wasno statistically significant heterogeneity in the ERR between smoking categories, either with or without
adjustment for measurement errors. Furthermore, the ERR estimates and confidence intervals from theanalyses of effect modification were similar using the regression calibration and integrated likelihood
approaches. In a related methodological paper, Fearn et al. [F2] suggested that regression calibration
ought to perform very well in adjusting for measurement errors in studies of residential radon exposureand lung cancer and that more sophisticated approaches are not required.
B151. Uranium miners. Stram et al. [S31] analysed data on lung cancer among the United States
Colorado Plateau uranium miners, with corrections for errors in the measurement of radon exposures.
This involved the development of a multi-level model for the “true” average exposure rate (expressedin Working Levels, WL, of radon progeny) in a given year, mine, locality and district, combined with amultiplicative measurement error model that described the variability in measurements that were madeof exposure rates, classified by year and mine. According to the fit of the multi-level model to the
exposure rate measurements, the “true” average exposure rate decreased by about 11% per year overthe period 1950–1969, which is of particular relevance to the miners in the study. For each mine andyear in which at least one cohort member was exposed, the measured exposure rate was replaced in theepidemiological analysis by the expected value of this exposure rate, given all of the measurements
made in that district.
B152. Adjustment for measurement errors provided a statistically significant improvement in the fitof models to these data. The estimated slope of a linear exposure–response model increased by about

192 UNSCEAR 2012 REPORT

60% and the standard error of the estimated slope was nearly doubled as a consequence of thisadjustment. Both with and without adjustment of measurement errors, the data indicated a submultiplicative relationship for the joint effect of radon and smoking on the risk of lung cancer. Similar
patterns in the modifying effects of time since exposure and age at exposure were seen with andwithout adjustment for measurement errors, although again the estimates and their standard errors werelarger when this adjustment was made. There was less evidence for an inverse exposure rate (i.e. ahigher risk per unit exposure at lower rather than higher exposure rates) with adjustment formeasurement errors. This adjustment had little impact on the estimated risk per unit exposure at
relatively low exposure rates (below 15 WL) but increased the corresponding estimate at higher
exposure rates, to bring it closer to the value for lower exposure rates. This change was particularly
pronounced when miners who started work prior to 1952—and whose early exposures are highly
uncertain—were excluded from the analysis. However, it is unclear whether the lack of evidence for an
exposure–rate effect in the restricted cohort is a reflection of low statistical power rather than of errors
in the assessment of exposures before 1952.
B153. Fallout from nuclear weapons testing. Lyon et al. [L34] conducted a re-analysis of thyroid
disease in a cohort of persons exposed to radioactive iodine in childhood as a consequence of nuclear
weapons testing at the Nevada Test Site in the United States. This analysis included corrections to dose
estimates and to information on disease classification. When fitting dose–response models, the authors
used the arithmetic mean of the dose for each person, assuming a log-normal distribution for alternative
realizations of that person's dose. Because a multiplicative rather than an additive error model was used,
the arithmetic mean of the dose realizations was not equal to the output from the dosimetry model.
Whilst the focus of this analysis was not on the use of regression calibration to allow for dose
uncertainties, Lyon et al. commented on the impact of assuming, as here, that these uncertainties are
purely due to assignment. They referred to an earlier methodological paper by Mallick et al. [M6] thatanalysed earlier data from this study accounting for a mixture of assignment and classical measurement
errors. Mallick et al. showed that as the ratio of classical to assignment errors increases, the estimated
ERR per unit dose increases, as do the length and upper end of the corresponding 95% confidence
interval. For example, if 50% of the measurement errors are assumed to be classical and the remainder
to be due to assignment, rather than all of the errors being due to assignment, the estimated ERR per
unit dose for thyroiditis increases from 4.2 (95% CI: 1.4, 9.6) mGy−1 to 7.2 (95% CI: 2.9, 14.9) mGy−1.

2.

Other methods

B154. Generalization of regression calibration. Reeves et al. [R1] develop a simple error model,
originally suggested in [T6], that includes classical measurement error and assignment errors. The
additive version of the model describes the true (Xt) and observed/surrogate (Xs) value as functions ofan unobservable latent variable ( X ) with X= X + e and X= X + e , where X , e and e are
t

t

s

s

t

s

independent random variables with means µ, 0 and 0, and variances s 2 , s t2 and s s2 , respectively. If, as
is often the case for radiation doses, the measurement uncertainty is assumed to be proportional to themagnitude of the true dose, then the error model can be written in terms of the logarithms of the latent==X ), Z log( X=), and Z log( X ) ). This model canvariable and the true and surrogate doses:( Z log(
t

t

s

s

be used to develop the likelihood for a linear regression model ( Y= α t +β t X t ) and, an approximate

Pr(Y 1|=
X t ) eα t + β t X t (1 + eα t + β t X t ) ) regression model that depends
likelihood for the standard logistic ( =on true dose–response parameters ( α t and β t ) and four parameters (which are referred to here as“nuisance parameters”) not directly related to the dose response ( µ , s 2 , s s2 , s t2 ). The authors showthat it is possible to obtain good estimates of the dose–response parameters and their uncertainties usingANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 193

relatively simple methods that do not require difficult computations based on the full likelihood of all of
the parameters.
B155. Fearn et al. [F2] extend the method developed by Reeves et al. [R1] for use with a linear odds
model α (1 + β x) / (1 + α (1 + β x)) . They compare the results of this generalized regression calibration
approach to a more precise but computationally more demanding method involving Monte Carlointegration of the full likelihood (discussed below) in a pooled analysis of 13 European studies of theeffects of residential radon exposures on lung cancer risks [D2, D3]. It was found that not only did thesimpler regression calibration approach give virtually the same point estimates as the integrated likelihood
method, but that the adjusted confidence intervals were also virtually identical for the two methods.
B156. Regression calibration as described in this document requires computation of the expectedvalue of the true dose (Xt) conditional on the observed dose (Xs) and, possibly, other relevant
information. Unless information about the distribution of the observed dose given the true dose,f ( X s | X t ) , is available from a validation study in which the distribution of true doses is approximately
the same as in the study population, f (Xt), the determination of E(Xt | Xs) can be quite complicated.
Pierce and Kellerer [P5] have proposed a relatively simple method for the estimation of E ( X t | X s )when it is reasonable to assume that the distribution of the observed dose given true dose, f ( X s | X t ) ,is log-normal with a constant coefficient of variation and that the distribution of true doses isreasonably smooth. The method involves approximating the empirical density of the observed doses
using a smooth function with at least two continuous derivatives and then using simple Laplacetransformations [B1] to estimate correction factors that can be used to approximate E ( X t | X s ) .
B157. In addition to providing adjusted estimates of dose (and powers of dose) for use in simple
regression calibration, Pierce and Kellerer [P5] extend their approach for use in situations in which theuncertainty in individual dose estimates arises because of a combination of classical measurement error
and assignment error when one has information about both the coefficient of variation in the observed
doses associated with classical error and that associated with assignment error. The computation of theadjustment factors to be applied to the observed doses is no more difficult when the dose uncertainty
reflects a mixture of classical and assignment error than in the case in which the dose uncertainty arises
solely due to classical error. As noted above, Pierce and Kellerer [P5] have used these methods toanalyse the atomic bombing survivor data. Their results suggest that even fairly large dose uncertainties(coefficients of variation of 40% for classical error and 20% for assignment error) have a relatively
small effect on estimates of cancer risk that are assumed linear with dose (increasing them by 10% to15%), but tend to increase the evidence for upward curvature in the dose response for doses less than
2 Gy. It was also found that allowing for dose uncertainty has little impact on the precision of theestimates of cancer risk since the effect of the over-dispersion (see below) arising from this uncertainty
is much smaller than the uncertainty inherent in the cancer data.
B158. As discussed thus far regression calibration involves determination of an expected value of thetrue dose given the observed dose and possibly other relevant information, and the use of this expectedtrue dose in standard, often maximum-likelihood-based, risk analyses for the outcome of interest (y)with, possibly, some adjustment to allow for the uncertainty in the expected true dose. This is arelatively simple approximation to a full likelihood analysis. The likelihood of interest can be written asf ( y | X t , z , θ ) , where z are other factors that affect the risk of the outcome and θ is a set of unknown
parameters. However, Xt is not known and in its place we have an observed surrogate, Xs. Assumingthat the outcome is independent of Xs if Xt is known then the likelihood of interest is:=f ( y, X s | z , θ ) ∫ f ( y, X s , X t | z , θ )dX t ∝ ∫ f ( y | X t , z , θ ) f ( X t | X s ) dX t

(B.6)

194 UNSCEAR 2012 REPORT

Since risk modelling generally requires some specification of the likelihood in terms of the true doseand since any form of regression calibration involves some characterization of f ( X t | X s ) , it ispossible, at least in principle, to directly maximize this likelihood. This general form of regression
calibration is discussed in detail by Carroll et al. [C7]. In practice, direct evaluation of the integral in
the above expression is infeasible for all but the simplest problems. However for some problems theintegral can be evaluated using Monte Carlo methods especially if conditioning can be used to reduce
the problem to one involving only a single parameter.
B159. Regression calibration is an attractive method since after computing E(Xt |Xs) (which can bechallenging) the analyses generally proceed using standard methods with, possibly, some adjustment of
the variance of the parameter estimates to allow for the additional uncertainty associated with theestimation of the expected true dose. Pierce and Kellerer [P5] argue that when dealing with analyses ofrare events, such as cancer cases, the adjustment for this additional uncertainty will have little impact
on inference unless it is large relative to the uncertainty that is inherent in the basic statistical model forthe outcome. If a simple linear model is considered for (say) cancer incidence data of the formy=α + β X t + ε , where ε is an error term with variance σ ε2 determined by the nature of the data, theregression calibration model can be written as:y = α + β E ( X t | X s ) + β ( X t − E ( X t | X s )) + ε = α +β ( E ( X t | X s ) + u + ε

(B.7)

where
=
u β ( X t − E ( X t | X s )) is an unobserved random effect with variance s u2 = β 2 var( X t | X s ) , and
ERR = β α . Thus the regression calibration model is said to be over-dispersed relative to the model in2
2true dose since the error variance of the regression calibration model is σσ
ε + u . While this over-dispersion will increase the variance of the estimate of the ERR ( = β α ) (or the other parameters), thiseffect will be small provided that

2
2
σσ
u
ε << 1 . For data following a Poisson distribution=s u2 s ε2 β 2 var( X t | X s ) aa
(1 +=ERR X t )ERR 2 var( X t | X s ) (1 + ERR X t ) and σ ε2= α + β X t will
be much less than 1 even for relatively large dose errors, such as those seen in the LSS. Therefore incancer risk analyses there is little need to adjust the variance estimates in regression calibration.
However, in analyses of binomial outcomes, such as the proportion of chromosome aberrations in (say)
100 or 1,000 cells per subject, dose errors can lead to substantial over-dispersion, and adjustment of thevariance using methods such as those given in [R1] is important.
B160. Simulation-extrapolation (SIMEX) methods. In 1994, Cook and Stefanski [C15] proposed a
simple Monte Carlo-based method for estimating and reducing bias in regression estimates arising frommeasurement error. The method is easiest to describe for the case of normal, additive measurement
error but is readily generalized to handle multiplicative or many other types of non-additive errors. It isalso assumed that the variance of the measurement is known (or that an estimate is available). The
observed data consist of the outcome of interest (Yi) together with measures (surrogate) doses such thatX=
X t,i + ui with ui having a normal distribution with mean 0 and variance, and other variables, Z i ,s,ithat affect the risk. The dose–response model can be =taken as Yi f ( X t,i , Z i | β , θ ) where β represents
the dose–response parameters and θ are additional parameters. It is also assumed that we have somemethod, such as the maximum likelihood method, that can be used to provide estimates of β and θ
given dose estimates and values of the other variables. The basic idea is that by adding fixed amountsof additional variability to the doses and then examining the relationship between the parameter
estimates and the amount of additional variability in the doses, it is possible to obtain information thatallows one to extrapolate to the situation in which there is no dose error. In particular, SIMEX uses
simulation methods to examine how the parameter estimate changes as a function of an error varianceinflation factor, ξ ≥ 0 , chosen such that measurement error variance is σ u2 (1 + ξ ) and then extrapolates

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 195

this relationship back to the hypothetical value of ξ = − 1 for which, in principal, the measurement error
variance is 0.
B161. While SIMEX is a simple, attractive, alternative to the regression calibration method for
dealing with the effect of dose errors on risk estimates, it has some limitations that restrict its
applicability in realistic situations that involve complex dosimetry systems. It was designed forsituations in which the uncertainty arises primarily as a result of independent measurement errors and it
requires some knowledge of the measurement error variance. SIMEX can be used in situations where
the relevant dose is a function of a number of components (such as annual dose estimates or doses
arising from internal and external exposures), but the number of replications necessary to obtainreliable estimates for each variance inflation factor value increases. It is possible to apply SIMEX tosituations involving a mixture of measurement (classical) error and assignment error if the magnitude ofthe different types of error is known (see [B5, F10]).
B162. Kopecky et al. [K10] used SIMEX to adjust for the effect of dose uncertainty in an analysis ofchildhood thyroid cancer risks in a Russian population exposed as a consequence of the Chernobyl
accident. Assuming that all of the error in the doses was measurement error, the dose uncertainty
adjustment increased the point estimate of the ERR per unit dose by a factor of three. However, as
noted by the authors, the adjusted estimate is almost certainly too large since it is unlikely that all of thedose uncertainty arose from measurement error.
B163. More recently, Kukush et al. [K17] have compared the performance of various approaches toestimating risks from radiation exposure for a binary outcome (such as cancer incidence) when doses
are estimated as a ratio of two quantities determined with error, one of which (131I activity in their
example) is measured with classical error and the other (thyroid mass) is subject to assignment error.
The analysis was motivated by studies of thyroid cancer incidence in the Ukraine following theChernobyl accident [L15, T8].
B164. They used a simulation study to examine the bias and uncertainty in estimates of the baseline
rate and excess absolute risk per unit dose for seven approaches to error adjustment for a broad range of
uncertainties in the two values used in dose estimation. The methods used were the naive analysis (inwhich the measured doses are used without adjustment), two full maximum-likelihood methods (one ofwhich assumes that the error in the activity measurements is log-normal while the other uses a
categorical model to describe the measurement error), regression calibration methods (assuming either
log-normal or categorical models for the measurement error), and a pair of SIMEX methods (one ofwhich uses the ordinary method for parameter estimation and the other uses an efficient estimation
method developed specifically for the problem of interest). For each method they consider two
measurement area scenarios. In one of these the activity measurement errors follow a log-normal
distribution, while in the second scenario the measurement errors are from a truncated log-normal
distribution.
B165. The authors found that the full maximum likelihood and regression calibration methods
exhibited little bias when the measurement error distribution was characterized non-parametrically andthat the computationally efficient SIMEX method performed quite well for a broad range of errors.
They concluded that while the categorical full maximum likelihood or efficient SIMEX methods were
somewhat more accurate than simple regression calibration using a categorical measurement error
model, the latter method was much easier to apply and has the advantage that risk estimates can be
carried out using standard computer programs for risk estimation.
B166. Bayesian methods. The regression calibration methods described above deal with measurement
error and have all relied on frequentist methods. Bayesian methods provide a conceptually simple and196 UNSCEAR 2012 REPORT

attractive approach to characterization of the nature of the dose error on risk estimates. In the following
paragraphs a Bayesian framework for risk estimation is outlined in the context of dose uncertainties thatinvolve classical, and shared and unshared assignment error. Following this discussion some publishedapplications of these methods are described.
B167. An assumption is made that there is a dose–response model for an outcome (y) of interest (suchas an ERR or an EAR model for cancer incidence rates) that depends on the true dose (Xt) and some othercovariates (Z) with unknown dose response (and possibly effect modification) parameters ( β ) andadditional parameters ( θ ) related to the dependence of the outcome on the other covariates. The
likelihood of outcome y given the covariates and model parameters is represented by p y ( y | X t , Z , β , θ ) .
A Bayesian analysis involves specification of a prior density, π ( β , θ ) , for the model parameters and the
combination of the likelihood and the prior density to compute the posterior density for the parameters
given the observed data, π ( β , θ | y, X t , Z ) .
B168. Inference about the dose–response parameters can then be based on the (marginal) posterior
density for β . In general, determination of a posterior density for all but the simplest problems requires
evaluation of multi-dimensional integrals. However readily available Markov Chain Monte Carlo(MCMC) software [L33] can provide samples from posterior (marginal) densities for many fairly
complex problems. Given a sample of the posterior density for a parameter (or parameters) of interest it
is possible to present representative values (such as mode, mean, or median), credible (or Bayesianconfidence) intervals, or other quantities of interest for a specific parameter or for functions ofparameters of interest.
B169. The basic Bayesian inferential framework described above can readily (if not always easily) be
extended to address inference about dose–response parameters when there are uncertainties in dose. In
this case, in addition to the likelihood function and prior distribution noted above, a model (density
function) for distribution of the measured dose (Xs) given Xt , ps ( X s | X t , γ ) , is needed, as well as forthe distribution of true doses in the population of interest, pt ( X t | η ) and a prior density ( π X (γ ,η ) ) forthe parameters of these densities. Given this setup, the complete probability function used indetermining the posterior density can be written as

p y ( y | X t , Z , β , θ ) × ps ( X s | X t , γ ) × pt ( X t | η ) × p ( β , θ ) × p X (γ ,η )(B.8)

B170. A somewhat more specific formulation considers a Reeves-type [R1] error model for log-dose(indicated by the * superscript) in which the true and surrogate log-doses for person i are defined as=
X i*,t X i* ( Z i ) + ε i ,c=; X i*,s X i* ( Z i ) + ε i ,b , respectively. If the classical and assignment error components

22
are assumed to be normal with mean 0 and variance σσ
C and B , respectively, the latent variable taken
as normal with mean µ ( Z ) and variance σ 2 , and some correlation ( ρ ) between the X * then we
L

i

L

i

have a model with some shared error. The posterior density for this situation isp y ( y | X t , Z , β ,θ ) × φ ( X s , X t | X * , s C2 , s B2 ) × φ ( X * | µL , s L2 , ρ , Z ) × p (α , β ) × p (s C2 , s B2 , µ L , s L2 , ρ )where φ (...) are normal densities.
B171. This Bayesian framework is similar to that used in an analysis of data on the effects of
exposure to fallout from the Nevada test on thyroiditis and thyroid neoplasm risks in a cohort of about
2,500 people carried out by Li et al. [L14]. In this dataset the information on dose uncertainty had thefairly common form of an estimate of the total (classical plus assignment) geometric standard deviationfor each individual dose and with no explicit information on the magnitude of the correlation induced

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 197

by the shared error. To address the limited information on the nature of the dose uncertainty, theauthors used informative priors for the between-subject correlations (uniform on the range 0.3 to 0.5)
and assumed a constant, but unknown fraction of the total uncertainty was due to assignment error withprior distributions that were uniform on region-specific ranges. A custom MCMC algorithm was used
to obtain samples from the posterior parameter densities, and inference about the parameter of interest(the ERR per unit dose) was based on the posterior marginal densities resulting from two different
priors for the ERR. The first of these was a normal distribution truncated at 0 with a mean chosen as “aplausible point estimate” and a “reasonably large variance”. The second was a scale-invariant priorcalled a Jeffrey’s prior [J12]. The data were also analysed using simple regression calibration and using
a non-Bayesian approach in which the full likelihood was maximized using a complex Monte Carloestimation maximization (MCEM) algorithm [M9]. The Bayesian posterior mode and the MCEM
estimates of ERR were similar for each outcome. However, for the rarer outcome (neoplasms) the
posterior density for the ERR was skewed to the extent that posterior mean or median values weremuch greater than the non-Bayesian estimates. In comparison to estimates that allow for a mixture ofclassical, and shared and unshared assignment error, regression calibration estimates were considerably
less than estimates based on either Bayesian or MCEM estimates using general dose error models thatallowed for a mixture of shared and unshared assignment and classical error. Allowing for shared errors
had little impact on either the risk estimates or the width of the Bayesian credible or confidence intervals.
B172. Mallick and colleagues [M6] use earlier data on thyroid cancer in the Nevada test site fallout
cohort to illustrate a Bayesian risk analysis allowing for uncertainty in dose estimates. Except for somebrief comments in the discussion they do not consider shared errors but in other respects their analysis
is similar to that of Li et al. [L14]. A primary feature of this analysis is the consideration of bothparametric and rather complicated semi-parametric models for the distribution of the latent log-dose
variable ( X * ) in a Reeves-type measurement error model and the dose–response function. They findthat a model that allows for a mixture of classical and assignment error provides the best description of
the dose uncertainty and that while allowing for dose uncertainty leads to some increase in the risk
estimate, the main effect is a marked increase in the width of the confidence interval for the excess risk
parameter owing mainly to an increase in the upper bound.
B173. Even with the availability of software that can greatly simplify the conduct of MCMC
analyses, conducting full Bayesian risk analyses that incorporate dose uncertainty remains challenging,
especially if one wants to consider the impact of systematic uncertainties arising from the uncertainties
about the nature of the doses or the models used to estimate the doses. In addition, at this time, carryingout such analyses is difficult in large cohorts (such as the LSS) because of the intensity of computation
involved. However, since Bayesian analyses and the MCMC methods used to implement them provide
a natural way of looking at the impact of complex dose uncertainties on risk estimates, further researchand development of these methods is extremely important.
B174. Risk analyses using data from multi-realization dosimetry systems. In both of the analyses
discussed above, the data on dose uncertainty were limited to a single value for the uncertainty inindividual dose estimates. Ideally one would like to have more detailed information on, for example,
the nature and magnitude of classical and assignment errors and of the relative importance of sharederrors on individual dose estimates. However, except possibly for the simplest dosimetry systems, it isneither feasible nor, in most cases, possible to characterize this information in any simple way. In orderto deal with this issue dosimetrists are developing increasingly complex systems that provide multiple
realizations of individual dose (or dose component) estimates based upon an assessment of the natureand magnitude of uncertainties in various aspects of the dosimetry system.
B175. These systems are often two-dimensional Monte Carlo systems (see appendix A) that attempt
to take into account systematic uncertainties in factors that affect all relevant individuals in a

198 UNSCEAR 2012 REPORT

predictable manner (such as the values of parameters in a model for the source term or transport ofradiation from some environmental exposure) and uncertainties in individual doses that arise as aconsequence of assigning representative (but not necessarily correct) doses to members of specificgroups (such as when all residents of an exposed village are assigned the estimated mean dose for thevillage). A proper Monte Carlo dosimetry system provides alternative realizations of values of the
expected true dose for individuals conditional on what is known (or uncertain) about the individual’s
exposure situation and model uncertainties. It is important to understand that these systems should notprovide alternative realizations of surrogate doses. That is, Monte Carlo uncertainty systems areintended to capture variability arising from systematic and assignment errors but individual
measurement (classical) errors must be addressed independently. For example, if dose estimates depend
on individual values measured with error then a Monte Carlo dosimetry might make use of an errorcorrected (such as regression calibration) estimate of the measured value for that individual in eachrealization. A better, but more challenging, approach would be to characterize the distribution of thetrue values given the measured values and then incorporate sampling from this distribution into thedosimetry system.
B176. Hofer [H18] has highlighted the importance of removing effects of classical error in Monte
Carlo dosimetry systems. It would be useful if the documentation of Monte Carlo dosimetry systems
included some discussion of sources of classical error and how these were addressed in thedevelopment of the system.
B177. As indicated above, a properly specified Monte Carlo dosimetry system provides a sample
from the distribution of true dose given knowledge of the nature of the dosimetry system for each study
subject (including the value of dose surrogates if they exist). Given this information one could thencarry out a standard regression calibration analysis using the mean dose and any non-linear functions ofdose (such as dose-squared) that enter into the dose–response modelling for each subject. The main
limitations of this simple and straightforward approach are that it fails to allow for the effect of intersubject correlations arising from shared errors and it assumes that the uncertainties in the dosimetry
system were properly characterized in the sense that the system leads to unbiased estimates of mean
individual doses. As noted in [S32] ignoring shared errors will have little effect on testing of the
hypothesis of no dose response, but will tend to result in confidence intervals that are too narrow
primarily because of underestimation of the upper bound.
B178. More comprehensive analyses would make direct use of the information from all of the dose
realizations for each subject. A naive approach to doing this would be to carry out a separate risk
analysis for each dose realization, and describe the risk based on the distribution of the risk estimates
resulting from these analyses. However, this naive method will lead to risk estimates that are biased
toward zero. This is because the variability in individual dose estimates across realizations is an
instance of classical error in which the distribution of the differences between a dose realization for anindividual and the true dose for an individual is independent of the true dose for that individual.
B179. Stram and Kopecky [S32] describe complex “Monte Carlo dosimetry” systems based on a
generalized assignment error model that includes shared and unshared additive and multiplicative
errors. They then outline a Monte Carlo maximum-likelihood method to obtain estimates andconfidence bounds for dose–response parameters when one has a set of realizations from the
distribution of true dose conditional on what is known (or uncertain) about the dosimetry system andindividual characteristics (Z), (such as those provided by a “Monte Carlo dosimetry” system).
B180.

If the likelihood for the data given the true dose and some parameters is p y ( y | X t , α , β ) ,where β represents parameters describing the dose response and α represents other parameters (suchANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 199

as those related to the risk in the absence of exposure), then the likelihood ratio test (LRT) of the
hypothesis that β = β1 against the alternative that β = β 0 ,  p y ( y | X t , α ( β ), β )| y, Z , α 0 , β 0  
l0 ( β ) = log  E   py ( y | X t ,α 0 , β0 )

 

(B.9)

can be approximated by the average of the LRTs over realizations of the expected true dose, that is 1 p y ( y | X t,r , α ( β ), β ) lˆ0 ( β ) = log  n p ( y | X , α , β ) 
t,r
0
0
y



(B.10)

The approximation has some limitations. First, when β is far from β 0 the approximation can require alarge number of dose realizations. Second, the exact expression involves conditioning on the outcome
variable, y, while the dosimetry system provides estimates of Xt conditional only on Z. Since thelikelihood of the outcome does not depend on Xt when there is no dose response ( β 0 = 0 ), using thisapproach works best when testing the null hypothesis of no response. However, if there is a strong dose
response then it can take a large number of dose realizations to obtain a good approximation to the
LRT. Nevertheless, if these limitations can be overcome the above expression can be used to find point
maximum-likelihood estimates of the dose–response parameters and likelihood-based confidencebounds for these estimates.
B181. Stayner et al. [S25] use data on cancer mortality in the Oak Ridge National Laboratory nuclear
worker cohort to illustrate the use of the Monte Carlo maximum-likelihood method to adjust for shared
uncertainties. In their example the only uncertainty is a period-dependent bias-factor that is applied toindividual annual doses. For each of the 10,000 realizations of dose the dosimetry system chooses amultiplicative bias factor for each of four periods by sampling from period-specific log-normal
distributions, and all individual doses are adjusted by the same set of bias factors without allowance forany other dosimetric uncertainties. Radiation-induced health effects were modelled using a simple
linear ERR model without effect modification with age-dependent baseline rates. Even in this simple,
and relatively small (5,345 workers with 225 cancer deaths over 136,673 person–years), the authors
noted some computational challenges in dealing with 10,000 dose replications. In comparing the resultsfrom analyses that used average bias correction factors (unsimulated analyses) with the Monte Carlomaximum likelihood estimates based on 10,000 dose realizations (simulated analyses) they found smallchanges in the point estimate of the risk and only a slight increase in the confidence interval width.
Because of the simple shared assignment error structure used in this analysis, one would not expect a
substantial difference between the risk estimates in the unsimulated and simulated analyses. However,the simulated analyses ought to lead to wider confidence intervals, as was the case here. Nevertheless,even these differences were small. The authors speculate that this is a consequence of the fact that thebias factors were of similar magnitude for all four periods and that the effect on the width of theconfidence interval would be greater if the period-specific biases were more heterogeneous.
B182. As noted above, with considerable effort Stayner et al. [S25] used the results from a simplistic
Monte Carlo dosimetry system in which dose uncertainty arose owing to variability in a single bias
factor affecting a simple measure of total dose and one was interested in a single risk parameter (suchas the ERR per unit dose). However, in real-world problems there are a large number of sources of
uncertainty affecting dose estimates; the doses of interest are often time-dependent lagged values thatcombine doses to the (presumably) relevant organ or tissue received from various sources (such as
doses to different organs or tissues arising from a combination of external occupational orenvironmental exposures, internal occupational or environmental exposures and possibly even from200 UNSCEAR 2012 REPORT

medical diagnostic procedures). Furthermore, risk is almost certainly not adequately estimated from
simple ERR or excess rate parameters but depends on factors such as sex, age, or time since exposure.
Thus, there is a need to consider other methods for making use of the often vast amount of dosimetry
data that arises from a complex, multi-realization, Monte Carlo dosimetry system.
B183. One possibility that seems useful to explore involves the use of multiple dose realizations in a
Bayesian risk analysis. This might be done through the implementation of an MCMC analysis in whichsampling is from suitable prior densities for the risk model parameters and a (discrete) uniform priordensity over the dose realizations. The result of the analysis would be samples from the posterior
densities of the risk parameters and a set of unequal weights for the dose realizations. If this method
were carried out for a relatively simple risk model, it might be possible to use the posterior dose
realization weights to compute weighted mean doses that could be used in some relatively
straightforward regression calibration-like analyses for more complex risk models.
B184. While there is considerable interest in complex dosimetry systems and efforts are being madeto develop such systems for a number of populations, including X-ray technologists in the UnitedStates, Chernobyl emergency and recovery workers, people exposed along the Techa River, and Mayakworkers, there has been remarkably little progress in the development of methods that make effective
use of the resulting individual dose distributions. A primary reason for this is that, as challenging as it
can be to develop Monte Carlo dosimetry systems that adequately capture the nature of theuncertainties in individual dose components, using the resulting information about individual dosecomponent uncertainties in risk estimation is even more challenging. Except for the simplest problems,
the estimation of risks from radiation exposure is an iterative, exploratory process. Increasing thecomputational burden significantly by allowing for the effects of dose uncertainty, when fitting eventhe simplest risk models, tends to push investigators towards analyses that largely ignore the effects ofdose error or that focus on a single risk summary that may fail to capture adequately the nature of theradiation-associated risk. There is clearly a need for considerably more effort to develop practicalmethods that account for the impact of dose uncertainty in realistic dose–response models.

C. Impact of model uncertainties
B185. Models are designed to give a simplified description of the main processes or an assessment of
key parameters of complex processes. Thus, in the sense of giving a complete picture of reality “allmodels are wrong, but some are useful” [B19]. Various models may approximate a data set equally well
but give different results for some quantities of interest. An evaluation of the results from several
models is a tool of clarifying the messages contained in the data and, possibly, the artefacts introducedby the use of specific models. Evaluation of several models will increase the confidence in the resultsthat are obtained commonly by those models that exhibit a good quality of fit. If differences between
two model estimates are not statistically significant, then this is often considered as a confirmation of
the result. Nevertheless, this difference will have an impact on the uncertainty range. Taking bothmodels into account will generally result in an uncertainty range wider than each of the uncertainty
ranges of the two models. This may imply, for example, that a risk estimate, which is significant in apreferred model, does not remain significant, if other models are taken into account.
B186. There is a large body of publications on model uncertainties (for summaries, see [B25, C10,H15]). Fields of applications are manifold including ecology [W11], econometrics [L12], analysis of
microarray data [A8], phylogenetics [P8], and applications in meta-analyses [B9].

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 201

B187. In the frame of estimates of risk from radiation exposure, only initial approaches to theapplication of formal procedures for model selection and derivation of model uncertainties, forexample, by multi-model inference, have been reported. Consequently, most evaluations of results, forexample, on excess risks from radiation exposures, are overconfident. A number of reports, including
previous reports of the Committee, acknowledged model uncertainties but studies that quantified themhad not been conducted (such as NCRP and UNSCEAR [N9, U11]).
B188. In general, radioepidemiological data are obtained for a range of variables, such as age at
exposure, dose, or age at diagnosis of, or death due to, a disease. In most cases, central estimates are
relatively insensitive to the choice of the model [E3, J4, P14, W3]. However, model uncertainties are
greater in the border zone of the observed ranges of variables, for example, at young or old age at
exposure, at low dose, or young age attained.
B189. The Committee noted in the UNSCEAR 2000 Report that the outcome of cancer risk
modelling is often dependent on the initial biological assumptions made. This is clearly a source ofmodel uncertainty ([U11] annex G). Key questions concerning model uncertainties are how to selectmodels that have to be considered, and how the variability of results produced by different models canbe taken into account. One method of dealing with such model uncertainties is multi-model inference ofrisk quantities, which is also called in the statistical literature “model averaging”. Before addressingthese questions, this section summarizes types of models considered in the risk analyses, and theevidence for model uncertainties in the estimates of cancer risks after exposure to ionizing radiation.

1.

Model types

B190. Radioepidemiological data can be analysed with a variety of models. For the discussion below,
model types are subdivided into two major groups: empirical models and mechanistic models.
B191. Empirical models use simple mathematical terms to describe baseline morbidity or mortality
rates and excess risks associated with radiation exposure. Baseline rates can be modelled by allowing
for different baseline rates in a number of strata (groups) defined, for example, by sex and ranges ofbirth year and age. Conventionally, such models are called stratified. Other models use parameters for
relative risks in different dose categories (categorical models). Alternatively, functions of the variables
are used in so-called parametric models. Excess rates are expressed as excess relative risk (ERR) or
excess absolute rate (EAR) depending on dose and possibly further variables [U12]. Empirical models
have two advantages: (a) mathematical simplicity; and (b) often an estimate of a quantity of maininterest, for example, in a linear model, the ERR per unit dose and its uncertainty distribution are
obtained directly by the fit of the model to the data.
B192. In cohort studies, such as the Life Span Study (LSS) of atomic bombing survivors [P14],
baseline cancer rates and dose-specific EAR or ERR can be estimated as parametric functions of age at
exposure, attained age, sex, and other variables of interest, whereas in matched case–control studies,absolute rates can be estimated only if the baseline rates can be estimated from other data sources. In acohort study, a typical rate model where the rate is assumed to vary linearly with dose might have theform:
Total rate = exp(α0 + Σαixi) + βD × exp(Σδjyj),(B.11)

while a typical excess relative risk model has the form:
Total rate = exp(α0 + Σαixi) × [1+γD × exp(Σεjyj)].

(B.12)

202 UNSCEAR 2012 REPORT

Here, in these models β, γ, α0, α1, α2, … , δ1, δ2, … , and ε1, ε2, … are unknown parameters and x1,
x2, … , and y1, y2, … represent possible modifiers of baseline and dose-specific rates or relative risks,
respectively. For example, the baseline rate of female breast cancer might be represented by the
exponential function exp(α 0 + ∑ α i xi ) , where x1 has value 1 for Hiroshima and value −1 for Nagasaki,
x2 is the attained age in years and x3 is age at first full-term pregnancy; D might be breast tissue dose ingrays; and exp(∑ δ j y j ) , representing possible modification of dose-related excess rate, might have y1
as age at radiation exposure, y2 as attained age in years, and y3 as age at first full-term pregnancy (often
the same variables can be modifiers of both baseline and excess rate). More complex dose dependencesas, for example, linear–quadratic, linear–quadratic–exponential or threshold-type dose dependences, aretypically considered as well.
B193. In the field of risks from radiation exposure, the main use of mechanistic models is related tocancer induction and development. These models were initially developed to describe the age
dependence of cancer [A12, M18, M19]. Although more recent models are quite complex (such as[L19]), they still represent a huge simplification because not all of the many processes leading to cancer
induction and development are well understood. The relevant molecular pathways, cellular processes,
tissue reactions* and influences of the immune system depend on the site and the type of cancer.
Because of insufficient knowledge of these processes and to the limited statistical power of
epidemiological studies, it is generally not possible to identify uniquely one mechanistic model ofcarcinogenesis that is superior to others. Nevertheless, a main advantage of mechanistic models is thatthey provide the possibility of integrating knowledge on radiobiological processes in the evaluation ofradioepidemiological data [J6]. For example, Eidemüller et al. [E3] concluded that the age dependenceof the radiation-related excess incidence of breast cancer among the Swedish haemangioma patients
may be related to a radiation-induced genomic instability,* which causes a lifelong increase of the(otherwise spontaneous) initiation rate of carcinogenesis. Shuryak et al. [S16] related the limitation of
the growth of pre-neoplastic lesions to age and dose dependencies of cancer after exposure to ionizing
radiation. Brugmans et al. [B23] incorporated the effects of decreased cellular proliferation at very
advanced age for improving the description of the baseline lung cancer risk among miners.
B194. An attempt has been made to assess the impact of individual radiation sensitivity on theestimation of risk factors for population groups [M13].
B195. The Committee recommends applications of empirical and of mechanistic models to the sameradioepidemiological data in order to explore model uncertainties.

2. Evidence for effect of model uncertainties on estimates of risk fromradiation exposure
B196. A study by Preston et al. [P14] of solid cancer incidence was based on 17,448 first primarycancers (including non-melanoma skin cancer) diagnosed from 1958 to 1998 among 105,427 survivorsof the atomic bombings in Japan. In their standard model with an ERR decreasing exponentially withage at exposure, the ERR at age 70 after an exposure of 1 Gy at age 60 was 0.27. Describing the age-atexposure dependence by a log–quadratic spline with a single knot at age 40 improved the quality of fit(P = 0.02) and resulted in an ERR estimate that was higher by a factor of 2.5.
B197. Lung cancer mortality risk was studied by Jacob et al. [J3] for male Mayak workers, for whom
lung doses were estimated from the measured plutonium content of urine and for whom additional
information was available on external exposure and smoking behaviour. Among 6,293 workers, 301
lung cancer cases were registered in the follow-up period until the end of 2002. At age 50, after a

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 203

plutonium exposure of the lung during the age period of 20–40 years with a cumulative dose of 0.1 Gy,an ERR of 0.12 was obtained with the preferred model of carcinogenesis. With an empirical model,
however, the value was larger by a factor of four.
B198. Richardson et al. [R2] analysed leukaemia mortality among Japanese atomic bombings
survivors. The analysis included 310 deaths due to leukaemia during the period 1950–2000 among
86,611 people in the LSS. In their preferred model, the dependence of the ERR on time after exposure
was a cubic spline function with a knot at 30 years. For a bone marrow dose of 1 Gy, a best estimate of
the ERR of 0.8 was found for 30 years after an exposure that occurred at age 10. BEIR VII [N19]obtained for the same specification with a simpler model, an ERR of 4.5. Thus, based on very similardata, the two risk estimates differ by more than a factor of five.
B199. The three examples discussed above demonstrate that considerable model uncertainties havebeen observed for estimations of cancer risk after exposure to ionizing radiation in specificcircumstances. A first step to dealing with the problem is to select models that are appropriate foranalysing the epidemiological data.

3.

Selection of a preferred model

B200. Plausibility considerations are an important part of model selection. For example, fits ofmechanistic models may result in biologically implausible parameter values; thus parameter values
need to be restricted to plausible values.
An important quantity in model selection is the likelihood, L, of the data given a model, k,and the maximum likelihood estimator, θ k , of the parameters. Because of technical reasons, theB201.

logarithm of the likelihood multiplied by −2 is used, which is for generalized linear models, apart froma constant, the deviance:*
devk = −2 ln[L(data|k, θ k )](B.13)In analyses with a large number of degrees of freedom, as is normally the case in analysing
epidemiological data, generally only differences of the deviance are considered so that the constantterm does not play a role. The term “deviance” is also used for other models than generalized linear
models as a convenient abbreviation for minus twice the logarithm of the likelihood (plus an unknown
constant).
B202. The addition of more terms to a model generally increases the likelihood and thus reduces thedeviance. However, the resulting more complex model is not necessarily an improvement, because amodel with many parameters may result in over-fitting of the data. The relevance of various possible
parameters for a description of the data can be tested by calculating measures of the quality of fit as, forexample, the deviance. Generally, the uncertainty of parameter estimations increases with thecomplexity of the model (see figure B-V). As a consequence only parameters that really matter ought tobe included in the selected model [C10]. Already in the fourteenth century, this has been expressed by
the principle of parsimony (the so-called “Occam’s razor”) (Occam, ca. 1320, referenced by Posada andBuckley [P8]). Methods for model selection aim at avoiding too large deviances by oversimplificationand too large uncertainties by over-fitting.

204 UNSCEAR 2012 REPORT

Figure B-V.

Deviance and parameter uncertainty as a function of the number of parameters

Generally, the deviance (more generally expressed by minus twice the logarithm of the likelihood) decreases and the uncertainty
of parameter estimates increases with the number of parameters in a model [P8]. Methods for model selection aim at finding abalance between these two trends

B203. Methodologies for model selection depend on whether the models considered are nested or
non-nested. Model selection may also depend on the procedure for adapting the models to the data
[C10]. The Committee emphasizes the importance of defining the criteria for model selection before astudy is performed and of making the criteria transparent in the publications.
B204. Two models are called “nested”, if the simpler model can be obtained from the more complex
model by deleting one or several terms in the model equations. Thus, deletion of one term δ j y j inequation (B.11), where y j is, for example, the risk modifier “age at exposure”, in a model, 1, results
in a model 2, which is nested in 1. An approach to selecting one of the two models is based on thelikelihood ratio test. This test is based on the fact that the difference of the deviances of two nested
models in Poisson regressions is approximately chi-square distributed [H4, N14]. If the deviance of themore complex model is according to the chi-square statistics significantly lower than the deviance ofthe simpler model, then the more complex model is selected, because it is considered to have an
improved quality of fit. Otherwise, the additional terms in the more complex model are dropped and thesimpler model is retained. Table B14 gives the limiting values for the difference in deviance for an
improvement of the fit at the 95% confidence level [W2]. Thus, if the two models differ by a term with
one additional parameter, then the model including this term will be selected if its deviance is smaller
than the deviance of the simpler model by more than 3.84. The likelihood ratio test is not only applied
to Poisson regression but also to analyses of individual data.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 205

Table B14. Difference in deviance indicating an improvement of fit of nested models at the 95%
confidence level [W2]For example, if two nested models differ by terms with two additional parameters, then the more complex model will beselected if its deviance is smaller than the deviance of the simpler model by more than 5.99

Δ number of parameters

Δ deviance

1

3.84

2

5.99

3

7.81

4

9.49

B205. A criterion for the relative quality of fit of non-nested models has been derived by extension of
the maximum likelihood principle using information theory [A3, A4, B25, C10, W2]. Akaike used the
Kullback-Leibler information as the fundamental basis for model selection [A3, A4]. The KullbackLeibler (K-L) information, I(f, k), is the information lost, when the model k is used to approximate
full reality, f [A7, K3]. Akaike’s major invention was the idea to calculate not the K-L information
itself, but the expectation of the K-L information and linking it to the log-likelihood function at its
maximum. The complex mathematical analysis yielded a simple expression, the Akaike Information
Criterion, AIC, as a measure of the “distance” in information between a model and full reality.
B206. In its first approximation, the AIC is defined by twice the difference of the number ofparameters and the natural logarithm of the likelihood:
AICk = 2 (nk – ln(Lk))(B.14)

where nk is the number of parameters of a model k. The model with the lowest value of AIC isselected as the one with the highest probability. In this algorithm, a model is preferred to one with Δnfewer parameters, if twice the logarithm of its likelihood is larger by at least 2Δn. Unlike the likelihood
ratio test for nested models, the Akaike approach prefers more complex models. The term 2nk is often
called the “penalty term”, because the more parameters there are, the more the model is weighed downby the information criterion.
B207.

In the approach of Akaike, the probability for a model improvement is given by:
p = 1 – exp(-0.5 ΔAIC) / (1 + exp(-0.5 ΔAIC))(B.15)

where ΔAIC is the difference of the AICs for the two models under consideration [W2]. Under these
conditions, a model has a 95% probability of improvement if the difference in the AICs amounts to 5.9.
B208. Based on Bayesian statistics, an alternative criterion for the relative quality of fit of non-nested
models has been proposed by Schwarz and Yang [S10, Y2]. The Bayesian Information Criterion isdefined by:
BICk = nk ln(N) –2 ln(Lk)(B.16)

where N is the sample size [C10, P8]. Again the model with the lowest BIC is selected. Compared to
the AIC, the BIC prefers simpler models for sample sizes larger than 7. Most authors in the field ofradioepidemiology have tended to favour the use of the AIC [K2, L19, W4]. The BIC, however, hasbeen used for the selection of a model describing lung cancer risk after exposure to radon and cigarette206 UNSCEAR 2012 REPORT

smoke in a joint analysis of three European case–control studies among uranium miners [L12]. Somepapers include both indices in their model selection procedure [J3, J6, W3]. None of the papers state,
however, why the AIC or the BIC has been chosen for model selection.
B209. The Deviance Information Criterion, DIC, is specifically designed for model adaptations todata based on Bayesian MCMC methods [S24]. In these methods, the prior information may beconsidered to reduce the degrees of freedom. Correspondingly, the number of parameters, nk, in the
penalty term in the definition of the AIC for a model k (see equation (B.14)) is replaced by the
number of “effective parameters”, pD. The number of effective parameters is defined by the difference
between the posterior average of the deviance and the deviance evaluated at the average of the posterior
parameter distribution. Little et al. [L17] have calculated the DIC for some models, which they
considered for the evaluation of radiation-induced lifetime cancer risk and its uncertainty employed in
the UNSCEAR 2006 Report [U12].
B210. Besides AIC, BIC and DIC, other criteria have been developed that are designed for special
purposes or small-size data sets [C10].
B211. Model selection techniques as described above generally reject stratified or categorical models
in favour of parametric models [C10], because the number of parameters that have to be determinedfrom the data is considerably larger for the parametric models. Walsh et al. [W3] used additional tests
to select between parametric and semi-categorical models (models that described some variables byfunctions and other variables by parameters for different categories). They analysed thyroid cancer
incidence after the Chernobyl accident. The results on the time and age dependences of the excess
relative risk estimates of the parametric and non-parametric models were significantly different.
Quality-of-fit tests based on the AIC and on the BIC favoured modelling of the baseline incidence bycontinuous functions, because the number of parameters in the semi-categorical model is considerablylarger. The authors finally preferred the model with a parametric description of the baseline risk*,because the number of thyroid cancer cases in various age and time-after-exposure classes was better
predicted than by the semi-categorical model.
B212. Posada and Buckley [P8] noted that model selection techniques may not result in one optimalmodel. A possible way of overcoming this problem is to use multi-model inference.

4.

Multi-model inference

B213. In order to take into account more than just one preferred model, a strategy is needed to selectthose models that are to be considered in the assessment of model uncertainties. In principle, there are
an infinite number of models that could be tested. For example, one may start with the model inequation (B.11). There is already an infinite number of new models with one additional parameter, ε,obtained by adding a term with one of the covariates, xi, to the power of k, that is ε(xi)k. Multi-model
inference strategies based on an infinite or very large number of models are dealt with shortly in thefollowing paragraph, whereas the focus of this section is on strategies that base the inference on a more
limited selection of models.
B214. An approach based on a very large number of models is the MCMC model composition, MC3[H15, M4]. The Markov chain starts with some model M and constructs a neighbourhood to the model.
For example, if the model represented by equation (B.11) is the starting point, then models as
constructed in the last paragraph (such as up to a specified power, kspec) can be defined to be part of theneighbourhood of . A model ´ is sampled from the neighbourhood of . If the conditional

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 207

probability of ´, p´ = p(´|data), is larger than the conditional probability of , p = p(|data),then M´ is accepted as the next model in the Markov chain. If the conditional probability of ´ issmaller than the conditional probability of , then ´ is accepted with probability p´/p. Otherwise,
the chain remains in state . The approach is known in physics as the Metropolis-Hastings algorithmof importance sampling [C8]. The Committee is not aware of any application of this approach inevaluating the risks from radiation exposure.
B215. An approach with a more limited selection of models has been proposed by Madigan and
Raftery [M3]. This approach corresponds to discarding all models that are less supported—to 95%
probability—by the data than the model with the highest probability. Applying the approach to models,as they have been constructed in the first paragraph of this subsection, would result in an infinite
number of selected models.
B216. A simple approach to selecting models is to analyse only models that have been defined in theliterature as preferred models, and to apply model selection approaches to such a set of models [P8].
B217. Jacob et al. [J4] discussed model uncertainties in estimation of risk from radiation exposure forsolid cancer among the survivors of the atomic bombings in a three-step procedure:(a) Definition of four groups of models: (i) empirical models; (ii) two-step clonal expansion,
TSCE, models with a radiation action on the promotion rate of precancerous cells; (iii) TSCE
models incorporating a classical cell-killing term for precancerous cells; (iv) TSCE models
incorporating low-dose hypersensitivity in cell killing of precancerous cells;(b) Application of the likelihood ratio test within each group of models to select for each group ofmodel with the best quality of fit;(c) Comparison of the risk estimates obtained by the four selected models.
The TSCE model was found to represent the data more economically than the empirical risk model: asimilarly good description of the data was achieved with a smaller number of parameters. However, thestatistical power of the data was sufficient to give a clear preference to one of the four selected models.
Central ERR and EAR estimates (at 1 Sv, for age at exposure 30 y and age attained 70 y) were similarin all of the four selected models. The TSCE models with radiation-induced cell killing tended to givefor young ages at exposure lower risk estimates than the empirical model.
B218. Various approaches to multi-model inference are discussed in the statistical literature [C10,H15, P8]. An estimator of a quantity, µ̂ , is calculated by a weighted average of estimators, µˆ k ,obtained with model k:µˆ = ∑ wk µˆ k

(B.17)k

Generalizing equation (B.15) to a number of k models, and choosing the weights of the models
according to the probability of the data in the Akaike approach, results in:wk =exp(−0.5AICk ) / ∑ exp(−0.5AICi )i(B.18)

208 UNSCEAR 2012 REPORT

where AICi is the AIC for model i. In a Bayesian approach to multi-model inference, a similar result isobtained, in which the AIC in equation (B.18) is replaced by the BIC. Again, other information criteria
are used for special purposes or if the data set has a limited size [C10].
B219. Analytical approaches have been developed to derive parameters of the distribution of aquantity of interest, μ [C10, H15]. Alternatively, a straightforward Monte Carlo procedure can beapplied [W4]. The procedure is based on probability density functions for a quantity of interest as
derived from the various models under consideration. The probability density function of the quantityof interest according to multi-model inference is then obtained by sampling with probability wk fromthe probability density function according to model Mk.
B220. Walsh and Kaiser [W4] included nine recently published relative risk models (see equation(B.12)) in a multi-model inference study of leukaemia mortality among the Japanese atomic bombing
survivors. Walsh et al. fitted all models to the same data set (DS02CAN.DAT from www.rerf.or.jp).
The model selection and weighting procedure was based on the AIC. The lowest AIC was obtained by
the model published by the Committee in 2006 [U12]. According to the weighting procedure inequation (B.18), 51% of the samples in the pdf for the multi-model inference were drawn from the pdf
produced by the model of the Committee. Corresponding results are summarized in table B15 for allnine models considered. The different models give similar results for ages attained and ages at exposurethat are in the central regions of the data set (see table B16 for a = 55 and e = 30). In this central dataregion, best estimates and confidence intervals in the multi-model inference are close to those in themodel with the highest weight. Larger variability is observed, however, for ages that are not in thecentral region of the data. For attained age 17 after an exposure at age 7, for example, best estimates of
the nine models for the ERR at 1 Gy range from 11.3 to 86.4. Multi-model inference resulted in an ERR
of 18.4 (95% CI: 0.6, 35.6) [W4]. The best estimate is close to the best estimate of the model of theCommittee [U12]. The confidence interval, however, is wider. The ratio of the upper and lower boundsof the 95% confidence interval is 38 in the model of the Committee and 59 according to multi-model
inference [W4]. The impact of dose uncertainty on the width of the uncertainty ranges for the risk
estimates has not been considered in the analysis.
B221. Kaiser et al. [K2] analysed breast cancer incidence in the LSS cohort of Japanese atomic
bombing survivors. Applying a formal selection procedure to a large number of models, one empiricalmodel and three versions of the TSCE model of carcinogenesis were selected for multi-model
inference. Carcinogenesis of baseline cases in the TSCE models was characterized by an initiation rateincreasing with age from birth up to about 25 years, and a growth rate of preneoplastic lesions thatdropped for those in their forties. Multi-model inference resulted in uncertainty ranges of values for the
ERR per unit dose that were larger than uncertainty ranges of the preferred empirical model, especiallyfor young ages at exposure. For aged 10 at exposure and age 70 at diagnosis, for example, ratio of the95th to 5th percentiles increased from 2.5 to 5.9 (see table B17).
B222. The Committee notes that neglecting model uncertainties may lead to a considerable
underestimation of the total uncertainty of risk estimates, and recommends the application of multimodel inference techniques in future risk evaluations. This will allow more realistic assessment of theuncertainty of risk estimates than in most analyses up to now.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 209

Table B15. The number of parameters, minus twice the logarithm of the likelihood, the AICk andthe sampling weight wk applied in multi-model inference for leukaemia risk among the Japaneseatomic bombing survivors [W4]
Model

nk

−2 ln(Lk)

AICk

wk

Preston et al. [P13]222 258.7

2 302.7<0.0005

BEIR VII, phase 2 [N19]192 255.2

2 293.2

0.001

Richardson et al. Model 2, table A1 [R2]21

2 250.1

2 292.1

0.001

Schneider and Walsh LQ model [S9]13

2 258.0

2 284.0

0.069

Schneider and Walsh LQ-exp model [S9]142 253.9

2 281.9

0.198

Little et al. [L17]112 259.7

2 281.7

0.219

UNSCEAR [U12]102 260.0

2 280.0

0.512

Richardson et al. Main model [R2]448

1 915.5

2 811.5<0.0005

Richardson et al. Model 3, table A1 [R2]

1 086

1 560.3

3 732.3<0.0005aa

The functional form of the EAR model of [P13] has been used to construct a corresponding ERR model.

Table B16. Best estimates with 95% confidence intervals of the ERR for leukaemia mortality among
Japanese atomic bombing survivors at attained age a after exposure at age e following a bonemarrow dose of 1 Gy [W4]Modele = 7; a = 17e = 30; a = 55

Preston et al. [P13]a11.3 (4.3, 21.9)b

2.72 (1.21, 4.24)

BEIR VII, phase 2 [N19]19.9 (−12.2,37.9)

2.11 (−0.09, 2.98)

Richardson et al. Model 2, table A1 [R2]

22.7 (−12.1, 43.8)

2.50 (−0.10, 3.59)

Schneider and Walsh LQ model [S9]19.2 (−0.6, 38.8)

2.73 (1.60, 4.03)

Schneider and Walsh LQ-exp model [S9]19.3 (2.0, 36.5)

2.95 (1.51, 4.06)

Little et al. [L17]18.5 (0.2, 35.6)

2.78 (1.53, 4.04)

UNSCEAR [U12]17.9 (0.9, 34.6)

2.71 (1.49, 3.88)

Richardson et al. Main model [R2]

86.4 (12.1, 582)

2.55 (1.12, 4.18)

Richardson et al. Model 3, table A1 [R2]

31.0 (−32.6, 66.6)

2.72 (1.12, 4.18)

Multi-model inference

18.4 (0.6, 35.6)

2.77 (1.43, 3.84)

a

The functional form of the EAR model [P13] has been used to construct a corresponding ERR model.

bResults for the age group 0–19 years were taken.

210 UNSCEAR 2012 REPORT

Table B17. Best estimates with 90% confidence intervals of the ERR for breast cancer incidence
among Japanese atomic bombing survivors at attained age a after exposure at age 10 following abreast dose of 1 Gy [K2]Modela = 30a = 70

Empirical, linear dose response modified
by age attained

5.2 (2.6, 9.8)

1.1 (0.60, 1.5)

TSCE, lifelong effect of acute exposure on
growth rate of pre-neoplastic lesions

8.9 (4.2, 20)

1.2 (0.91, 1.5)

TSCE, immediate initiation of preneoplastic lesions by acute exposure

3.2 (2.4, 4.1)

0.44 (0.14, 0.96)

Multi-model inference

5.1 (2.6, 14)

1.1 (0.27, 1.6)

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 211

APPENDIX C. UNCERTAINTY IN TRANSFERRING RISKQUANTITIES FROM GIVEN STUDIES TO OTHER EXPOSURESITUATIONS OR POPULATIONS OF INTERESTI.

TRANSFER TO ANOTHER POPULATION .................................................................................... 213

II. EXTRAPOLATING RISKS OVER LIFETIME.................................................................................... 219
III. TRANSFER TO LOW-DOSE AND LOW-DOSE-RATE EXPOSURE WITH LOW-LETRADIATION ................................................................................................................................................. 221
A. Statements of various bodies up to the UNSCEAR 2006 Report ............................. 222
B. New radiobiological information ........................................................................................ 224
C. New epidemiological information ..................................................................................... 225
D. Evaluation of the uncertainty of the DDREF ................................................................... 226
E. Uncertainty associated with the projection of risk to the region of low
and very low doses................................................................................................................... 227
IV. TRANSFER FOR EXPOSURES TO OTHER TYPES OF RADIATION............................................. 228
A. Modifying factors to estimate risks of cancer for different radiation
types .............................................................................................................................................. 228
B. Quantification of modifying factors up to UNSCEAR 2006 Report ...................................... 229
C. Modifying factors for neutrons ............................................................................................ 229
D. Modifying factors for alpha particles ................................................................................. 230
E. Modifying factors for lower-energy photons ................................................................. 233
F. Modifying factors for low-energy electrons.................................................................... 236
G. Summary of modifying factors ............................................................................................ 239
V. INTEGRATIVE APPROACHES FOR QUANTIFYING THE OVERALL UNCERTAINTY IN RISKESTIMATES .................................................................................................................................................. 239

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 213

I. TRANSFER TO ANOTHER POPULATIONC1.
The UNSCEAR 2006 Report (annex A, I. Features of Epidemiological Studies, H. Transfer ofradiation risk estimates between populations, and interactions of carcinogens, paragraphs 39–48) [U12]considered that the question of how to transfer risk estimates derived from one population to a different
population remains unanswered, and that available data suggest that there is no simple solution to the
problem. The question is related to the issue of how one should model interactions between radiationand other agents in relation to cancer risk, as extensively reviewed in annex H of the UNSCEAR 2000
Report [U11]. It was concluded, however, that for the foreseeable future, the most useful information
relevant to transferring radiation-related risk coefficients from one population to another will comefrom multinational comparisons of site-specific, radiation-related risk, rather than from investigationsof underlying cancer risk factors and their interactions with radiation dose.
C2.
Baseline and excess risk. Epidemiological information about radiation-related cancer risk is
obtained by studying population groups characterized by individual demographic data such as sex, birthyear, nationality, lifestyle factors, history of exposure to ionizing radiation, site-specific cancer
incidence and/or mortality, and other factors that conceivably might be informative about “baseline”
cancer risk unrelated to radiation dose, and by dose-related “excess” cancer risk. Useful site-specificdata on baseline cancer risks as functions of attained age are readily available for many populations, as
published periodically by the International Agency for Research on Cancer [I5]. Dose–response
analyses of data from a particular population of interest are conducted to determine the extent to whichcancer risk in this population may depend upon radiation dose, and the extent to which baseline andexcess risk may vary according to factors other than radiation dose. In particular, evidence aboutmodification of baseline risk and/or radiation dose response by demographic factors such as sex, age at
exposure, and attained age, and by lifestyle factors such as tobacco use, diet, and reproductive history,
is of interest because such findings might lead to more useful risk estimates and, ultimately, to better
understanding of the biological processes of radiation carcinogenesis in man.
C3.
Additive and multiplicative expressions of risk. It is computationally and cognitively
convenient to express excess risk in absolute terms, as an addition to baseline risk:
additive risk = baseline risk + excess absolute risk (EAR)(C.1)

and in relative terms as a multiple of baseline risk:
multiplicative risk = baseline risk × (1 + excess relative risk (ERR))(C.2)“Baseline” risk, by definition, is not influenced by radiation dose and therefore its estimate would be
expected to be essentially the same whether the excess risk is expressed in absolute terms using an
additive model or relative terms using a multiplicative model as in equations (C.1) or (C.2). An
immediate practical problem concerns the portability of radiation-related, site-specific risk estimatesfrom one population to another. If the two populations have distinctly different age-specific baseline
rates for a given cancer site, additive and multiplicative projections of risk from one population, such as
the LSS cohort of atomic bombing survivors [P14], to another, for example, to the population ofanother country, will yield discordant risk estimates in the second population. Additive andmultiplicative projections will not differ much if the two populations have similar baseline rates,214 UNSCEAR 2012 REPORT

although of course it does not necessarily follow that the projection to the second population will be
accurate.
C4.
Breast cancer example: Projection of radiation-related risk between Japanese and American
populations. Baseline rates for female breast cancer are substantially different between Japan and theUnited States, which historically have had among the world’s lowest and highest breast cancer rates,
respectively [I5, M2]. Table C1 shows linear model estimates, with 90% confidence intervals, of ERR
and EAR per unit dose for LSS female breast cancer at age 70 following exposure at age 30 (i.e. in1985) ([P14] table 29). Under the reasonable assumption that the ERR and EAR estimates are
consistent in describing the same phenomenon, the relevant LSS baseline risk for breast cancer atage 70 in 1985 can be estimated as the ratio of the EAR and ERR per unit dose estimates, i.e. 9.2 per(104 PY Gy) divided by 0.87 Gy−1 resulting in 10.6 per 104 PY (table C1). A recent estimate of theUnited States baseline female breast cancer rate at age 70, based on data from the 14-centre SEER
Registry tumour registry [I5], is 41.4 per 104 PY; or 3.9-fold higher than the corresponding estimate forthe 1985 LSS baseline. Multiplying the contemporary United States baseline rate by the LSS-based
estimate of ERR per unit dose gives a multiplicative projection of 36.0 (90% CI: 22.8, 53.8) per(104 PY Gy), which is 3.9 times the estimated additive projection of 9.2 (90% CI: 6.8, 12.0) per(104 PY Gy) as provided by the LSS estimate of EAR per unit dose.
C5.
Female breast cancer: International pooled analysis of radiation-related risk. In a pooled
analysis of female breast cancer incidence data from the LSS cohort and from seven western
populations exposed to medical X-rays, Preston et al. [P11] found that age-specific EAR estimates perunit tissue dose to the breast were consistent among the LSS cohort of Japanese atomic bombing
survivors, two United States cohorts of tuberculosis patients given multiple chest fluoroscopies during
lung collapse therapy [B16], and a cohort of United States children given X-ray therapy for what was at
one time considered to be enlarged thymus glands [H13]. As discussed in the previous paragraph, ERR
estimates differed significantly between the LSS and United States cohorts. Therefore the “restricted
pooled-analysis” EAR estimate based on these four populations was adopted for the United States
population as a whole by the BEIR VII committee [N19], after including more recent LSS breast cancer
data [P14]. Despite the large United States–Japan difference in baseline rates, this estimate is very close
to the additive projection estimate discussed in the previous paragraph and in part 1 of table C1.
C6.
Female breast cancer: Inconsistencies among irradiated study populations. Data from each offour additional study populations (comprising United States women treated for acute post-partum
mastitis [S15], Swedish women treated for benign breast disease [M8], and two populations of Swedish
women treated with radium plaques for skin haemangioma in infancy [L16, L32]) were found to bestatistically inconsistent with a common model for EAR per unit dose as discussed in the previous twoparagraphs or indeed with each other [P11]. Thus, the Preston et al. [P11] analysis supports the use ofan additive projection of radiation-related breast cancer risk from the LSS cohort to the general UnitedStates population, or (equivalently) of the “restricted pooled-analysis” risk model discussed in thepreceding paragraph. However, the additive models may not be appropriate for populations with benign
breast disease such as acute post-partum mastitis, or for infants treated with radium plaques forhaemangioma.

Table C1. Best estimates and 90% confidence intervals (CI) of risk for specific cancers at age 70 per unit dose of low-LET radiation at age 30 using a linear model
Risk quantity on whichtransfer is based

LSS coefficients(90% CI)

LSS baselinea

Estimated LSS excess rate per unit
dose (90% CI)b

United States (SEER)
baselinec

Extrapolated excess rate per unit dose
(90% CI) for US population

Female breast cancer risk per unit dose (Gy−1) [P14], table 29
ERR per unit dose

0.87 (0.55, 1.3) Gy−1

10.6 per 104 PY

EAR per unit dose

9.2 (6.8, 12.0) per (104 PY Gy)

9.2 (5.8, 13.7) per (104 PY Gy)

41.4 per 104 PY

36.0 (22.8, 53.8) per (104 PY Gy)d

9.2 (6.8, 12.0) per (104 PY Gy)

Gastric cancer risk per unit dose (Gy−1), sex averaged [P14], table 16
ERR per unit dose

0.34 (0.22, 0.47) Gy−1

27.9 per 104 PY

EAR per unit dose

9.5 (6.1, 14.0) per (104 PY Gy)

9.5 (6.1, 13) per (104 PY Gy)

3.63 per 104 PY

1.2 (0.80, 1.70) per (104 PY Gy)d

9.5 (6.1, 14.0) per (104 PY Gy)

Colon cancer risk per unit dose (Gy−1), sex averaged [P14], table 18
0.54 (0.30, 0.81) Gy−1

EAR per unit dose

8.0 (4.4, 12.0) per (104 PY Gy)a

Estimated as the LSS ratio of site-specific EAR to ERR coefficients.

b

LSS ERR × LSS baseline.

cBaseline incidence at age 70 from SEER 14-registry data [I5].

dLSS ERR × SEER baseline.

14.8 per 104 PY

8.0 (4.4, 12) per (104 PY Gy)

15.2 per 104 PY

8.2 (4.6, 12.3) per (104 PY Gy)d

8.0 (4.4, 12.0) per (104 PY Gy)

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 215

ERR per unit dose216 UNSCEAR 2012 REPORT

C7.
Gastric cancer: Baseline rates in Japan and the United States. For gastric cancer, age-specificpopulation incidence rates in Japan are roughly an order of magnitude higher than those in the UnitedStates [I5], and there is strong evidence of a radiation dose response over the dose range 0–4 Gy among
members of the LSS cohort [P14]. Along with the LSS breast cancer estimates just discussed, table C1
presents sex-averaged, linear model estimates of ERR per unit dose and EAR per unit dose for gastriccancer at attained age 70 following exposure at age 30, with 90% confidence intervals ([P14] table 12).
As is the case with breast cancer, the relevant LSS baseline risk for gastric cancer at age 70 in the year
1985 can be estimated as the ratio of the EAR to the ERR per unit dose estimates, i.e. 9.5 per(104 PY Gy) divided by 0.34 = 27.9 Gy−1. According to [I5], the current sex-averaged gastric cancer
rate at age 70 in the United States, as represented by the 14-centre SEER Registry, is 3.63 per 104 PY,
or 7.7-fold less than the corresponding LSS rate. Multiplying the LSS estimate for ERR per unit dose,
0.34 (90% CI: 0.22, 0.47) Gy−1, by this baseline rate yields a multiplicative model projection of the LSS
estimate for the United States population, EAR per unit dose of 36 (90% CI: 23, 54) per (104 PY Gy)
that is 4-fold higher than the corresponding additive model projection given by the LSS EAR per unit
dose estimate, 9.2 (90% CI: 6.8, 12) per (104 PY Gy).
C8.
Gastric cancer: United States cervical cancer study. Unlike breast cancer, very few publishedestimates of radiation-related gastric cancer risk are available for comparison with the LSS ERR andEAR estimates in table C1. One source is a large case–control incidence study of women treated for
cervical cancer, mostly by radiotherapy [B16]. Cases (i.e. patients who developed a second cancer) andtheir matched controls were identified based on records from 20 clinical centres and 19 tumour
registries in Canada, Europe, and the United States. Stomach doses averaging 2 Gy were associatedwith a borderline elevated gastric cancer risk (ERR at 1 Gy = 0.69 with 90% CI: 0.01, 2.25). As in mostepidemiological studies, the confidence interval is just based on statistical fluctuations and does nottake into account other sources of uncertainty, such as uncertainties of the dose estimates. A “crude”
approximate estimate of EAR per unit dose, 3.16 (90% CI: 0.05, 10.4) per (104 PY Gy), was calculated
from the estimated ERR at 1 Gy multiplied by an estimate of baseline gastric cancer incidence based on
previous cohort analyses for the appropriate person-years of observation [B16]. That estimate is
statistically consistent with both the LSS multiplicative and additive gastric cancer projections intable C1 part 2, but is closer to the multiplicative projection. However, the authors cautioned that a
relatively large number of the second cancers identified in the stomach were without pathologicalconfirmation [B16]. An additional, somewhat minor consideration is that women with cervical cancer
might not have the same baseline gastric cancer risk as the general population.
C9.
Gastric cancer: United States peptic ulcer study. A long-term follow-up study of American
peptic ulcer patients given multiple therapeutic doses of 250 kVp X-rays to the stomach found a
statistically significant overall excess of gastric cancer mortality in 1,860 patients irradiated between
1937 and 1965 compared to 1,859 non-irradiated patients treated between 1929 and 1959 [C6, G19].
Cumulative radiation doses, averaged over the entire stomach (mean 14.8 Gy, standard deviation
5.6 Gy, and range 1–42 Gy) and delivered in one or two 6- to 14-day courses of treatment, were far
higher among the irradiated patients than those estimated for any members of the LSS cohort. The
estimated ERR per unit dose over the entire dose range, based on 1,475 patients with more than
10 years of follow-up and an approximately equal number of non-exposed patients, was 0.06 (95% CI:
0.02, 0.10) Gy−1, significantly lower than the LSS estimate of 0.34 (90% CI: 0.22, 0.47) Gy−1 [P12].
However, the estimated ERR per unit dose based on the 309 patients who received stomach doses of
10 Gy or less (mean dose 8.9 Gy) was 0.20 (95% CI: 0.0, 0.73) Gy−1, which is statistically consistent
with the LSS estimate based on radiation doses under 5 Gy.
C10.
Gastric cancer: implications for projection from the LSS cohort. The estimated values of ERR
per unit dose obtained from the peptic ulcer study [C6, G19] for different dose ranges are consistentANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 217

with the LSS estimate of 0.34 (90% CI: 0.22, 0.47) Gy−1 and inconsistent with estimates an order ofmagnitude higher, as would be implied by an additive model projection from the LSS to the UnitedStates SEER population. The cervical cancer study results [B16] are also consistent with multiplicative
projection from the LSS but, because of wider confidence bounds for the ERR per unit dose, they are
not significantly different from the LSS additive projection.
C11.
Colon cancer. The third analysis shown in table C1, for sex-averaged colon cancer, ismethodologically similar to those for female breast cancer and for gastric cancer. In the case of coloncancer, however, baseline rates at age 70 are similar between the LSS cohort and the SEER registry,
and consequently there is little difference between additive and multiplicative projections from the LSS
cohort to the United States SEER population. Risk estimates based on populations other than the LSS
cohort pertain mainly to patients receiving radiotherapy directed at nearby organs, and are generally
consistent with the LSS cohort findings, for example, an ERR per unit dose of 0.5 Gy−1 for colon cancer
mortality among women who received colon doses under 5 Gy following irradiation with intra-uterine
radium (226Ra) capsules (used for treating benign gynaecological bleeding disorders) [I21]. In this casethere is some support for multiplicative projection, but with essentially no consequences in terms ofprojected risk.
C12.
Possible relevance of biological mechanisms for radiation-related cancer. Both additive andmultiplicative projections are plausible in terms of biological mechanisms. For example, to the extent
that different baseline rates in the two populations reflect differential exposure to cancer initiators, andassuming that ionizing radiation acts mainly as a cancer initiator, one might expect the dose-specific
EAR to be the same regardless of baseline rate while, to the extent that the difference in baseline rates
reflects differential population exposure to cancer promoters, the dose-specific EAR might be expected
to increase or decrease proportionally to the baseline rate [N7]. Probably, both kinds of interaction are
involved to some extent and, in the absence of more detailed information on competing initiators andenabling or disabling promoters, it may be useful to model the process as a random mixture ofinteractions of radiation with such baseline risk modifiers. Thus, additive projection would seem to bestrongly supported by the analytical results for the pooled breast cancer analysis involving only the
LSS, pneumothorax, and thymic irradiation cohorts, but not by the results for women therapeutically
irradiated for benign breast disease in general, acute post-partum mastitis in particular, or skinhaemangioma. The gastric cancer dose–response comparisons are more consistent with multiplicative
projection from the LSS compared to the additive projection. However the support from thesecomparisons is not as clear-cut as that provided for breast cancer by the data on the atomic bombing
survivors, pneumothorax patients and thymic irradiation patients. Both analyses, and particularly thegastric cancer example, leave room for uncertainty about the appropriateness of choosing either of thetwo simple projection models.
C13.
Expressing uncertainty about the relationship between excess and baseline risk: the interactive
NIH radioepidemiological tables program (IREP) and NRC BEIR VII committee examples. In cases
where baseline risk differs between two radiation-exposed populations, as it does in the breast cancer
and gastric cancer examples given above, it is certain that multiplicative and additive projections ofradiation-related risk from one of the populations to the other will differ, and thus there is a very realpossibility that whatever projection is chosen will be wrong if it is not supported by comparisons ofdose–response data from both populations. In general, it seems reasonable to incorporate subjective
expressions of the uncertainty about the choice of projection model into the estimate of radiationrelated risk for the population of interest. This is particularly so when the choice of estimate has
consequences for public policy such as radiation protection or adjudication of compensation claims forradiation-related cancer as was the case for the 2003 NIH radioepidemiological tables report [L5]. Thisis also the case for the 2006 BEIR VII report [N19], which is an important information resource for
lifetime risk projections developed at the National Cancer Institute [B7].

218 UNSCEAR 2012 REPORTC14.
For most cancers, the 2003 NIH working group [L5] used a subjective, uncertain mixture ofadditive and multiplicative projection models for transferring cancer risk from the LSS cohort (based
mainly on LSS Tumor Registry data [T4]) to the United States population, as follows:
Projected risk = X × (additive risk) + (1 – X) × (multiplicative risk)(C.3)

where X is a Bernoulli (p) random variable with uncertain parameter p uniformly distributed over theunit interval (0, 1) with probability 0.95, triangular (-0.1, 0, 0) with probability 0.025, and triangular(1, 1, 1.1) with probability 0.025 to express complete uncertainty between the two simple projection
models and to allow for the possibility that the truth might lie outside the additive-multiplicative
domain. For breast cancer, the uncertain Bernoulli distribution parameter was assigned the value p = 1
with probability 0.5, and the model described by equation (C.3) was uniformly distributed withprobability 0.5. For stomach cancer the IREP task group assigned probability 0.5 to the value p = 0 and
0.5 probability to model (C.3).
C15.
Like the 2003 NIH working group, the BEIR VII committee [N19] expressed radiation-related
risk as a stochastically weighted average of an addition (EAR) to and a multiplier (ERR) of baseline
risk. EAR and ERR were formulated as sex-specific functions of radiation dose (D), age at exposure(e), attained age (a), and time (t) between exposure and observation for risk (essentially, t = a – e):Risk(pop, D, e, a, t) = baseline(pop, a) + EAR(D, e, a, t)(C.4)

Risk(pop, D, e, a, t) = baseline(pop, a) × (1 + ERR(D, e, a, t))

(C.5)

and

Most site-specific formulations of EAR and ERR for solid cancers were based solely on analyses ofincidence data from the LSS cohort of atomic bombing survivors studied by the Radiation Effects
Research Foundation [P14]. One exception was the female breast, for which the approach of [P11], as
discussed above, was used with the 1958–1984 LSS tumour registry data replaced by then unpublished
1958–1998 data [P14]. Another exception was thyroid [R3], also used by NIH IREP, for which theformulations were based on pooled analyses of site-specific dose–response data from several different
study populations, including the atomic bombing survivors; and another was leukaemia (all types
combined except CLL) which was based on mortality data from an earlier LSS analysis [P13].
C16.
Comparison of IREP and BEIR VII. For most cancer sites, the BEIR VII algorithm is based
upon more recent data than the earlier NIH (IREP) algorithm, and is to be preferred for that reason.
However, there are other differences that may favour the IREP approach. Both committees assumed
that thyroid cancer risk was multiplicative and that leukaemia risk was additive with respect to sitespecific population baseline risk. BEIR VII used additive risk for breast cancer, with no probability
assigned to multiplicative risk, whereas the NIH IREP committee [L5] used a random mixture ofadditive and multiplicative risks, strongly weighted toward additivity. For all other cancers addressed
except lung cancer, the BEIR VII mixture between additive and multiplicative interaction was on alogarithmic scale with weights of 0.7 for a multiplicative projection and 0.3 for an additive projection.
For lung cancer this weighting was reversed: 0.3 for the multiplicative and 0.7 for the additive
projection. Compared to arithmetic averaging, as in IREP, the BEIR VII multiplicative averaging
scheme is biased towards lower estimated risk because the geometric mean (weighted or unweighted)of two positive numbers is never greater than the arithmetic mean (figure C-I), that is:x p × y1− p is always less than or equal to p × x + (1 − p) × y for 0 < p < 1, y > 0 and x > 0.

(C.6)

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 219

Figure C-I. Comparison of p-weighted arithmetic and geometric means of 1 and 10 for fixed valuesof the parameter p between 0 and 1
Given p, the arithmetic mean is p × 1 + (1-p) × 10 and the geometric mean is 1p × 101-p

1098p × 1 + (1-p) ×

7

Arithmetic mean
Geometric mean

6
5

1p ×

4
3
2
1
0
0

0.2

0.4

0.6

0.8

1

p

C17.
Summary. The comparison of the IREP and BEIR VII approaches to transfer between
populations of risk estimates when additive and multiplicative risk projections differ, show that choiceof a mixture algorithm can make a substantial difference. The geometric and arithmetic mixture
algorithms agree at the extremes, where p= 0 or p= 1, but as shown by the ratio of arithmetic tologarithmic mixtures, the geometric mixture always gives a smaller risk estimate for intermediate
values of p. When the two projections differ substantially, and when the mixture algorithm is more orless evenly weighted between additive and multiplicative mixtures, (e.g. for p=0.5), the difference canbe substantial. In this case, a choice made for computational convenience may unduly influence theconclusions.

II. EXTRAPOLATING RISKS OVER LIFETIME
C18.
Typically, for epidemiological studies of cancer risk in irradiated populations which have been
followed over time following a single exposure, accumulated information on radiation dose will be
specific with respect to age e at exposure and information on subsequent disease events will be specificwith respect to age a at observation or (equivalently) time t = a – e following exposure, assuming
survival until age a. In the BEIR VII report [N19] site-specific, radiation-related solid cancer risks and220 UNSCEAR 2012 REPORT

leukaemia risks in the LSS cohort were modelled as uncertain parametric functions of sex s, neutronweighted radiation dose D, exposure age e, and attained age a. Both additive and multiplicative models
were estimated, as follows:
Riskadd(D, s, e, a) = Base(s, e, a) + βs,add D exp(γ e*) (a/60)η

(C.7)

Riskmult(D, s, e, a) = Base(s, e, a) [1 + βs,mult D exp(γ e*) (a/60)η

(C.8)

The above representation is adapted from BEIR VII table 12–2 [N19] to represent total, rather thanexcess risk as in the original table. The uncertain, sex-specific parameters βs,add and βs,mult are specified
in the BEIR VII report [N19] as log-normal random variables with tabulated medians and 95%
confidence intervals, pertaining to exposure age e and attained age a. The symbol e* represents(e - 30)/10 for e ≤ 30 and zero for e > 30 for all cancer sites represented by the BEIR VII committee. 5
Both the original and the adapted formulae are complex, requiring eight footnotes in the original
publication to record details.
C19.
For present purposes, which are concerned with lifetime risk projection, it is sufficient toconsider two examples: female breast cancer, and stomach cancer among males. The BEIR VII
committee’s preferred model [N19] for female breast cancer was that of additive risk which, as
estimated from a pooled analysis by Preston et al. [P11], was consistent across four exposed population
data sets including the Japanese atomic bombing survivors and three populations of American women
exposed for reasons unrelated to breast disease, two of which received multiple chest fluoroscopy
examinations during lung collapse therapy for tuberculosis and one which received radiation therapy
during infancy for a condition that was at one time considered to be a dangerously enlarged thymus
gland. The preferred linear model risk estimate, that for excess absolute risk per 104 person–years pergray at age a following exposure at age e, isEAR(D, e, a) = β D exp(-0.51 max (0, e–30)/10) (a/60)η

(C.9)

where β is distributed as log-normal with median 9.4 and 95% confidence intervals (6.7, 13.3), and thevalue of η is 3.5 for a ≤ 60 and 1.1 for a > 60, and where a 5-year minimum lag period was assumed
between radiation exposure and cancer diagnosis.
C20.
An interactive computer program under development at the United States National Cancer
Institute and called RadRAT for “Radiation Risk Assessment Tool,” calculates estimated lifetime, sitespecific excess cancer risks associated with user-provided data on organ-specific radiation dose, age at
exposure, sex, and other factors of interest [B8]. The concept is straightforward: age-specific excess
risk at age a following a single exposure at age e is modelled as an uncertain function of a, e, and doseD as in the BEIR VII-based risk model formula given in the previous paragraph. For a single exposure,
age-specific risk estimates are calculated for each attained age a following the stipulated exposure
age e, and summarized as a life table-weighted sum over all ages a greater than e, conditional on
survival until age e. For several exposures at different ages, separate calculations could be performed
for each exposure and summed, conditional on survival until the oldest exposure age.
C21.
For gastric cancer among males, the additive BEIR VII model [N19] for excess absolute risk at
age a per 104 person-years per gray following exposure at age e is
EARadd(D, e, a) = β D exp(-0.41 max(0, e–30)/10) (a/60)2.8
where β is log-normal 4.9 (95% CI: 2.7, 8.9).
5There is a possible exception for breast and thyroid, because the text on BEIR VII pages 272-273 [N19] is contradictory.

(C.10)

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 221

C22.
The BEIR VII report [N19] allows for the possibility that radiation-related gastric cancer risk
is multiplicative as well as additive with respect to baseline risk. The corresponding absolute risk value
for a multiplicative risk model is
EARmult(D, e, a) = Base(s, a) ERR(D, e, a)(C.11)

where Base(s, a) is the baseline risk for sex s and attained age a at dose zero assuming survival until
age a.
ERR(D, e, a) = β D exp(-0.30 × max(0, e–30)/10) (a/60)−1.4(C.12)

again assuming survival to age a, and where β is log-normal 0.21 (95% CI: 0.11, 0.40).
C23.
The BEIR VII report recommended that the multiplicative and additive model estimates should
be combined in the form of a weighted geometric mean of EARadd(D, e, a) and EARmult(D, e, a) ([N19],
table 12–5B). As discussed above in section A of this appendix, there are some arguments against theuse of geometric as opposed to arithmetic means.

III. TRANSFER TO LOW-DOSE AND LOW-DOSE-RATEEXPOSURE WITH LOW-LET RADIATIONC24.
The estimates of excess cancer risks among the atomic bombing survivors relate to acuteexposure with mainly moderate to high doses of low-LET radiation. Most radiation exposures in
occupational or medical diagnostic settings, however, occur at low doses or low dose rates and overlonger times. For radiation protection purposes, an extrapolation of risk coefficients obtained from the
LSS for the atomic bombing survivors has been used in conjunction with a “dose and dose-rate
effectiveness factor (DDREF)” [I14]. This specific interpretation of DDREF has to be differentiatedfrom the results of biological experiments, in which some biological end points are studied for animals
or cell cultures with different radiation exposures but otherwise similar conditions. To be more specific,
it is not straightforward to apply radiobiological results of the DDREF derived from biologicalexperiments directly to transfer risk values from the LSS to occupational or medical exposures in
populations that have a lifestyle and genetic background different from the atomic bombing survivors.
However, such an application of radiobiological results is justified as an approximate approach so longas no sufficient epidemiological data are available. In this context it is important to note thatepidemiological studies of cancer risks after low-dose or low-dose-rate exposures are becoming
increasingly relevant because of the longer follow-up of the historical cohorts of exposed persons, andbecause of improvements in dosimetry, health data and statistical methods. The present section reviewsthe emergence of the concept of DDREF and relevant new radiobiological and epidemiologicalevidence; and provides an evaluation of the uncertainty related to extrapolating risk coefficients fromthe LSS to low-dose and low-dose-rate exposures of other populations.

222 UNSCEAR 2012 REPORT

A. Statements of various bodies up to the UNSCEAR 2006 Report
1.

UNSCEAR

C25.
In the UNSCEAR 1977 Report, the Committee based the derivation of dose–response
relationships for radiation-induced cancer on experimental work on animals, because “the humanepidemiological evidence is (in general) too limited, either in the range of radiation exposures or in the
precision of estimated cancer induction at each dose, to establish clearly the mathematical form of thisdose–effect relationship” [U6]. The Committee concluded that the excess cancer risk per unit dose at
low doses might be substantially lower than the values derived from the atomic bombing survivors with
exposures to gamma rays with doses of the order of 1 Gy. According to annex G, “Radiation
carcinogenesis in man”, of the UNSCEAR 1977 Report, the Committee concluded on the basis ofobservations of genetic effects of low-LET radiation that excess risks per unit dose at low doses could
be lower by a factor of 2 to 4 than those for doses of the order of 1 Gy. The Committee emphasized thatdose–response curves varied among cancer locations, with cancer in the female breast possibly notshowing any dose or dose-rate effect.
C26.
In annex B, “Dose–response relationships for radiation-induced cancer”, of the UNSCEAR
1986 Report, the Committee used a linear–quadratic dose–response model for analysing experimental
data on chromosomal exchanges, mutations and induction of some malignancies [U7]. It was estimatedthat incidence of radiation-induced health effects per unit dose at about 10 mGy are lower than at about
1 Gy by a factor of about 1.5 to 3.0. Based on animal data, the Committee concluded that a linear
extrapolation of risk coefficients obtained at acute exposures with doses of the order of 1 Gy to lowdose or low dose rates “would very likely overestimate the real risk, possibly by a factor of up to 5”.
The Committee defined low dose as being less than 0.2 Gy and low dose rate independent of the doseas being less than 0.05 mGy/min.
C27.
In its 1988 Report, the Committee concluded that the risk at low doses might be lower than theestimated values by a factor in the range of 2 to 10, depending on the dose, dose rate and exposed organ [U8].
C28.
Based on fractionation effects observed for the induction of cancer in animal studies, theCommittee defined in its 1993 Report [U9] low dose rates as those less than 0.1 mGy/min of low-LET
radiation averaged over an hour. The Committee recommended the application of a DDREF for theassessment of cancer risks from low-dose or low-dose-rate exposures. Annex F of the 1993 Reportconcluded that DDREF values obtained from animal experiments ranged up to 10. However, theCommittee pointed out that there was little evidence in epidemiological studies of a lower effectivenessfor solid cancer induction after low-dose exposures, with the exception of breast and thyroid cancer.
For cancer in these two tissues, the Committee judged the DDREF to be of the order of 3. The
Committee recommended the adoption of a value for the DDREF not larger than 3.
C29.
In its 2006 Report, the Committee notes that a value of DDREF much larger than 2 would not
be consistent with the data for the atomic bombing survivors ([U12] annex A). In contrast to its earlier
reports, the Committee explicitly calculated lifetime cancer risks using a linear–quadratic and a linear–quadratic–exponential dose–response model. In a related publication, the linear–quadratic model was
favoured [L19]. According to this model, the lifetime risks per unit dose at doses of 0.01 Sv and 0.1 Sv
were lower than that at a dose of 1.0 Sv by about 20%. In the linear–quadratic–exponential model, therisks per unit dose at 0.01 and 0.1 Sv were lower than that at a dose of 1.0 Sv by about a factor of 2 and3, respectively. Both models implicitly adjust for extrapolation to low doses. The Committee added thatno extra adjustment for chronic exposure (i.e. the application of a DDREF) was needed. Because of theANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 223

large uncertainties involved, the calculations are consistent with an assumed value of 2 for the DDREF
at low-dose and low-dose-rate exposures. Based on these considerations, the Committee defined a valueof 0.1 Gy as an upper value of the low dose range ([U12] annex A, table 6).
C30.
Non-targeted and delayed cellular effects of radiation (including genomic instability), i.e.
bystander effects* that manifest in neighbours or descendants of cells directly hit by radiation, havebeen reported for exposures with low and moderate dose. These effects raised concerns about the linear
no-threshold dose–effect model. Annex C of the 2006 Report of the Committee surveyed these newdevelopments in radiation biology [U13], but concluded at that time that the data currently available did
not require changes in risk coefficients for cancer and hereditary effects in humans of radiation
exposure. Nevertheless the Committee continues to follow developments in this area.

2.

Other bodies

C31.
In its 1990 Recommendations of the International Commission on Radiological Protection,
ICRP included a DDREF in the calculation of nominal risk coefficients for exposures with absorbed
doses below 200 mGy and for exposures with higher absorbed doses when the dose rate is less than
100 mGy per hour [I26]. These values are broadly consistent with the definition of low dose and low
dose rate adopted by the Scientific Committee in its 1988 Report [U8]. ICRP noted that “the full rangeof DDREF values obtained from studies in animals, namely 2–10, may extend over a broader dose
range than human data and therefore include higher values than are relevant,… some human experience
shows little evidence of fractionation effects while others indicate possible effects of up to 3 or 4 atmost” and “direct statistical assessment of the A-bomb survivor data does not seem to allow for much
more than a factor of 2 for the DDREF”. Based on these observations, ICRP adopted a value of 2 forthe DDREF and considered this as conservative. In the 2007 Recommendations of the International
Commission on Radiological Protection ICRP continued to use a value of 2 for the DDREF in
calculations of nominal risk coefficients for exposure with doses below about 100 mSv and emphasizedthat “different dose and dose-rate effects may well apply to different organs/tissues” [I14].
C32.
The BEIR VII committee of the United States National Research Council derived a probability
density function for the DDREF for an analysis of cancer risks at low doses or low dose rates ofionizing radiation and its uncertainties [N19]. Low doses were defined by the range of doses below
100 mGy of low-LET radiation, low dose rates by the range below 0.1 mGy per minute. Medium doses
are defined as doses in excess of 100 mGy up to 1 Gy. BEIR VII analysed mouse data to motivate theassumption that the reduction in risk for low doses is equal to the reduction in risk for dose protraction.
Based on a Bayesian analysis of animal data on cancer risk and life shortening, a probability density
function of the DDREF with a mode of 1.5 and a 95% credible interval from 1.0 to 4.4 was obtained.
An analysis of the atomic bombing survivors resulted in a probability density function for the DDREF
with a mode of 1.3 and a 95% credible interval from 0.8 to 2.6. Combining both distributions, BEIR
VII obtained a probability density function for the DDREF with a mode of 1.5 and a 95% credibleinterval from 1.1 to 2.3. Having performed this analysis, BEIR VII considered the resulting uncertainty
distribution as misleadingly narrow and increased the variance of the logarithm of the DDREF to a
subjectively chosen value of 0.09. Assuming a log-normal distribution this corresponds to a geometricstandard deviation of 1.35, which leads to a 95% adjusted credible interval of 0.82 to 2.73.
C33.
In the Interactive RadioEpidemiological Program (IREP), Kocher et al. use a discrete
probability density function for the DDREF [K7]. The distribution has a mean of 1.8, the lowest value
assumed is 0.5, the highest value is 4.0 (see figure C-II).

224 UNSCEAR 2012 REPORT

Figure C-II.

Cumulative probability density functions for the DDREF

The smooth solid line corresponds to the inverse of a combined estimator of the ratio of the excess relative risks for solidcancer in low-dose-rate, moderate-dose studies and the excess relative risk among atomic bombing survivors for the samegroup of cancer types, organ dose, gender distribution and corresponding age at exposure and age attained [J5]. The smoothbroken line gives the distribution as derived by BEIR VII [N19]. Note that BEIR VII used in its risk calculations an uncertainty
distribution with a width larger than that given in the figure. The dotted line gives the discrete distribution used in IREP [K7]B. New radiobiological information
C34.
The Committee summarized biological effects at low radiation doses in annex G of its 2000
Report [U11] and updated the statement by information on non-targeted and delayed biological effects
of exposure to ionizing radiation in the 2006 Report [U12]. This present section summarizes shortly
new information in the field of radiobiological research potentially relevant to an evaluation of theuncertainty in the DDREF for solid cancer after exposure to low-LET radiation with low doses, or withmoderate doses with low dose rates.
C35.
Recent research supports the thesis that radiation causes damage to DNA in linear proportion
to dose over a wide range of doses down to very low doses [L20]. Also, the reduction rate of thenumber of phosphorylated ataxia telangiectasia mutated (ATM) foci with time after exposure did notdepend on dose in a range of 10 mGy to 1,000 mGy [S34]. However, a number of observations showthat the DNA damage response to that damage might well be non-linear [G24, N13, O2]. A DNA
damage threshold level seems to be required, for example, for the activation of the early G2/M cell
cycle checkpoint resulting in low-dose hypersensitivity in the survival of many—but not all—cell types[D7, L21, W12]. In summary, it is unclear whether double-strand-break (DSB) repair is equally
efficient after exposures with low and moderate/high doses.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 225

C36.
Bystander effects, such as mutations, chromosomal aberrations or apoptosis, are induced at
low doses and saturate at moderate doses [N1, P7]. It is presently unclear whether such bystander
effects influence carcinogenesis after radiation exposure, and, if yes, whether they are protective or
detrimental.
C37.
Gene expression and phosphoproteomics profiling suggest differences in processes induced by
low and moderate doses of low-LET radiation. A number of studies identified genes that weremodulated by low doses but not by high doses [F6, J14, K18, L24, S13]. In another study, the numberof genes with changed expression was found to increase with dose rate, indicating that higher dose rates
influence more cellular processes than low dose rates [U4]. Analyses of the proteome indicatedoverlapping and unique biological processes after exposures with 20 mGy and with 500 mGy [Y2].
Overall, the state of knowledge on gene expression and proteome abundance after exposure to ionizing
radiation and its relevance to carcinogenesis is still very limited.
C38.
In its 2006 Report [U12], the Committee stated that the implications of non-linear dose
responses of cellular effects for the form of the dose response of carcinogenesis in humans are unclear.
The statement remains valid for the new finding described above. In summary, cellular radiation
biology contributes in only a limited manner to an extrapolation of observable cancer risks at
high/moderate doses to low doses, and thus to quantifying the DDREF.
C39.
Recent experiments on solid cancer in irradiated mice resulted in values of the excess relativerisk per unit dose at about 0.1 Gy comparable or even larger than those at about 1.0 Gy [C19, S3, S4].
There is thus little evidence in recent animal experiments that the ERR per unit dose for solid cancer islower for low doses than for dose values that were relevant for determining risk values in the LSS(0.2 to 2 Gy).
C40.
It has been argued in the literature that the response of cells, tissues, organs or the whole bodyto damage caused by ionizing radiation may involve deterministic mechanisms that may lead topractical thresholds in the dose response [F3, T9]. Such mechanisms include: scavenging of toxins;
molecular repair of DNA; removal of damaged cells by apoptosis, necrosis, phagocytosis, cellsenescence or immune responses; or loss of the potential for self-renewal of preneoplastic cells bydifferentiation. A prolongation of life span of mice exposed at low dose rates has been found andassociated with immunological modifications [I20]. The Committee acknowledges that developments
in studies on these kinds of mechanisms need to be followed to gain better insight for the evaluation ofhealth risks from low-dose or low-dose-rate exposures.

C. New epidemiological information
C41.
Muirhead et al. analysed an update and extension of mortality and cancer incidence data for
the United Kingdom National Registry for Radiation Workers [M21]. This study is a large study ofcancer after occupational exposures. It includes 114,541 workers with exposures mostly to X-rays andgamma-rays. The mean badge dose was 24.9 mSv. In total, 68% of the workers had doses below
10 mSv, 26% in the range of 10−100 mSv, and 6% of the doses exceeded 100 mSv. The data on
workers demonstrated a strong healthy worker effect: the standardized mortality ratio for malignant
neoplasms was 0.84 with a 95% confidence interval from 0.82 to 0.86. As in most epidemiologicalstudies, the confidence interval is just based on statistical fluctuations and does not take into accountother sources of uncertainty, such as uncertainties of the dose estimates. In analyses with a linear dose–
response model, all four estimates of excess relative risks per unit dose for mortality from and226 UNSCEAR 2012 REPORT

incidence of leukaemia and of malignant neoplasms excluding leukaemia were found to be significant(table C2) and to be consistent with corresponding values among the atomic bombing survivors.
Table C2. Best estimates and 90% confidence intervals of excess relative risks per unit dose (Sv−1)
in the third analysis of the United Kingdom National Registry for Radiation Workers [M21]
Outcome

Leukaemia excluding CLL

Malignant neoplasms excluding leukaemia

Mortality

1.7 (0.06, 4.3)

0.28 (0.02, 0.56)

Incidence

1.8 (0.17, 4.4)

0.27 (0.04, 0.51)

C42.
A larger number of epidemiological studies on solid cancer risks after low-dose-rate,
moderate-dose exposures has been published recently and is summarized in appendix D.
C43.
Jacob et al. evaluated 12 recent studies of solid cancer mortality and incidence after protracted
exposure with moderate cumulative doses [J5]. For each of the low-dose-rate, medium-dose studies,
they calculated the risk for the same types of cancer among the atomic bombing survivors with thesame gender proportion and matched quantities for dose, mean age attained and mean age at exposure.
The main analysis included seven independent mortality studies: five on radiation workers, one on
emergency and clean-up workers after the Chernobyl accident, and one on the residents of villages
located along the banks of the Techa River in the Southern Urals. Analyses of the remaining mortality
studies and of the incidence studies were consistent with the main analysis. In the main analysis, thecombined estimator of the ratio of the excess relative risk per unit dose from the low-dose-rate,
medium-dose study to the corresponding value for the atomic bombing survivors was found to be 1.21
(90% CI: 0.51, 1.90). Omitting one of the studies changes the best estimate of the ratio at most by 26%.
The lowest risk ratio with a value of 0.96 (90% CI: 0.12, 1.80) was obtained when the study of the
Techa River residents was excluded. The highest risk ratio with a value of 1.44 (90% CI: 0.48, 2.41)
was obtained when the study of the United Kingdom radiation workers was excluded. It is noted thatnone of the low-dose-rate, moderate-dose studies took dose uncertainties into account. It can be
expected that the uncertainty ranges of the risk estimates become larger, if such uncertainties are taken
into account.

D. Evaluation of the uncertainty of the DDREF
C44.
This section summarizes results on the distribution of the DDREF specifically for the transferof excess risks as observed among the atomic bombing survivors to low-dose or low-dose-rate
exposures. Figure C-II illustrates distributions obtained by:(a) BEIR VII from a Bayesian analysis of cancer and life shortening data in mouse experiments,and of solid cancer incidence among the atomic bombing survivors [N19];(b) Kocher et al. by evaluating radiobiological and epidemiological data for an application in theInteractive RadioEpidemiological Program [K7];(c) Jacob et al. by a comparative analysis of recent low-dose-rate, medium-dose epidemiologicalstudies and data for the atomic bombing survivors [J5].
The ratio of the upper and lower bounds of the 95% confidence intervals for the DDREF were 3.2 in therisk calculations of BEIR VII [N19] and 5.7 in the distribution assumed in [K7]. In the analysis of

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 227

recent epidemiological data the ratio of the bounds of the 90% confidence interval was 3.7 [J5]. Basedon these results, the Committee considers that the present knowledge or degree of belief of the value of
the DDREF may be expressed by an uncertainty range with a ratio of the upper and lower bounds of the
90% confidence interval in the order of four but not smaller.
C45.
The Committee acknowledges that recent epidemiological studies do now allow for a direct
assessment of the uncertainty distribution for the ratio of relative cancer risks in low-dose-rate,
medium-dose exposure scenarios and among atomic bombing survivors. Such exposure scenarios are
typical for workers with higher occupational exposures. Recent epidemiological work indicates risk perunit dose values for such exposures similar to those observed in the LSS for the atomic bombing
survivors. The geometric standard deviation of the probability density function for the DDREF isestimated to be about 1.5 (see figure C-II). For higher dose rates/doses the uncertainty of the DDREF is
assumed to be less, for lower dose rates/doses to be larger.

E. Uncertainty associated with the projection of risk to theregion of low and very low doses
C46.
Sometimes situations arise where a projection of risk is required for exposed or potentially
exposed individuals or populations in which cumulative doses are substantially below levels for which
there is direct epidemiological evidence of a statistically significant increase in health effects. In thesesituations, the uncertainty in risk projection should include uncertainty in the dose–response models
used to extrapolate risk beyond the domain of direct epidemiological evidence. Model uncertainty (seeappendix B) ought to be addressed through consideration of alternative dose–response functions each ofwhich represents a plausible biological explanation for the extrapolation of risk to low and very low
cumulative doses (cumulative doses substantially less than 100 mGy in addition to the 1 mGy to
10 mGy contributed annually by background from natural sources of radiation).
C47.
Alternative risk projection models used to extrapolate risk to the region of low and very low
cumulative dose may include dose–response functions that are non-linear with respect to theincremental cumulative dose above background. Such dose–response functions may include a threshold
dose, below which the incremental increase in risk with increasing dose is zero, or negative. The degreeof plausibility attributed to a given dose–response model is represented by an assigned fraction orweight. This weight would be determined by (a) the extent to which the model adequately explains thedose–response function in epidemiological studies for which there is direct evidence of a statisticallysignificant relationship between an increase in cumulative dose and an increase in disease and (b) the
extent to which there is evidence for biological mechanisms that support the extension of the model toestimate risk in the region of low and very low cumulative dose.
C48.
Information about biological mechanisms that could be used to support a risk projection model
applied at low cumulative doses may come from in vivo experiments in animals or in vitro cultures ofhuman or animal tissues and cells. Models of carcinogenesis are particularly suited to integrateknowledge about biological mechanisms in the risk projection. In the case of maximum uncertainty, allrisk projection models that are considered reasonably plausible are assigned equal weight (the weight
would be 1/N, where N is the number of plausible alternative risk projection models underconsideration).

228 UNSCEAR 2012 REPORT

C49.
When risk estimation involves risk projection to the region of low and very low cumulative
dose, the overall uncertainty in the risk ought to be larger than the uncertainty in risk at dose levels forwhich there is direct epidemiological evidence.
C50.
At low to very low dose, the lower bound of the uncertainty interval may overlap zero
additional risk. The final result will depend on the dose–response functions employed by the models
used for low-dose risk projection and the plausibility weights assigned to each of the alternative risk
projection approaches. It is likely, however, that the upper limit of uncertainty on the estimated risk will
not be substantially affected by uncertainty in dose–response models used for risk projection, unless theweight of evidence supporting risk thresholds at low and very low dose is strong [I12, L4].

IV. TRANSFER FOR EXPOSURES TO OTHER TYPES OF RADIATION

A. Modifying factors to estimate risks of cancer for different
radiation types
C51.
Estimates of cancer risks from exposure to ionizing radiation are based primarily on analysesof data on dose response for members of the LSS cohort, who mainly received acute exposures to highenergy photons. When those data are used to estimate cancer risks from exposure to other types ofradiation (for example, neutrons, alpha particles, and lower-energy photons and electrons), estimatedrisks for the LSS cohort should be modified to account for the possible dependence of risks at a given
absorbed dose in radiation type. In radiation protection, this dependence is represented by the quality
factor (Q) and radiation weighting factor (wR) [I14]. However, those quantities are defined point values
with no uncertainty that are used to calculate the protection quantities dose equivalent, equivalent dose,and effective dose; they are not intended for use in estimating risks of cancer from actual exposures ofidentified individuals or groups [I7, I14].
C52.
This section discusses a modifying factor to represent the effectiveness of different radiation
types, compared with high-energy photons, in inducing cancer in humans. It also discusses uncertainty
distributions for that factor that were developed for use in estimating risks from actual exposures. For agiven radiation type, this factor is a quantity analogous to Q and wR that modifies an estimate ofabsorbed dose in an organ or tissue of concern to obtain a biologically significant dose on which therisk of cancer in that organ or tissue is assumed to depend. Modifying factors for different radiation
types and their uncertainties are estimated mainly on the basis of data on relative biologicaleffectiveness (RBE) obtained from radiobiological studies. Modifying factors for some radiation types
can also be estimated on the basis of epidemiological data.
C53.
The modifying factor to represent the effectiveness of a given radiation type in inducing cancer
in humans for the purpose of estimating risks from actual exposures was called a “radiation
effectiveness factor” by Kocher et al. [K6]. Use of a term other than RBE to denote this modifying
factor was based on two considerations: (a) an RBE, as strictly defined [N4], represents the results ofradiobiological studies under controlled conditions; and (b) whereas an RBE is a ratio of absorbed
doses of different radiation types that give the same biological response [N4] the quantity of interest in
estimating cancer risks is a ratio of risks at the same absorbed dose, in a manner analogous to the use of

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 229

Q and wR in radiation protection. The two ratios generally are not the same. Other investigators haveincorrectly referred to this modifying factor as an RBE.
C54.
Specification of a reference radiation, with a defined biological effectiveness of one, is
important in estimating modifying factors to represent the effectiveness of different radiation types in
inducing cancer in humans. In radiobiological studies to estimate RBEs, the reference radiation often ishigh-energy gamma rays from decay of 60Co or, less commonly, 137Cs or orthovoltage (180–250 kVp)
X-rays. However, many radiobiological studies have shown a significant difference in the effectivenessof high-energy gamma rays and X-rays in inducing stochastic effects.* High-energy photons, such as
60
Co gamma rays, are the more appropriate reference radiation when it is considered that their energies
are closer to the mean energy of photons in exposures of the LSS cohort [I11, K6].

B. Quantification of modifying factors up to UNSCEAR 2006 Report
C55.
In past UNSCEAR reports, including its 2006 Report [U12], the Committee did not evaluate
radiobiological and epidemiological data for the purpose of estimating modifying factors to represent
the effectiveness of different radiation types in inducing cancer in humans. Although ICRP [I11]evaluated data on RBE, the purpose was to inform judgements about values of Q and wR for use inradiation protection. ICRP’s evaluation was not aimed at developing estimates of modifying factors for
specific radiation types and their uncertainties for use in cancer risk assessments.
C56.
Prior to the UNSCEAR 2006 Report [U12], Kocher et al. [K6] presented the first effort toestimate modifying factors and their uncertainties for all the radiation types of primary concern in
exposures of workers and the public, including lower-energy low-LET radiations as well as neutrons
and alpha particles. Subjective probability density functions of modifying factors to represent theiruncertainty were developed on the basis of an evaluation of radiobiological and epidemiological data.
Those probability density functions are incorporated in models to estimate cancer risks and theiruncertainty in the Interactive RadioEpidemiological Program (IREP) [K7, L5].
C57.
Since the analysis by Kocher et al. [K6] was first presented, other investigators have developed
estimates of modifying factors and their uncertainties for alpha particles and tritium beta particles.
C58.
The following sections discuss values for modifying factors and their uncertainties forneutrons, alpha particles, lower-energy photons, and low-energy electrons that were developed for use
in cancer risk assessments. Modifying factors for other radiation types that are of concern only incertain medical procedures, unusual occupational exposures, or travel in space (i.e. protons, fission
fragments, and heavy ions) are not considered. A recent NCRP report [N12] includes a detailed review
of modifying factors and their uncertainties for all radiation types of potential concern, including
radiation types not considered in this report.

C. Modifying factors for neutrons
C59.
An analysis by Kocher et al. [K6] is the only effort to date to develop subjective probability
density functions of modifying factors for neutrons. Modifying factors were developed that applied
over the ranges of energies defined by the step-function representation of wR recommended in ICRP
Publication 60 [I7]. Separate modifying factors for induction of solid cancers and leukaemias were230 UNSCEAR 2012 REPORT

developed on the basis of estimates of RBE for cancer induction or life shortening due primarily tocancer in laboratory animals, which indicated that the effectiveness of neutrons in inducing leukaemias
is substantially lower. Ratios of the upper bound to the lower bound of the 95% CI of subjective
probability density functions ranged from 10 to 30, depending on the cancer type (solid cancers or
leukaemias) and neutron energy.
C60.
Several issues arise in estimating modifying factors for neutrons and their uncertainties [K6,N12]. In addition to accounting for a difference in the effectiveness of neutrons in inducing solidcancers and leukaemias, challenges include (a) the paucity of relevant data on RBE at energies outside
the energy range of most fission neutrons, (b) the likelihood that RBEs for induction of cancers and life
shortening due primarily to cancers in laboratory animals overestimate the effectiveness of neutrons in
inducing cancer in humans [I11], and (c) the observed increases in RBEs with decreasing dose. In
addressing the last issue, Kocher et al. [K6] adopted an approach of developing modifying factors for
induction of solid cancers that applied at any dose and dose rate on the basis of estimates of RBE athigh acute doses, RBEH [C9, E1, E2]. The advantage of that approach, which can be used when a linear
dose response in humans is assumed, is that it reduces uncertainty in modifying factors. That approach
could not be used in developing modifying factors for induction of leukaemias, given the assumption ofa linear–quadratic dose response in humans. Those modifying factors were based on estimates of RBE
at low doses and low dose rates, RBEM.
C61.
Kocher et al. [K6] applied a small correction to the assumed probability density functions ofmodifying factors for neutrons to account for a possible inverse dose-rate effect in cases of chronic
exposure. That correction, which was assumed to be uncertain, takes into account that the effectivenessin inducing cancer may increase when a given dose of neutrons is delivered at lower dose rates [C9, I7,
I11, N4].

D. Modifying factors for alpha particles
C62.
Several issues arise in developing modifying factors for alpha particles and their uncertainties[K6, N12]. Perhaps the most important issue is a consequence of the short ranges of alpha particles intissue [I19]. When the location of critical target cells relative to the location of internally depositedalpha-emitting radionuclides is not known precisely, estimates of absorbed dose in the critical cells may
be highly uncertain, and estimates of RBE for alpha particles and inferences about modifying factors
may be erroneous. This issue may be especially important when alpha emitters are incorporated in theskeleton and bone cancer or leukaemia is the disease of concern.
C63.
Other challenges in developing modifying factors for alpha particles include (a) the
pronounced increases in values of RBE with decreasing dose in radiobiological studies [N4], (b) the
possible dependence of modifying factors on cancer type, including differences in modifying factors for
induction of specific solid cancers as well as a difference in modifying factors for induction of solidcancers and leukaemias, and (c) the use of low-LET reference radiations other than high-energy gamma
rays in radiobiological studies to estimate RBEs, especially the use of beta-emitting radionuclides instudies of bone or lung cancer in animals. Given that most estimates of RBE for alpha particles wereobtained under conditions of chronic exposure, risks of solid cancers, as well as leukaemias, must be
estimated using modifying factors at low doses and low dose rates that are based on estimates of RBEM.
C64.
Estimates of modifying factors for alpha particles and their uncertainties developed by various
investigators are summarized in table C3 and described below.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 231

Table C3. Summary of subjective probability density functions of values of modifying factors for
exposures to alpha particles developed by various investigators for use in cancer risk assessmentsa
Reference

Cancer type

Modifying factor
95% subjective
confidence intervalMedianMean

Kocher et al. [K6]

All solid cancers(3.0, 80)b

15.5

22

Grogan et al. [G20, G21, G22]

Lung

b

(9.3, 96)

30

36

Liver

(8.0, 50)b

20

22

Bone

(10, 156)b

40

51

b

(4.1, 49)

14

17

EPA [U3]

All solid cancers except bone

Gilbert et al. [G9]Lung(14, 98)

33d

Jacob et al. [J3]Lung

(6, 112)15d

ICRP [I11]Bone(6.7, 380)b50

85

Kocher et al. [K6]

Leukaemias(1.0, 33)e

Grogan et al. [G20, G21]
EPA [U3]

c

3.6

6.7

Leukaemiasb(0.95, 9.5)

3.0

3.6

Leukaemias(1.0, 3.9)b

2.0

2.1

a
Modifying factors are intended to represent the effectiveness of alpha particles in inducing cancer in humans, compared withhigh-energy photons; they apply at low doses and low dose rates.
b

Assumed probability density function is log-normal.

cModifying factor of 10 for bone cancer is assumed; uncertainty was not assessed.

dValue was “central estimate” and was not identified as median or mean.

eAssumed probability density function is three-component hybrid distribution.

1.

Modifying factors for alpha particles and solid cancers

C65.
Kocher et al. [K6] developed a subjective probability density function of a modifying factor
for induction of all solid cancers on the basis of estimates of RBEM for induction of bone or lung cancer
in laboratory animals [I6, M20, N4]. This distribution was supported by estimates of RBEM for various
stochastic effects in cell systems.
C66.
Grogan et al. [G20, G21, G22] developed separate subjective probability density functions ofmodifying factors for induction of lung, liver, or bone cancer. These distributions were based in part on
estimates of RBEM for induction of cancers in laboratory animals [I6, M20, N4]. The probability
density functions for liver and bone cancer also were based on comparisons of estimated risks inmedical patients who were administered Thorotrast with estimated risks for the LSS cohort. The
probability density function for bone cancer also took into account an estimate of the relative toxicitiesof 239Pu and 90Sr in inducing bone tumours in beagles.
C67.
The United States Environmental Protection Agency (EPA) used an analysis of selected data(including a comparison of estimated risks of lung cancer for underground miners from exposure toradon decay products with estimated risks for the LSS cohort) to develop a subjective probability
density function of a modifying factor for induction of all solid cancers [U2]. That distribution was
retained in EPA’s recent revision of its cancer risk models [U3], except a modifying factor of 10 for232 UNSCEAR 2012 REPORT

bone cancer, with no uncertainty, was adopted on the basis of a comparison of data on induction ofbone cancer in beagles injected with 226Ra or 90Sr. EPA [U3] also discussed (a) recent estimates of
RBEM for induction of lung cancer in beagles, which range from about 1.5 (95% CI: 0.7, 9) to about 20,
and (b) comparisons of risks of lung cancer for underground miners and for the LSS cohort based onrecent data, which suggest that the modifying factor for lung cancer could be in the range ofabout 2−11.
C68.
Gilbert et al. [G9] and Jacob et al. [J3] developed subjective probability density functions of amodifying factor for induction of lung cancer on the basis of comparisons of estimated risks for Mayakworkers exposed to plutonium with estimated risks for the LSS cohort. The modifying factor developedby Gilbert et al. [G9] applies to male and female workers, whereas the modifying factor developed by
Jacob et al. [J3] applies to males only. By using an alternative risk model for Mayak workers, Jacob et
al. [J3] also obtained a modifying factor with a 95% CI of (9, 81).
C69.
ICRP [I11] reviewed estimates of RBE for alpha particles and derived a subjective probability
density function of a modifying factor for induction of bone cancer. ICRP [I11] also discussed
estimates of RBE obtained in studies of stochastic effects in cells.

2.

Modifying factors for alpha particles and leukaemias

C70.
Kocher et al. [K6] developed a subjective probability density function of the modifying factor
for induction of leukaemias on the basis of three lines of evidence: (a) a comparison of estimated risks
for medical patients who were administered Thorotrast with an estimated risk at low doses and low
dose rates of high-energy photons derived by EPA [U3] from data for the LSS cohort and an assumed
DDREF; (b) an evaluation by EPA [U2] of risks of leukaemias for radium dial painters who ingested
226
Ra and for medical patients who were administered 224Ra compared with risks for Thorotrast
patients; and (c) estimates of RBE for induction of leukaemias in mice by fission neutrons and anassumption that RBEs for alpha particles and fission neutrons should be similar [I18, S21]. Subjective
weights were assigned to probability density functions that were assumed to represent each of thosedata sets.
C71.
Grogan et al. [G20, G21] developed a subjective probability density function of a modifying
factor for induction of leukaemias on the basis of (a) a comparison of estimated risks of leukaemia for
Thorotrast patients and the LSS cohort and (b) estimates of RBE for induction of leukaemias in mice byfission neutrons. A single probability density function was assumed to represent both data sets.
C72.
As noted above, EPA [U2] initially derived a modifying factor for induction of leukaemias on
the basis of estimated risks in radium dial painters and two groups of medical patients. That modifying
factor was in the range 0–1. In the recent revision of its cancer risk models, EPA [U3] took into account(a) estimated risks for Thorotrast patients; (b) recent estimates of risks for the LSS cohort; and (c) arecent analysis of risks for ankylosing spondylitis patients who were injected with 224Ra. The higher
modifying factor now assumed by EPA was supported by an RBE for induction of leukaemias in miceby fission neutrons [U3].
C73.
ICRP [I11] discusses data for Thorotrast patients and the LSS cohort, which indicated that themodifying factor for induction of leukaemias is much less than the wR of 20, and notes a conclusion by
the International Agency for Research on Cancer [I4] that the modifying factor is in the range of 1–2.
ICRP [I11] also discusses a study in haematopoietic stem cells in mice, which indicated an RBE
relative to X-rays of about 11 for a chromosome aberration associated with leukaemia. The RBE
relative to high-energy gamma rays could be higher.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 233

C74.
Assessments of risks of leukaemias due to intakes of alpha-emitting radionuclides depend on
an assumption that ICRP’s dosimetric models for alpha emitters deposited in the skeleton are accurate.
However, this assumption can be questioned when the location of alpha emitters relative to critical stem
cells in bone marrow is not known precisely [K6, U3]. Possible errors in dosimetric modelling could
result in an underestimation of the uncertainty in the modifying factor for induction of leukaemias.
Possible errors in dosimetric modelling can be taken into account, at least to some extent, byincorporating estimates of RBE for induction of leukaemias in mice by fission neutrons into theprobability density function for the modifying factor for alpha particles [G20, G21, K6]. Kocher et al.
[K6] also emphasized the desirability of separating the problem of dosimetric modelling for internalalpha emitters from the problem of estimating the effectiveness of alpha particles in inducing cancer.

3.

Correction for inverse dose-rate effect

C75.
Kocher et al. [K6] applied a small correction to their assumed probability density functions ofmodifying factors for alpha particles to account for the possibility of an inverse dose-rate effect at low
doses. The uncertain correction was assumed to be smaller for alpha particles than for neutrons.
C76.
It can be argued that an inverse dose-rate effect should not be taken into account explicitly inestimating cancer risks in humans from intakes of alpha-emitting radionuclides [K6]. For example, thiseffect has not been seen in studies of underground miners at the lowest levels of exposure to radon
decay products [L25], and estimates of RBEM obtained in radiobiological studies under conditions ofchronic exposure may account for any such effect in humans. However, an assumption of a small
inverse dose-rate effect at low doses may be supported by an analysis of risks of lung cancer fromexposure to radon decay products in homes [F4], which suggests that the risk per unit exposure issomewhat larger in residential settings than at higher levels of exposure in underground mines.

4.

Discussion of modifying factors for alpha particles

C77.
The subjective probability density functions of modifying factors for alpha particles
summarized in table C3 illustrate a number of important points. Uncertainties in the modifying factors
are large, ranging from about 6 to nearly 60. Central estimates and their uncertainties can depend on
cancer type, even for different solid cancers. Some differences in modifying factors are a consequenceof differences in assumptions about radiobiological and epidemiological data to be used in an analysis.
Finally, all the analyses illustrate the importance of subjective scientific judgement in estimating
modifying factors and their uncertainties.

E. Modifying factors for lower-energy photons
C78.
Many radiobiological studies and microdosimetric calculations have indicated that theeffectiveness of X-rays at about 250 kVp or less in inducing stochastic effects at low doses and low
dose rates is a factor of about 2–3 higher than the effectiveness of high-energy gamma rays [B18, I18].
The BEIR VII Committee [N19] and ICRP [I11, I14] acknowledged that the greater effectiveness of
X-rays is potentially important in cancer risk assessments.

234 UNSCEAR 2012 REPORT

1.

Modifying factors as a function of photon energy

C79.
An analysis by Kocher et al. [K6] is the only effort to date to develop subjective probability
density functions of modifying factors for lower-energy photons. One modifying factor was assumed toapply at energies of 30−250 keV, and a higher modifying factor was assumed to apply at energies lessthan 30 keV. The uncertainty in the assumed modifying factors was a factor of about 5 at 30−250 keV
and about 6 at the lowest energies. Photons of energy greater than 250 keV were assumed to have amodifying factor of 1.0, with no uncertainty.
C80.
The subjective probability density function of the modifying factor at photon energies of30−250 keV [K6] was based in large part on estimates of RBEM for induction of dicentric chromosome
aberrations in human blood lymphocytes by 220–250 kVp X-rays [N4]. That distribution also took into
account (a) indirect estimates of RBE for X-rays obtained by comparing estimates of RBE for radiations
other than photons relative to X-rays with estimates for the same end point in the same biological system
relative to high-energy gamma rays; (b) comparisons of risks of specific cancers for the LSS cohort (forexample, thyroid and breast cancer) with risks for medical patients exposed to X-rays; and (c) acomparison of incidences of thyroid tumours in rats exposed to 131I beta particles or X-rays. Comparisonsof cancer risks for the LSS cohort and medical patients and the study in rats were inconclusive owing tolarge uncertainties in the data. For example, the 95% CI of the RBE for X-rays inferred from the data on
risks of thyroid cancer for the LSS cohort and medical patients was 0.2–4.0 [K6].
C81.
The subjective probability density function of the modifying factor at photon energies less than
30 keV [K6] was based on the probability density function at 30–250 keV and an increase in theeffective quality factor for photons at energies less than 30 keV ([I18] Fig. 3).

2.

Recent estimates of RBE for lower-energy photons

C82.
A variety of radiobiological data more recent than data reviewed by NCRP [N4] could be used
to develop subjective probability density functions of modifying factors for lower-energy photons.
Examples include an extensive set of estimates of RBEM and their uncertainties for induction ofdicentric and acentric chromosome aberrations in human blood lymphocytes [B24, K16, S7, S8]. ICRP
[I11] concluded that the data for dicentrics provide the most reliable information on RBEM for
conventional (orthovoltage) and lower-energy (for example, mammography) X-rays. RBE and theiruncertainties also have been obtained in studies of chromosome aberrations in human mammary glandepithelial cells [B10], micronucleus formation in various human and mouse cells [H20, L11, S22, V2],and neoplastic transformations in CGL1 human hybrid cells [F7, G13, H12]. However, several of thesestudies used orthovoltage X-rays as the reference radiation, and not all estimates are for an RBEM.
C83.
Estimates of RBE for induction of various aberrations in human blood lymphocytes by lowenergy photons also have been obtained in recent studies using multi-fluor fluorescence in situ
hybridization (mFISH) or FISH [M11, M12]. Data on dose response for induction of dicentricchromosome aberrations or apparently simple translocations obtained in one study [M11] gave
estimates of RBEM for 30 kVp X-rays relative to 60Co gamma rays substantially lower than the RBEM
for induction of dicentrics by 29 kVp X-rays reported by Schmid et al. [S7]. Other estimates of RBE forlow-energy photons obtained in studies using FISH or mFISH are relative to 120 or 180 kVp X-rays.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 235

3. Validity of estimates of RBEM for induction of dicentric chromosome
aberrations
C84.
Studies of induction of dicentric chromosome aberrations in human blood lymphocytes
provide the most extensive set of data on RBEM over a wide range of photon energies. Recent estimatesof RBEM for dicentrics [B24, K16, S7, S8] and the earlier estimates used by Kocher et al. [K6] wereobtained in studies in which aberrations were scored by conventional Giemsa staining [I2]. However,recent studies using mFISH have raised doubts about the validity of using such estimates of RBEM toestimate modifying factors for lower-energy photons. Studies using mFISH revealed two concerns
about the data for dicentrics and the conventional use of a linear–quadratic model to represent the dose
responses for lower-energy photons and the reference radiation and to derive estimates of RBEM
[N12, T7].
C85.
A study of induction of chromosome aberrations in human lymphocytes following acuteexposure to high doses of high-energy gamma rays using mFISH [L22] showed that the upwardcurvature in the dose response that is commonly observed when those aberrations are scored byconventional Giemsa staining is due mainly to the competing influences of simple chromosome
exchanges (which are important at any dose) and complex exchanges (which are important only at highdoses), rather than a curvature in the dose response for a single end point (simple exchanges).
Furthermore, the dose response for simple exchanges was nearly linear at all doses, with only a slight
upward curvature. When a linear–quadratic model is used to represent a dose response for multiple end
points, none of which is linear–quadratic in form, derivation of an RBEM from the initial slopes of themodelled dose responses for the lower- and higher-energy photons may produce misleading estimates[L23]. In such an analysis, the curvilinear dose responses for complex exchanges, which are important onlyat higher doses, distort (mask) the initial linear slopes in the dose responses for simple exchanges only.
C86.
The second important observation resulted from a study of induction of chromosome
aberrations in human fibroblasts by high-energy gamma rays using mFISH [L23]. Data for simple
aberrations were obtained under conditions of acute exposure or chronic exposure at low dose rates. As
in the study discussed above [L22], the dose response for simple aberrations following acute exposure
was nearly linear at all doses. The dose response for chronic exposure at low dose rates also was linear,
but the slope was a factor of 5–6 less than the slope of the dose response at high dose rates. This large
difference was contrary to an expectation based on an assumption of a linear–quadratic model that theslope of the linear dose response for simple chromosome exchanges ought to be independent of dose rate.
C87.
Studies using mFISH described above indicate that data on dose response for dicentricchromosome aberrations in human lymphocytes that are scored by conventional Giemsa staining
probably cannot be used to estimate modifying factors for lower-energy photons and their uncertainty.
The same concern arises in using data on acentric aberrations.

4.

Adequacy of data to estimate modifying factors for lower-energy photons

C88.
Given the problem with conventional studies of dicentric chromosome aberrations in human
lymphocytes noted above, which probably invalidates the use of the most extensive data on RBEM toestimate modifying factors for lower-energy photons, other radiobiological data appear to be inadequate
to characterize the energy dependence of the modifying factor for photons. This limitation is an
important concern when X-rays over a broad range of energies are commonly used in medicine.
Although radiobiological data for other end points and recent data on chromosome aberrations using236 UNSCEAR 2012 REPORTmFISH could be analysed, those data are not extensive, and their applicability to cancer induction inhumans can be questioned.
C89.
Ideally, modifying factors for lower-energy photons would be estimated on the basis of
epidemiological data. However, definitive analyses of cancer risks for populations exposed to lowerenergy photons, such as medical X-rays of various energies, compared with risks for the LSS cohort
have not been performed. Such comparisons are difficult for several reasons. The statistical power ofstudies must be high, given that cancer risks for populations exposed to lower-energy photons may be
no more than a factor of 2–3 higher than comparable risks for the LSS cohort. It is apparent, forexample, that the sizes of populations exposed to medical X-rays that were used in the analysis byKocher et al. [K6] were too small to detect a difference in the effectiveness of those radiations andhigh-energy photons in inducing cancer. Other sources of uncertainty not considered in that analysis
include (a) the possible importance of a DDREF in dose responses for lower-energy photons in medical
patients who received highly fractionated exposures and (b) an assumption about the transfer of risks
for the LSS cohort to medical patients of other nationalities with different baseline cancer rates.
C90.
The biological effectiveness of lower-energy photons relative to high-energy photons also canbe investigated using microdosimetric calculations, as described in a recent review [N16]. Analyses oftrack structure and biophysical models of radiation action suggest that the primary determinant of
biological effects of low-LET radiation is damage to DNA produced by secondary electrons withenergies of about 0.1–5 keV at the ends of radiation tracks. On the basis of such analyses, an RBE forlower-energy photons relative to 60Co gamma rays can be estimated from calculated fractions of theabsorbed dose from each radiation type delivered by low-energy secondary electrons. Calculations
suggest that the RBE for orthovoltage X-rays should be about 1.5 and the highest RBE at lower photon
energies should be about 3 [N15]. Nikjoo and Lindborg [N16] also caution, however, that it probably isnaive to assume that there are such simple relationships between microdosimetric calculations, which
are based on physics only, and biological effects including cancer.
C91.
Estimation of modifying factors to represent the effectiveness of lower-energy photons in
inducing cancer in humans and their uncertainty over a wide range of energies of interest is difficult at
the present time. Nevertheless, cancer risk assessments that attempt to account for uncertainty in risks
from exposure to lower-energy photons should include an estimate of this modifying factor and its
uncertainty. Given the current state of knowledge, it might be said that the modifying factor fororthovoltage X-rays and other photons of similar energies could be in the range of about 1–4, and thatthe modifying factor for lower-energy photons could be somewhat higher. An assumption that themodifying factor for photons of all energies is 1.0 with no uncertainty would not be consistent with thecurrent state of knowledge.

F. Modifying factors for low-energy electrons
1.

Beta particles from tritium decay

C92.
Many radiobiological studies, including studies of induction of cancer in animals, haveindicated that low-energy electrons from beta decay of tritium are more effective in inducing stochastic
effects than high-energy gamma rays or orthovoltage X-rays [A2, C12, N4, S33]. However, several
issues arise in estimating a modifying factor for tritium beta particles on the basis of estimates of RBE
from those studies [K6]. Some studies used orthovoltage X-rays, rather than high-energy gamma rays,

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 237

as the reference radiation. The reference radiation dose was delivered as an acute exposure in somestudies, rather than as a chronic exposure to match typical exposures from tritium. In studies in which
tritium was administered as tritiated water (HTO), which is the usual practice, the uncertainty in theabsorbed dose due to uncertainty in the water content of an organism or cell type can be substantial.
Finally, RBEs for organically-bound tritium (OBT) are substantially higher than RBEs for HTO ortritium incorporated in amino acids [S33].
C93.
In estimating cancer risks for humans, the quantity of interest is the modifying factor at low
doses and low dose rates. Probability density functions of modifying factors for tritium beta particles
developed by various investigators are summarized in table C4 and described below.
Table C4. Summary of probability density functions of modifying factors for tritium beta particles
developed by various investigators for use in cancer risk assessmentsa
Reference

Reference radiation

Modifying factor
95% credible intervalMedianMean>250 keV photons(1.2, 5.0)b

2.4

2.6

Hamby [H2]

High-energy gamma rays

(1.0, 3.5)

2.3

2.3

Harrison et al. [H6]

High-energy gamma rays

(1.0, 2.5)dLittle and Lambert [L18]

Kocher et al. [K6]

c

1.8

1.8

High-energy gamma rayse

(2.04, 2.33)

2.19

2.19

Orthovoltage X-rays(0.96, 1.39)

1.17

1.17

e

a

Modifying factors are intended to represent the effectiveness of beta particles from tritium decay in inducing cancer in humans,
compared with indicated reference radiation; they apply at low doses and low dose rates.

b

Assumed probability density function is log-normal. Probability density function is assumed to apply at energies of discrete
electrons, including internal conversion and Auger electrons, and at average energies in continuous spectra of beta particles lessthan 15 keV, except when Auger-emitting radionuclide is incorporated in DNA.
c

Assumed probability density function is normal.

dAssumed probability density function is uniform with lower and upper bounds of 1.0 and 2.5.

eForm of assumed probability density function is not specified.

C94.
Kocher et al. [K6] developed a subjective probability density function of the modifying factor
on the basis of estimates of RBE for various stochastic end points, including induction of solid tumoursor leukaemias in animals, obtained in studies reviewed by Straume and Carsten [S33]. Estimates of
RBE obtained in studies using X-rays as the reference radiation were taken into account by assuming anominal modifying factor for X-rays relative to high-energy photons of 2. Those data and data
indicating higher RBEs for OBT compared with RBEs for HTO influenced the upper bound of theassumed probability density function.
C95.
The modifying factor developed by Kocher et al. [K6] was assumed to apply to electrons ofenergy less than 15 keV, including low-energy internal conversion electrons and certain Auger
electrons emitted in radioactive decay. In cases of exposure to beta-emitting radionuclides, themodifying factor was assumed to apply when the average energy of the continuous spectrum ofelectrons is less than 15 keV.
C96.
Hamby [H2] used estimates of RBE for HTO in studies of stochastic end points reviewed by
Straume and Carsten [S33] to develop a subjective probability density function of the modifying factor
that represents estimates of RBE in studies that used high-energy gamma rays as the reference
radiation. Estimates of RBE relative to X-rays and estimates for OBT were not taken into account.

238 UNSCEAR 2012 REPORTHarrison et al. [H6] used estimates of RBE for HTO and OBT relative to high-energy gamma rays
obtained from the same review [S33] to develop a subjective probability density function of themodifying factor. Upper bounds of the probability density functions developed by Hamby [H2] andHarrison et al. [H6] are substantially lower than the upper bound of the probability density function
developed by Kocher et al. [K6].
C97.
Little and Lambert [L18] used estimates of RBE for several stochastic end points obtained instudies reviewed by the United Kingdom’s Advisory Group on Ionising Radiation (AGIR) [A2] todevelop probability density functions of the modifying factor. Studies that used high-energy gamma
rays or orthovoltage X-rays delivered chronically as the reference radiation were considered separately.
By applying strict selection criteria, only six studies using high-energy gamma rays as the reference
radiation and three studies using X-rays were judged to provide reliable estimates of RBE. The small
uncertainties in the modifying factors estimated by Little and Lambert [L18] were a consequence ofcombining estimated uncertainties in RBE from each study by assuming statistical independence. Suchsmall uncertainties based on radiobiological data may not represent the current state of knowledge ofthe effectiveness of tritium beta particles in inducing cancer in humans.
C98.
Similar to the analyses for alpha particles discussed above, differences in the modifying factors
for tritium beta particles and their uncertainties developed by different investigators are a consequenceof different assumptions about relevant radiobiological and epidemiological data and the importance of
subjective scientific judgement.
C99.
Epidemiological data that could be used to estimate the effectiveness of low-energy tritium
beta particles in inducing cancer compared with high-energy photons have not been reported [A2, C12].
The lack of epidemiological evidence to support estimation of a modifying factor for tritium beta
particles is a potentially important shortcoming.

2.

Biological effectiveness of Auger electrons

C100. The biological effectiveness of Auger electrons requires special consideration as aconsequence of their very low energies (often a few kiloelectronvolts or less [I15]), their highintensities (often exceeding one per disintegration of a radionuclide [I15]), their short range in tissue(usually less than 1 μm [S14], and the tendency of some Auger-emitting radionuclides to beincorporated in DNA [I7, I11].
C101. Limited data on RBE are summarized by ICRP [I7, I11]. When an Auger-emitting
radionuclide penetrates a cell but is not incorporated in DNA, estimates of RBE for a number of end
points are similar to RBEs for low-energy tritium beta particles. However, when Auger emitters areincorporated in DNA, much higher RBEs have been reported (for example, for cell transformation).
Such high RBEs are supported by calculated patterns of energy deposition.
C102. On the basis of these considerations, Kocher et al. [K6] assumed that the modifying factor fortritium beta particles applies to Auger electrons of energy less than 15 keV unless an Auger-emitting
radionuclide is known to be incorporated in DNA. Those investigators concurred with arecommendation by ICRP [I7] and NCRP [N5] that the biological effectiveness of Auger emitters
incorporated in DNA should be evaluated as special cases using techniques of microdosimetry (see also [I14]).

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 239

G. Summary of modifying factors
C103. Assessments of uncertainties in estimated risks of cancer from exposure to ionizing radiation
should take into account modifying factors to represent the effectiveness of radiation types other thanhigh-energy photons in inducing cancer and their uncertainties. The quantities Q and wR developed foruse in radiation protection generally are inappropriate for use in estimating risks of cancer from actual
exposures of identified individuals or groups. However, neither the Committee nor other authoritative
national or international organizations (such as ICRP, NCRP, or the BEIR committee) have developed
recommendations on these modifying factors and their uncertainties for use in cancer risk assessments.
C104. Various investigators have used radiobiological and epidemiological data to develop subjective
probability density functions to represent uncertainty in modifying factors for different radiation types
including neutrons, alpha particles, lower-energy photons (such as orthovoltage or mammography
X-rays), and low-energy electrons (especially beta particles from decay of tritium). Those probability
density functions indicate that uncertainties in the modifying factors based on the current state ofknowledge are substantial. If the ratio of the upper bound to the lower bound of a 95% credible interval
is used to represent uncertainty, the uncertainty may range from about 10 to 30 or more for neutrons
and alpha particles, and may be a factor of about 4 for lower-energy photons and low-energy electrons.
C105. Many of the probability density functions of the modifying factors developed by various
investigators may not properly represent the effectiveness of particular radiation types in inducing
cancer in humans. Estimates of modifying factors and their uncertainties may be particularly
problematic (a) for neutrons at energies lower or higher than the predominant energies of fission
neutrons, owing to the scarcity of radiobiological data, and (b) for lower-energy photons, for which
there are concerns about the validity of radiobiological data on induction of dicentric chromosome
aberrations in human lymphocytes. For all radiation types, there are concerns about the applicability ofradiobiological data in cells or laboratory animals to cancer induction in humans, and relevant
epidemiological data are limited. Estimation of modifying factors for lower-energy photons on the basisof epidemiological data is especially desirable, given the widespread use of X-rays of various energies
in medicine. Obtaining reliable estimates of modifying factor for various radiation types of concern in
exposure of workers and the public is an important area of future research.

V. INTEGRATIVE APPROACHES FOR QUANTIFYING THE
OVERALL UNCERTAINTY IN RISK ESTIMATES
C106. Once uncertainties and their dependencies have been identified and quantified for each term ina risk assessment algorithm, they must be properly combined in order to produce an estimate of theuncertainty in risk. This procedure would include uncertainties in exposure for specific age groups ofthe exposed population and for each sex. When the risk assessment algorithm is simplified to a series of
uncertain multiplicative terms, estimation of the uncertainty in risk can proceed using algebraic closedform solutions to the propagation of the variances of logarithms of all terms used to estimate risk (seeappendix A). This simplified approach was used to quantify uncertainty in risk coefficients by BEIR
VII [N19]. Propagation of the variances of logarithms through a multiplicative series of uncertain terms
was also employed to estimate uncertainty in thyroid dose for the dose reconstructions performed for
public exposures to Nevada Test Site fallout [N3, S20].

240 UNSCEAR 2012 REPORT

C107. In most cases, however, risk assessment algorithms cannot be simplified to a multiplicative
series of terms and these algorithms are sufficiently complex that there are no closed form solutions to
the propagation of uncertainty. In these cases, Monte Carlo simulation is applied to propagate
uncertainty in risk (see appendix A). Monte Carlo uncertainty propagation was the method used toquantify uncertainty in risks from CT scan exposures [B7], from exposures to fallout from atmospherictesting of nuclear weapons in the Marshall Islands [L6], and for estimation of uncertainty in radiogenic
cancer risk coefficients for absorbed doses received by specific organs and tissues [B8, K7, N7, U3]. It
is also the most common form of uncertainty propagation used in dose reconstructions to support risk
assessments or epidemiological studies [N10].
C108. The terms in the risk assessment algorithm that contribute most to the overall uncertainty inrisk will vary according to the specific question being addressed. For the estimate of the risk to allorgans combined resulting from low-dose-rate uniform whole-body exposure from external radiation,
uncertainty in the dose and dose-rate effectiveness factor (DDREF) and uncertainty in the form of thedose–response model will dominate over statistical uncertainties and uncertainty of risk transfer
between populations [K7, U3]. For the estimate of the risk to specific organs from internal emittersaffecting only a few organ sites (i.e. thyroid gland), uncertainty in the estimate of the absorbed organdose, and statistical uncertainty in the risk coefficient for that organ site will tend to dominate overother sources as long as the cumulative dose received is above levels at which there are substantial
questions about the correct form of the dose–response model. For specific organ sites in which there aresubstantial differences in the baseline rates of disease between the exposed population of interest andepidemiological cohorts from which risk coefficients have been obtained, the transfer of risk between
populations can be an important source of uncertainty [K7, U3]. The use of the excess relative risk to
calculate the assigned share for a given diagnosed case of disease includes (a) all of the uncertainties
involved with the estimation of the uncertain dose received and the relevant age and sex-specific excess
relative risk per unit dose, as well as (b) uncertainties associated with the extrapolation of a cohortbased risk estimate to infer the chance that radiation caused or contributed to a specific case of disease
in a specific person [K7, R4].

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 241

APPENDIX D. UNCERTAINTIES IN SELECTED RISK EVALUATIONSI.

INTRODUCTION ................................................................................................................................. 241

II. SOLID CANCER RISKS AFTER EXTERNAL EXPOSURE TO RADIATION WITH
CUMULATIVE DOSES OF THE ORDER OF 100 MILLIGRAYS ....................................................... 242
A. Summary of the UNSCEAR 2006 Report ........................................................................... 242
B. Epidemiological studies ......................................................................................................... 244
C. Studies with focus on uncertainty analysis ..................................................................... 250
D. Selected risk evaluations........................................................................................................ 251
E. Summary...................................................................................................................................... 258
III. THYROID CANCER AFTER RADIATION EXPOSURE DURING CHILDHOOD .................... 259
A. Summary from previous UNSCEAR reports..................................................................... 259
B. New evidence, not accounting for the impact of dose and model
uncertainties............................................................................................................................... 260
C. Impact of dose and model uncertainties ......................................................................... 261
D. Selected risk evaluation.......................................................................................................... 262
IV. LUNG CANCER AFTER RESIDENTIAL EXPOSURE TO RADON DECAY PRODUCTS....... 267
A. Uncertainties in radon exposure assessment ................................................................. 268
B. Implications of exposure uncertainties on risk estimates .......................................... 271
C. Use of glass objects for radon dosimetry ......................................................................... 279
D. Evaluation of the risk and its uncertainty......................................................................... 280

I. INTRODUCTION
D1.
This appendix contains examples of risk evaluations that (a) summarize the present relevant
knowledge; (b) provide estimations of risk quantities and their uncertainty; and (c) indicate the impact
of different sources of uncertainty on the estimation of the risk and its uncertainty. Criteria for selecting
the examples of risk evaluations were: (i) importance for decisions involving the safe use of ionizing
radiation or addressing public controversy; (ii) availability of a sufficient amount of information
allowing a meaningful assessment of uncertainties; (iii) existence of publications also addressing
sources of uncertainty other than simple statistical uncertainty (for example, exposure or dose242 UNSCEAR 2012 REPORT

uncertainties, or model uncertainties); and (iv) existence of a recent epidemiological study related to theissue of the risk evaluation. Based on these criteria, the following risk issues were evaluated:(a) Solid cancer after external exposure to radiation with cumulative doses in the order of
100 mGy above normal background radiation;(b) Thyroid cancer after childhood exposure to radioiodine;(c) Lung cancer after exposure to residential radon.
D2.
For each of the first two risk evaluations, two calculations are performed in this appendix: one
is based on studies excluding the recent study of the issue of interest, and one takes the recent study into
account. The purpose of this approach is to elucidate how the recent studies have actually improved
knowledge on the specific risk issue that they had addressed.

II. SOLID CANCER RISKS AFTER EXTERNAL EXPOSURE TORADIATION WITH CUMULATIVE DOSES OF THE ORDER OF
100 MILLIGRAYS
D3.
In the past, risk estimates for solid cancer after protracted exposures with cumulative doses ofthe order of 100 mGy have mainly been derived from data on survivors of the atomic bombings. Owing
to the nature of the event, atomic bombing survivors were acutely exposed to a wide range of doses.
More recently, observational studies focussing on populations with protracted exposures leading tocumulative doses of the order of 100 mGy have become available. In some of these studies sources of
uncertainty beyond statistical random variation were taken into account in estimating solid cancer risks.
These studies, together with recent data published by the Committee and other material, aresummarized and discussed. The focus in terms of risk coefficients is on the excess relative risk per unit
dose, one of the core statistical risk measures estimated in many radiation epidemiology studies.

A. Summary of the UNSCEAR 2006 Report
D4.
The impact of dose levels on the precision of risk estimates was discussed in the UNSCEAR
2006 Report, annex A [U12]. It was concluded that very large studies are needed to provide bounds on
the risk estimate at low doses that will be informative and useful. It was also noted that the influence ofconfounding factors becomes increasingly important at low doses. The risk of solid cancer after
external irradiation with cumulative doses of the order of 100 mGy has been investigated in large
studies, and increases in rates of solid cancer are judged to be the main contributor to excess mortality
after such exposures.
D5.
The UNSCEAR 2006 Report also summarized the impact of dose measurement errors andother uncertainties on study associations and risk estimates, pointing out recent developments inmethods for evaluating such uncertainties. The core concepts outlined in that report included systematicand random error; the topics of differential and non-differential errors, as well as different error models,
are developed in more detail in this report. It was also noted that new epidemiological studies had
begun to provide estimates of risk from radiation exposure corrected for dose uncertainties. Newly
developed statistical approaches to deal with other uncertainties including those arising from

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 243

methodological biases such as misclassification, non-response and confounding [G16] were still underscientific debate.
D6.
The UNSCEAR 2006 Report noted that a complete model to correct for uncertainties would
need to take into account all the sources of uncertainty in a given study. However, as frequently only
limited information is available in this regard, researchers have to use whatever information is available
to make judgements about the distributions of these uncertainties. It was also noted that somesystematic biases in studies may be difficult or impossible to account for properly in analyses.
D7.
In terms of total solid cancers in the LSS cohort, the report included mortality data withfollow-up until the end of the year 2000, using the most recent dosimetry system DS02 [P12]. Risk
estimates were found to be somewhat lower than in previous follow-ups. Other features such as thelinearity in dose of the excess solid cancer risk and the modification of ERR per unit dose by age at
exposure and attained age as well as previously noted sex differences in risk were similar to those fromearlier evaluations.
D8.
For solid cancer mortality in the LSS, the average ERR at 1 Sv was given as 0.48 (90% CI:
0.40, 0.57) for the total cohort excluding survivors with weighted colon dose below 0.005 Sv, over thefull range of doses. When restricting the analysis to specific dose ranges, a statistically significant
positive trend first occurred over the 0−0.2 Sv dose range, with an ERR per unit dose estimate of 0.53
(95% CI: 0.02, 1.07) Sv−1. For lower dose ranges, the risk coefficient was not statistically significant.
The corresponding values for solid cancer incidence were given as 0.62 (90% CI: 0.55, 0.69) Sv−1, witha statistically significant positive trend, 0.58 (95% CI: 0.20, 0.98) Sv−1 in the dose range 0–0.25 Sv.
Some reasons for the discrepancy of these findings to previous evaluations, mainly related to themethodological approach, were discussed in the report.
D9.
The report also included risk estimates for solid cancer derived from other cohort studies,mainly among workers in the nuclear industry, for comparison. For mortality from solid cancer, theaverage ERR per unit dose in these studies ranged from -0.07 to 0.97 Sv−1, and for solid cancer
incidence from −0.67 to 2.3 Sv−1. In general, workers in these studies received low radiation doses at
low dose rates. Some of these studies included explicit approaches for dealing with uncertainties, andhave been reviewed in more detail here.
D10.
The UNSCEAR 2006 Report also presented a series of estimates for lifetime cancer risk basedon mortality [P12] and incidence [K13] data from the LSS cohort of atomic bombing survivors.
Projected lifetime cancer risks were calculated at three test doses: 0.01 Sv, 0.1 Sv and 1 Sv. The reportdiscussed several important factors on which the results depended, notably:(a) The exposed population for which risk estimates were developed;(b) The models used to describe risk at low doses;(c) The methods used to extend the excess risk models beyond the period of observation of the
population used to develop those models;(d) The cause-specific incidence and mortality rates and the age structure of the populations towhich rates were applied;(e) The methods used to transfer estimates of excess cancer risk based on models for one
population to another population;(f) The method used to allow for dose fractionation or dose-rate effects.

244 UNSCEAR 2012 REPORT

D11.
Annex A, chapter IV of the UNSCEAR 2006 Report [U12] adjusted the risk estimates for
dosimetric errors using a regression calibration approach. Following work of Jablon [J1], theCommittee assumed dose uncertainties to be log-normally distributed, and used a central estimate of
35% for the general dose uncertainty.
D12.
The Committee’s report used several linear and linear–quadratic models specifically developed
for the lifetime risk estimations; these included models employing Bayesian MCMC methods toaccount for uncertainty in dose estimates. The results illustrated the sensitivity of lifetime risk estimates
to variations in underlying rates. Differences in risk estimates were of a similar magnitude to those due
to different transfer or risk projection methods. It was also noted that uncertainties in estimates of risk
for specific types of cancers were generally greater than for all cancers combined.
D13.
Applying the linear models to five specific populations, the report estimated the mean lifetime
risk of exposure-induced death due to solid cancer after an acute exposure to a dose of 100 mSv(equivalent to about 100 mGy) to be about 3.6%–7.7% Sv−1. Bayesian models yielded slightly lower
risk estimates, ranging from 2.3%–5.4% Sv−1. These estimates were noted to be somewhat lower thanthose previously estimated by the Committee, owing mainly to the use of different risk projection andtransfer models. A smaller contribution of the revised dosimetry—in the order of 8%—was also noted.
The statistical uncertainty of the estimates was assumed to be in the order of a factor of 2, and lower
bounds of the confidence interval included zero.

B. Epidemiological studies
1.

Worker studies

D14.
The UNSCEAR 2006 Report reviewed the international worker study of Cardis et al. [C4]. In
short, the authors had studied mortality in a large cohort of workforces from 15 countries and154 nuclear facilities, including 407,391 workers monitored for external photon (X and gamma)
radiation with personal dosimeters. The average individual effective dose was 19.4 mGy, and 90% of
the workers received doses less than 50 mGy. Thus, this study is regarded as potentially highly
informative for the dose range of interest in this report, also owing to the fact that specific attempts
were made to study errors in recorded doses across facilities and time [T2], as well as conducting
sensitivity and confounding factor analyses.
D15.
The surprisingly large influence of the data from Canada and potential reasons for this werediscussed in the UNSCEAR 2006 Report. Major differences between an earlier analysis of Canadian
nuclear workers and the Canadian cohort included in the international worker study were apparently
related to the exclusion of a particular group of workers, namely Ontario Hydro employees, from thepooled study. Thus the Canadian cohort results were largely driven by the cohort of workers from
Atomic Energy of Canada Limited (AECL) sites. In the framework of a sensitivity (or influence)
analysis of the international worker study, the removal of the Canadian cohort resulted in a markedly
diminished ERR per unit dose for all cancer other than leukaemia, 0.58 (95% CI: −0.22, 1.55) Gy−1,
compared with the statistically significant value of 0.97 (95% CI: 0.14, 1.97) Gy−1 for all cohorts
combined. Problems associated with the Canadian data were assessed in detail by Ashmore et al. [A13].
From their analysis it could be concluded that the handling of records for the AECL cohort contributed
importantly to the observed upward shift in risk found in the international analysis. In particular there
was a failure to include records of workers with zero recorded doses during the period 1956–1970 inANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 245

the data set used for the international workers study. The Canadian Nuclear Safety Commission has
recently published a preliminary summary of their re-analysis of the Canadian nuclear worker data
[C13], which also indicates that there were problems with the reporting of dose for the early AECL
workers. In general terms, this example shows how influential systematic errors in a subset of data for alarge pooled study can be with regard to the overall study results.
D16.
In terms of measures of uncertainties of effect, vital status in the international worker study
was ascertained through linkage with national or regional death registries, or in some cases throughcompiling death records individually from relevant authorities. Follow-up completeness ranged from
87% to 100%, and for over 90% of deaths the cause was known. No systematic missing valuemechanism seems to have been assumed in the study.
D17.
The separate study of errors in dosimetry had the objectives: (a) to evaluate the comparability
across facilities and time of currently available dose estimates; and (b) to identify and quantify bias anduncertainties in available dose estimates [T2]. Dosimetry technology, workplace exposure conditions,and calibration practices were identified as major sources of dosimetric errors for doses from highenergy photons, with administrative practices contributing little to errors. Through detailed sub-studies,
errors were quantified and bias factors specific to the doses to each organ of interest calculated for eachdosimeter model and by facility type (nuclear power plants and mixed activities facilities), withassociated uncertainties. Finally, “corrected” organ doses were calculated by dividing recorded dosesby the appropriate organ dose bias factor.
D18.
The study of dosimetry errors did not reveal major biases as the result of using any specificdosimeter or calibration technique. Therefore, bias correction factors were generally close to one, withvarying magnitude of the uncertainties. It was noted that biases were time-dependent, with larger bias
in earlier study periods, where also the doses received by the workers tended to be larger. Since also theinformation on technology, exposures and practices were less detailed for these periods, this study
confirms the challenges inherent in attempts to quantify errors and uncertainties. Even if reasonableassumptions about the magnitude of errors and the distribution of uncertainties can be made insituations of scarce information, a considerable risk of bias remains.
D19.
Confounding in the international worker study was assessed through various statistical
approaches. However, the quality and extent of information on potential confounding factors varied
between cohorts. For smoking, only indirect approaches (via the exclusion of lung and pleural cancers
strongly associated with smoking) could be implemented [C3, C4]. Excluding these cancers from thecategory of “all cancers except leukaemia” markedly reduced the power and thus increased thestatistical uncertainty of risk estimates. Duration of employment as a known confounding factor was
included in the main analyses.
D20.
Risks of solid cancer were also estimated by Atkinson et al. [A15] from the workforce cohortof the United Kingdom Atomic Energy Authority (UKAEA). This cohort includes 51,367 workers, ofwhom 51% were classified radiation workers. The mean cumulative dose was given as 18.8 mSv.
Adjustments to recorded doses were made to account for doses below the detection limit, non-returned
dosimeters and unit changes. The standardized mortality ratio (SMR) for all cancer in the total
workforce was 0.80 (95% CI: 0.77, 0.83) and 0.76 (95% CI: 0.72, 0.79) for radiation workers. In trend
analyses, no association with dose was found, and no estimates for ERR per unit dose were given.
Issues of uncertainty beyond statistical variability were not addressed.
D21.
Muirhead et al. [M21] studied cancer incidence and mortality among 174,541 workers in themost recent analysis of the United Kingdom’s National Registry of Radiation Workers, with follow-up
to the end of 2001. The mean lifetime dose was just below 25 mGy, but varied markedly between

246 UNSCEAR 2012 REPORT

facilities. Values of ERR per unit dose were calculated with a linear model, using maximum likelihood
methods. Age, sex, calendar period, industrial classification and first employer were included as risk
factors in the analyses. For all cancers excluding leukaemia, an ERR per unit dose of 0.275 (90% CI:
0.02, 0.56) Gy−1 for mortality and of 0.266 (90% CI: 0.04, 0.51) Gy−1 for incidence were calculated.
Very similar ERR values were found when the strongly smoking and asbestos-related lung and pleuralcancers were excluded, which indicates that smoking and asbestos were probably not confounding the
ERR estimates to a large extent. The study is notable for its size, completeness of follow-up (only 0.6% nottraced) and length of follow-up. Uncertainties in dose estimates or from other sources were not modelled.
D22.
Wing and Richardson [W10] estimated cancer risks for workers at the Hanford facility whowere exposed both to internal and external radiation. Missing values in the dosimetry records wereprimarily confined to the early time periods after 1944 and missing doses from external exposure were
imputed through a stepwise algorithm. The mean (median) dose for all ages was 27.9 (4.3) mGy. Risk
factors included in the analyses were age-at-risk, birth cohort, sex, race, socio-economic status,
employment status, in vivo monitoring, and plutonium exposure potential. Risk analyses focused on age
at exposure, and statistical models linear and exponential in dose were used. The ERR per unit dose forall cancers (assuming a minimal lag time of 10 years) was 0.28 (90% CI: −0.30, 1.00) Gy−1. For all
cancers combined, no differences between workers potentially exposed to plutonium and other workers
were noted. Also, only marginal differences between the models (linear versus exponential) were
found. However, a strong potential for confounding due to smoking was noted, but no direct
information on smoking was available. Furthermore, the analyses indicated that the confounding effectof smoking varies strongly with age, as high lung cancer risk coefficients were seen particularly forcohort members aged 55 and above.
D23.
Telle-Lamberton et al. [T1] estimated the risk of all cancers for a French cohort of 29,204
nuclear workers that were partially included in the international worker study [C4]. A substantial
number of workers in this cohort analysis were also exposed to internal radiation contamination. The
mean cumulative external radiation dose was 8.3 mGy, and recorded doses were categorized in
11 groups for dose–response analyses. Relative risks for a dose of 100 mGy were calculated, adjusted
according to the protocol of the international worker study. For all cancers the RR estimate was nonsignificantly elevated, RRlinear = 1.2 (90% CI: 0.99, 1.45) for 100 mGy. Confounding due to smoking
and other factors could not be assessed.
D24.
Cancer mortality of about 21,500 workers at the Mayak complex was reported by Shilnikova et
al. [S12]. Individual uncorrected gamma dose estimates were used in the analyses, and dose–response
analyses were adjusted for internal exposures via a surrogate index of plutonium exposure. Average
worker doses were 0.8 Gy. Cohort follow-up was 90%, and information on cause of death was rather
complete for workers at the main plants, but somewhat less so for workers at auxiliary plants. A highpercentage of autopsies for deaths of cohort members residing in Ozyorsk, a town close to the Mayakcomplex, was noted. Linear ERR models involving doses from both internal and external exposure
were employed. The ERR per unit dose for solid cancers excluding lung, liver and skeletal cancer was
estimated as 0.08 (90% CI: 0.03, 0.14) Gy−1 from a linear model. Adding a quadratic dose term
indicated non-linearity of the dose–response, and led to a more than doubled risk coefficient for doses
below 3 Gy; the ERR per unit dose was 0.21 (90% CI: 0.06, 0.37) Gy−1. No sex differences were seen,
but there was a decreasing risk with increasing age at hire. Several sensitivity analyses were conducted,
including separate analyses for migrated and non-migrated cohort members, which showed nosignificant differences. With regard to uncertainties, issues related to the precision and possible errorsof external and internal exposure estimates, as well as confounding due to smoking and otheroccupational exposures, are limitations of the study.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 247

D25.
Silver et al. [S19] examined cancer mortality in an updated cohort of Portsmouth Naval
Shipyard (PNS) workers in the United Kingdom, who were employed at PNS between 1952 and 1992,
and followed until 1996. The total cohort comprises 37,853 workers, including a subcohort of 13,468
workers with monitoring records for external radiation exposure. The mean doses from shipyard
exposures were 19.95 mSv, and the mean total exposures were 20.59 mSv when off-site doses were
included. Further non-radiological exposures to potential carcinogens (asbestos, silica, welding fumes,
and organic solvents) were considered. Cancer mortality varied substantially among subcohorts. Cancer
cases were slightly increased in the total cohort, SMR = 1.06 (95% CI: 1.02, 1.10), while cancer deathsin the unexposed group were close to unity, SMR = 1.01 (95% CI: 0.87, 1.18). Strong dose–response
relationships were found for leukaemia (with a 2-year lag), and lung cancer (a 15-year lag). Bothexposure groups presented very different occupational exposure histories, which might have led to adifferential distribution of risk factors such as smoking/health lifestyle within the subcohorts. These
differences might partially explain the observed variations in cancer mortality within the different
exposure groups. Asbestos exposure as a confounding factor is likely to explain a proportion of theelevated lung cancer risk observed in the cohort. Further limitations may be due to unknown/missing
information on vital status, under-ascertainment of the cause of death, and misclassification of exposure
status, as well as missing information on prior exposures. Owing to the absence of quantifiable
information, risk estimates did not take these sources of uncertainty into account.
D26.
Boice et al. [B15] analysed mortality among nuclear technology development workers at
Rocketdyne facilities in California, United States who were employed between 1948 and 1999. Vital
status was obtained from various mortality databases, while cumulative doses were collected fromcompany records in addition to record linkage with national dosimetric registers. The 5,801 workers, ofwhom 2,232 were monitored for radionuclide intake, had a mean radiation dose of 13.5 mSv. The SMR
analysis (compared with the general population of California) found no significant elevation of the riskof all cancers combined, with an SMR of 0.93 (95% CI: 0.84, 1.02). The RR at 100 mSv for all cancers,
excluding leukaemia, was 1.00 (95% CI: 0.81, 1.24). When considering radiation exposure due to
Rocketdyne activities only, there was an increase in the RR to 1.11 (95% CI: 0.81, 1.52). However, nosignificant dose–response trends were observed for any cancer. Overall, the results in this study arebased on small numbers of deaths and low occupational doses.
D27.
Ivanov et al. [I24, I26] assessed the mortality among Chernobyl emergency workers in a cohortof 65,905 persons with registered low to moderate doses from external exposure between 1991 and 1998.
The cumulative doses ranged between 5 mGy and 300 mGy with a mean dose of 116 mGy. Relative to theRussian population as a whole, the risk for cancer (malignant neoplasms) was slightly reduced: the SMR
was 0.87 (95% CI: 0.80, 0.95). Circulatory disease mortality however showed an increased risk: SMR was
1.07 (95% CI: 1.03, 1.13). Furthermore, statistically significant dose–response analyses presented elevatedexcess risks for cancer with ERR per unit dose of 2.11 (95% CI: 1.31, 2.92) Gy−1 (with an external
control: Russian population) and 2.04 (95% CI: 0.45, 4.31) Gy−1 (internal control), respectively. Theserisk estimates are in accordance with those derived from the LSS cohort. Uncertainties wereacknowledged by Ivanov et al. with regard to the potential impact on risk estimates of theadministrative control of recording maximum permissible doses, in particular due to varying values ofmaximum permissible doses at different times after the accident. When a worker exceeded the
maximum permissible dose, the worker was simply ordered to leave the radiation area. Thus, thedocumented doses may be equal or even less than the maximum permissible dose, even though theworker in fact exceeded the dose limit. This may have led to overestimates for the mortality risk. These
uncertainties were not accounted for in risk estimates. A further important source of uncertainties in therisk estimates is the adopted value for the time of the latent period in the development of radiationinduced cancers. Both the latent period and the ERR for solid cancer incidence were assessed by Ivanov
et al. [I25] in a cohort of 59,770 Chernobyl emergency workers for the follow-up period 1986 to 2005.

248 UNSCEAR 2012 REPORT

Using maximum likelihood methods, the minimal latent period was estimated to be 4 years (95% CI:
3.3, 4.9), with the corresponding ERR per unit dose of 0.96 (95% CI: 0.28, 1.72) Gy−1. The maximum
estimated latent period of 10 years corresponded to an estimate for the ERR per unit dose of 0.20
(95% CI: −0.04, 0.80) Gy−1.
D28.
Risk estimates for the solid cancer incidence during the period 1991–2001 in this cohort (basedon 55,718 emergency workers) resulted in an ERR per unit dose of 0.33 (95% CI: −0.39, 1.22) Gy−1 forthe period 1991–2001, and a slightly lower value of 0.19 (95% CI: −0.66, 1.27) Gy−1 for the truncatedperiod 1996–2001. As is known for this cohort, some 15% of dose estimates are not based on individual
measurements but on group measurements or imputations. Large uncertainties may thus be associatedwith the dose estimates, but for the majority of doses the uncertainties are not likely to exceed 50%.
D29.
Sigurdson et al. [S18] analysed the cancer incidence among 90,305 United States radiologic
technologists between 1983 and 1998 including a large proportion of women (77%). Cancer incidence
was collected from mailed questionnaires and from death records. Individual dose information was notavailable, and exposure time windows were used as surrogates. Female technologists showed anincreased risk for all solid cancers combined; the standardized incidence ratio, SIR, was 1.06 (95% CI:
1.02, 1.10). For breast cancer the SIR was 1.16 (95% CI: 1.09, 1.23). Since no individual doses were
estimated for this analysis, risk coefficients could not be calculated. No relevant uncertainties werementioned apart from minor limitations related to design of the study (such as non-responses). Cohort
workers may not be representative of the general population (a possible healthy worker effect), but as
indicated the study contributes little to improving risk estimates for solid cancer associated withspecific radiation dose levels.

2.

Environmental exposures

D30.
Residents along the Techa River have been exposed to ionizing radiation due to releases from
the Mayak complex. Cancer mortality for the extended Techa river cohort of 29,873 residents (of whom
60% are women) was reported by Krestinina et al. [K12]. The follow-up included the period 1950 to1999. There was considerable loss to the cohort owing to migration out of the catchment area.
Residence and vital status and causes of death were registered through collaboration with local address
bureaux and local statistical offices, as well as through interviews. Dosimetry was provided through aspecific dose reconstruction system, including internal and external exposure, with individual doses
based on local measurements and individual-specific modifications such as detailed residence histories.
Dose to the stomach was used for the analysis. For solid cancers excluding bone cancers (owing topotential effects of 90Sr exposure), the ERR per unit dose was estimated as 0.92 (95% CI: 0.2, 1.7) Gy−1;
the risk coefficient is 70% higher for women than for men, but the difference is not significant. Risk
estimates increase with increasing age at exposure and attained age, contradicting findings from Mayakstudies or the LSS. Limitations of this study include the loss to follow-up and a high percentage of
missing information on cause of death, as well as uncertainties in individual dose estimates. Data on
potential confounding factors are generally not available. Preliminary assessments of the potential
impact of medical exposures suggested no serious biases in the health effect estimates. Improvements
to the dosimetry system are ongoing.
D31.
Cancer incidence in the extended Techa River cohort for the period 1956 to 2002 was alsostudied by Krestinina et al. [K13]. Some 60% of the original cohort could be included. Cancer incidence
data were obtained through various sources, and with different quality and completeness for the different
time periods. The mean and median stomach doses for cohort members were 40 and 8 mGy, respectively.
Using a linear model, the estimated ERR per unit dose was 1.0 (95% CI: 0.3, 1.9) Gy−1. In a model with a

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 249

quadratic dose–response term, markedly higher ERR per unit dose estimates were computed for highdoses, but for low doses the risks were lower than in the linear dose–response model. Women had
slightly lower risks than men in the analyses. Limitations are similar to the mortality analyses, but thecohort is even smaller and therefore estimates somewhat less precise. No systematic approach isprovided to include uncertainties related to dose or to confounding factors in developing the risk
estimates and their confidence intervals.
D32.
Background ionizing radiation in relation to cancer incidence was studied by Nair et al. [N2] inKerala, India. A cohort of 69,958 men and women (ages 30–84) from areas of high backgroundradiation was studied. Information on age and sex as well as other risk factors that could act asconfounding factors, such as smoking bidis, education and occupation, was available from a baseline
survey. Cancer diagnoses were based on histopathology and death certificate information, but a nonnegligible proportion (about 20%) came from clinical observations or tests. Individual gamma doses
were estimated from measurements conducted in households and outdoors, and occupancy as well as
migration were taken into account. Cosmic ray components were subtracted from the measured dose to
obtain estimates of terrestrial background radiation. The average individual cumulative (terrestrial) doseat the end of follow-up was estimated as 161 mGy. No associations between all cancer excluding
leukaemia and annual or cumulative radiation dose were found. The ERR per unit dose was −0.13 (95%
CI: −0.58, 0.46) Gy−1, calculated using a linear model. The study includes information on some
important potential confounding factors; however, limitations related to the dose estimation, to theaccuracy of the data on potential confounding factors, and to the end point verification are noteworthy.
D33.
In Taiwan, residents were exposed to high levels of external radiation in buildings where steel
contaminated with 60Co was used for construction [H22]. A cohort of 7,271 people was assembled andfollowed-up from 1983 to 2002. Doses were reconstructed through a specific dosimetry system basedon environmental measurements and taking occupancy and other factors into account. The 6,246
persons for whom doses could be reconstructed received mean cumulative doses of 47.8 mGy(excluding background), ranging from less than 1 to about 2,360 mGy. Cancers were ascertained
through the National Cancer Registry. Relative risks for different dose categories were calculated, andfor all solid cancers a RR of 1.2 (95% CI: 0.5, 2.9) for those receiving doses greater than 50 mGycompared to those receiving less than 1 mGy was estimated. Higher relative risk estimates were foundfor women compared to men. The most recent follow-up of this cohort includes three more years offollow-up (1983 to 2005); hazard ratios (HR) for an increase of 100 mGy in dose were estimated. For
leukaemia (excluding chronic lymphatic leukaemia, CLL) an increased HR at 100 mGy of 1.19 (90%
CI: 1.01, 1.31) was reported, and slightly lower hazard ratios for breast cancer (HR at 100 mGy of 1.12,
90% CI: 0.99, 1.21) [H23]. The risk estimates in both reports were adjusted for attained age, but noother confounding factors such as smoking and socio-economic status were included. Thus theconfidence intervals for the risk estimates do not reflect any uncertainties beyond statistical variability.
D34.
Bauer et al. [B2] analysed radiation exposure due to local fallout from atmospheric nuclear
weapons testing and reported results from a study on a historical cohort exposed in the vicinity of the
Semipalatinsk nuclear test site in Kazakhstan. The cohort of 19,545 inhabitants included residents fromexposed villages with a mean cumulative dose estimate of 634 mSv and residents of comparison
villages who were each assigned a common effective dose estimate of 20 mSv. The follow-up time
ranged from 1960 to 1999. The study found a significant dose trend for solid cancers with an ERR per
unit dose of 1.77 (95% CI: 1.35, 2.27) Gy−1 for the total cohort, and 0.81 (95% CI: 0.46, 1.33) Gy−1
when considering the exposed group separately. Uncertainties in this study were related to follow-up
loss (that is unclear information of vital status) due to emigration in the 1990s particularly in the
exposed group. However, sensitivity analyses restricted to 30-year follow-up showed fairly consistent
results compared to the 40-year follow-up. As additional selection bias in the comparison group could
not be ruled out, results from the exposed group were assumed to be more reliable than those for the250 UNSCEAR 2012 REPORT

total cohort. The exposure data used in this study did not allow for specific lag and age–time windows.
In addition, a risk assessment for low dose ranges could not be made as no individual exposure
information in the comparison group was available.

3.

A joint analysis of low-dose-rate studies

D35.
A joint analysis of epidemiological studies of populations with low-dose-rate exposures of theorder of several hundred milligrays included most of the studies mentioned previously [J5]. Both solidcancer incidence and mortality were investigated, and risk estimates from these studies of chronic
exposures were individually compared to ERR estimates derived from appropriately selected subsets ofdata from the LSS of acutely exposed atomic bombing survivors. A joint estimate of the ratio of the risk
estimates from these studies and the LSS was then derived. Individual estimates of the ERR per unit
dose ranged from 0 Gy−1 to 4.8 Gy−1 for mortality studies and from 0.3 Gy−1 to 1 Gy−1 for incidence
studies, whereas the comparison risk estimates from the LSS showed much smaller variation. In six oftwelve studies, the best estimate of the ERR per unit dose was larger than in the LSS, and in five studies
the estimates were of comparable magnitude to the LSS estimate. The overall study results as well as
sensitivity analyses indicated that the ERR per unit dose values from the studies of chronic exposure
were similar to those calculated from the LSS. Limitations of individual studies with regard to
dosimetry and to absence of information of potential confounding factors impair the ability to interpretthe result, but there was consistency between results of different analyses using varying study subsets.
Uncertainty beyond statistical variability could not be incorporated in the study.

C. Studies with focus on uncertainty analysis
D36.
Using data from the study of workers at Oak Ridge National Laboratory, Stayner et al. [S25]presented a method to estimate uncertainties from shared errors in exposure assessment. Morespecifically, they used Monte Carlo methods to estimate confidence intervals that specifically reflectstatistical sampling errors and errors from uncertainties in exposure estimates. Shared errors in
exposure estimates arise from the use of group means to assign individual doses, as commonly is thecase when job–exposure matrices are used. Similarly, shared errors occur when individual dose
estimates are available and corrections are applied that are the same across specific jobs or facilities,
which is the situation in the international worker study and the data used by Stayner et al. [S25].
D37.
Starting from a model with measurement errors of the assignment type, including both sharedand unshared errors between subjects, the authors propose a Bayesian approach, using Monte Carlosimulations techniques to randomly select realizations from the distribution of true dose given themeasured dose. Central estimates and confidence intervals are then computed using maximum
likelihood approaches. No additional covariates such as age or sex are included as potential effectmodifiers, and the authors note that this is a simplification.
D38.
Analyses of the risk of all cancers excluding leukaemia in the ORNL dataset were then carriedout, using the bias factors derived with the methods of the dosimetry errors sub-study for the international
worker study [S25]. The ORNL workers study had previously shown a positive dose–response
relationship between all cancers and radiation dose, but these analyses had not included any specificapproach to deal with exposure or other uncertainties [W10]. Whereas the earlier, non-simulated analysis
led to a value for ERR per unit dose of 5.38 (90% CI: 0.54, 12.58) Gy−1 (originally Sv−1), the Monte CarloANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 251

maximum likelihood method yielded an ERR per unit dose of 4.82 (90% CI: 0.41, 13.31) Gy−1. The
two risk coefficient estimates were statistically not distinguishable.
D39.
As expected, the simulation approach yielded broader confidence intervals than theconventional analysis, but in the case of ORNL data the differences seemed rather marginal; the lower
confidence bound decreased by about 24%, the upper increased by about 6%. This may be due to thecomparatively good quality of exposure information in this and comparable studies of radiation workers
with individual measurements. Overall, the authors point out that the Monte Carlo maximum likelihood
estimates appear to be indicated only for a situation where shared errors are of concern, while forsituations where unshared errors predominate, less complex approaches are recommended by the authors.
D40.
Little et al. [L17] expanded on the analyses in the UNSCEAR 2006 Report [U12] that
explicitly take account of dosimetric and other uncertainties. The general approach is very similar to the
UNSCEAR 2006 Report, fitting generalized linear, linear–quadratic and linear–quadratic–exponential
models to the most recent data on survivors of the atomic bombings. Lifetime risk projections for
5 contemporary populations are provided for test doses of 0.01 Sv, 0.1 Sv and 1 Sv, based on both
Bayesian and classical regression calibration approaches. In terms of model choice, simple models
linear in dose fitted the data about as well as the more complex models, but statistical and otherarguments were put forward to motivate the preferential choice of linear–quadratic models. Through theBayesian modelling, random dose errors as well as uncertainties in the model parameters describing theshape of the dose–response curve are taken into account. In addition, variations of risk with time since
exposure and age at exposure are considered. The estimated solid cancer risks did not differ markedly
between the different modelling approaches and test doses applied, however, central risk estimates were
somewhat lower than those calculated in earlier UNSCEAR reports. Uncertainties reflected in theBayesian credible intervals were slightly larger than those from regression calibration approaches
without adjustment for dosimetric errors.
D41.
A different approach to risk estimation is mechanistic modelling of the carcinogenic process.
A study by Jacob et al. [J4] focused on the inclusion of non-linear dose effects at low doses. Different
forms of the two-stage clonal expansion (TSCE) model of carcinogenesis were applied to data from theatomic bombing survivors, and the biologically motivated models were compared to empirical risk
models conventionally used in the LSS analyses. Including low-dose hypersensitivity in radiationinduced cell inactivation did not materially improve model fit, but differences in estimates of ERR per
unit dose between models with and without low-dose hypersensitivity were noted when doses below
1 Gy were studied. For young age at exposure, TSCE models yielded lower excess relative risks thanconventional models. As a way to take this model uncertainty into account, Jacob et al. proposed to use
the upper and lower limits of the uncertainty range for estimates derived from mechanistic andempirical models with comparably good fit as guidance. With such an approach, the uncertainty rangeof the empirical ERR estimate for the LSS data on solid cancer (age at exposure 10 years, attained age
70 years) would be inflated by some 30%, which is seen to reflect model uncertainty. The nominal
value of the factor by which the width of the uncertainty range would be expanded depends on thespecific exposure situation investigated as well as the choice of models that are being compared.

D. Selected risk evaluations
D42.
For this scenario the Committee has considered a hypothetical population of workers whobegan work at age 30 and received occupational exposures to low-LET radiation from the ages of 30 to
44 with a total dose of 100 mGy. More specifically, annual doses of 8 mGy are assumed for the first
five years, 7 mGy annually for the next 5 years and 5 mGy annually for the last five years. Follow-up is252 UNSCEAR 2012 REPORT

presumed to start at age 45. The quantities of primary interest are the rate of radiation-associated cases,
the attributable fraction (which is defined as the ratio of the number of excess cases to the total numberof cases), the mean life lost per case and the mean life lost per person.
D43.
The Committee has considered two approaches to the evaluation of radiation-related solidcancer risks and associated uncertainties are considered. The first approach relies on the NRRW for therisk levels for all organs combined and considers possible age-related changes in the magnitude of thehealthy worker effect. This is feasible for this scenario since the NRRW is a large study with publishedrisk estimates based on dose estimates of high quality and relatively lengthy follow-up. However, since
the published analyses provide little information on possible temporal variation, the Life Span Study
results were used to characterize potential temporal variation in the excess relative risks. Because risk
estimates were defined directly in terms of the results of an analysis of the population of interest,
DDREF was not considered in this uncertainty assessment. For the second approach, the nature of theradiation effect on solid cancer rates was characterized using site-specific BEIR VII risk models
derived primarily from LSS cancer incidence data without any consideration of the actual NRRW
results and with no allowance for healthy worker effects.

1.

NRRW-based risk and uncertainty assessment

D44.
Using information on the risk estimates from the third analysis of data from the United
Kingdom’s National Registry for Radiation Workers (NRRW) [M21] an estimate was made of the
expected rate of (occupational) radiation-associated non-leukaemia deaths in a population of maleworkers who receive a total dose of 100 mGy as a result of long-term low-dose-rate occupational
exposures. The focus here is on allowing for the effect of uncertainty in risk parameter estimates, in theform of the risk model and, to some extent, in the differences in solid cancer and all-cause mortality
rates between the NRRW workers and the general population of the United Kingdom. In this scenario
there is no attempt to deal with the effect of dose uncertainty since the published data do not include
enough information to address this issue. However since the doses were based on badge dose readings,
it is likely that classical measurement error is the primary source of dose uncertainty, but that themagnitude of this uncertainty is such that it should have little impact on the risk estimates. It is also
assumed that age-specific rates for all-cause and mortality and cancer incidence are fixed at the 2009
United Kingdom population values.
D45.
The fitted risk models in [M21] are limited to simple time-constant ERR models. The estimate
for the ERR per unit dose for solid cancer (excluding non-melanoma skin cancer) is given as 0.275(90% CI: 0.02, 0.56) Gy–1. The reported confidence interval for the time constant estimate is almost
symmetric, therefore the Committee considers it reasonable to approximate the (asymptotic) standard
error of the reported ERR per unit dose as 0.13 and describe the uncertainty in the parameter for thismodel as having a normal distribution N(0.28, 0.13).
D46.
Although [M21] notes that there was no evidence of significant temporal variation in the ERR,
the Committee considers it reasonable to assume that such variation is possible, and even quite likely. It
has allowed for this possibility by considering both time-constant and age-varying ERR models to beequally plausible. For this exercise the Committee developed uncertainty distributions for theparameters in the age-varying ERR model using expert judgement as follows. First, it assumed that the
time-constant ERR is a reasonable estimate of the ERR at age 60 with a standard error similar to thatfor the time-constant model and with an “estimated” attained age effect in which the ERR varies inproportion to a power of age. Based loosely on the atomic bombing survivor data the Committee
assumed that the ERR would tend to decrease in proportion to the inverse of age, i.e. attained age to theANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 253

power −1 but that this value is uncertain and could even be positive. Uncertainty in this parameter was
assumed to correspond to a standard error of about 0.75 (which, in terms of frequentist hypothesis
testing based on asymptotic normality implies a two-sided P value of about 0.2). Further the correlation
between estimates of the two parameters in the age-varying ERR model (ERR at age 60 and the powerof age) was assumed to be 0.5 (which is similar to the correlation between similar parameter estimatesin models fitted to the atomic bombing survivor cancer incidence data).
D47.
As for many occupational cohorts, the rate of deaths from all causes and from cancer for maleworkers in the NRRW are less than predicted on the basis of national rates. Such differences are often
said to reflect a “healthy worker effect”, in which people who are working or who had long working
careers tend to be somewhat healthier than the general population. The Committee decided to allow for
the healthy worker effect in these risk projections but to assume that there is some uncertainty in how
the ratio of rates in a (retired) worker cohort to that of the general population varies with age. In
particular, it assumed that rates in NRRW cohort members were less than the national rates throughout
the 40s but that this difference gradually attenuates as the population ages. The analysis in [M21] foundstandardized mortality (SMR) ratios of about 0.8 for both all causes and for cancer. The Committee hasapplied an SMR of 0.8 from the start of follow-up (at age 45) to age 50 but that from age 51 to 90 it
allowed the SMR to increase linearly to a random value between 0.8 and 1 (SMR90) and then remain at
this level for the remainder of life. The value of SMR90 for a specific trial was sampled from a beta
density function with parameters 1.5 and 0.5 that was scaled to the range of 0.8 to 1 with a mean of 0.95.
D48.
The computations made use of a United Kingdom life-table for 2009 obtained from [U5] andnational death and cancer incidence rates for the same year [O1]. These rates were given for the firstyear of life, for ages 1 to 4 years, then in five-year intervals to age 84 with rates for category of people
aged 85 and over. The life-table included ages up to 110 years. For ages up to 90, non-leukaemia cancer
incidence and mortality rates were defined for each year of age using linear interpolation between theavailable rates assuming that the reported values were a good approximation to the rates at the
midpoints of the age intervals. From age 91 onwards the age-specific rates were set equal to theestimated rate for age 90.
D49.
Computations of radiation-associated cases were based on the “risk of exposure-induced
deaths/cases” (REID/C) method described in [T3] and used in [U12]. The REID/C method computes
the exposure-associated “excess” in a given year as the product of probability of survival (cancer-freesurvival in the case of incidence data) to that year given the exposure and the difference between the
disease rates for exposed and unexposed populations for the outcome of interest in that year. (Equations
for the REID/C and some alternative measures of lifetime risks are given in the glossary.) The total
expected number of exposure-associated cases is then the sum of the expected excess cases over theyears of interest. Since the number of excess cases does not provide a complete summary of the impactof the exposure, it is useful to augment this value with some estimates of when the exposure-associatedcases are expected to occur. There are several possible summaries. One summary that has been used by
UNSCEAR [U10] and the ICRP [I14] and in various other reports (for example in [P12]) is the
expected years of (cancer-free) life lost per excess case. However the interpretation of this statistic is
not consistent with people’s intuitive sense, meaning it is not directly related to changes in life
expectancy or the time to cancer diagnosis among exposed individuals. One reason for this is that it isprobably more realistic to think of radiation exposure as resulting in a dose-dependent acceleration of
the cancer development process in exposed individuals than as affecting only those who develop aradiation-induced excess case. Therefore this report also considers two other, more intuitive summariesof the temporal impact of exposure. These are (a) the expected cancer-free life lost per person (i.e.
change in life expectancy) and (b) the expected cancer-free life lost per cancer case (changes in
expected age at cancer diagnosis/death). Because of the magnitude of these two summary statistics, thevalues are expressed in units of days of life lost per person or per cancer case.

254 UNSCEAR 2012 REPORT

D50.
Monte Carlo methods were used to generate samples from the probability densities for themodel, parameter estimates, and limiting SMR described above. For each of these samples the total riskin the exposed population, and the life expectancy of this population and an analogous unexposed
population, were estimated. Table D1 presents estimates and 95% credible intervals for these values
drawn from the empirical distribution of the statistics over 5,000 samples.
Table D1. NRRW-3 based estimates of lifetime exposure-associated non-leukaemia cancer casesa
and related quantities for United Kingdom nuclear workers who received an absorbed dose of
100 mGy between the ages of 30 and 44 with no additional occupational exposure
Statistic

Mean

95% credible interval
Lower

Upper

Cancer cases (baseline)

40.3

38.9

41.4

Excess cases (radiation-associated)

0.96

0.07

1.97

Attributable fraction (%)

2.4

0.2

4.8

Life lostb per person (days)

45

3

89

Life lost per cancer case (days)

111

9

217

Life lost per excess case (years)

12.8

12.1

14.4

Life expectancy, unexposed

77.7

77.3

78.5

Life expectancy, exposed

77.5

77.2

78.3

b
b

a

Cancer cases and excess cases are for an assumed population of 100 workers with follow-up from age 45 through to the end oflife. Risk estimates are based on risk models from the NRRW cohort studies.

b

Since these values are for incident cancer cases, life lost is actually cancer-free life lost and life expectancy is cancer-free lifeexpectancy.

D51.
The results indicate that for this scenario the lifetime risk of developing a non-leukaemia
cancer (other than non-melanoma skin cancer) is expected to be about 40 per 100 exposed workers
while the expected risk of an exposure-associated cancer is slightly less than 1 case per 100 exposed
workers. This indicates that about 2.4% of the cancers are expected to be associated with the exposure.
Exposure has only a small effect on life expectancy in the population as a whole, and cancers in the
exposed population are predicted to be diagnosed about 4 months earlier on average than in an
unexposed population.
D52.
Table D2 provides information on the expected age distribution of the risk of exposureassociated cancer death and the estimated proportion of the risk of death for each age group due to the
exposure. The results indicate that for each age-group considered, between 2.2% and 2.6% of therelevant cancer risks are expected to be associated with the exposure. However, because the Committee
has given some consideration to models for which the ERR is allowed to vary with age at diagnosis,
assuming a decrease more likely than an increase, there is a slight decrease in the expected attributablefraction for the older age groups.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 255

Table D2. NRRW-3 based estimates of exposure-associated non-leukaemia cancer risk andattributable fractions by age at diagnosis for United Kingdom nuclear workers who received anabsorbed dose of 100 mGy between the ages of 30 and 44 with no additional occupational exposure
Age at diagnosis

Mean

95% credible interval
Lower

Upper

EXCESS RISK (PER 100 WORKERS)
45–59

0.128

0.010

0.242

60–64

0.109

0.008

0.215

65–69

0.149

0.011

0.300

70–74

0.166

0.012

0.343

75–79

0.161

0.011

0.338

80–84

0.128

0.008

0.272

85–89

0.077

0.004

0.166

90+

0.047

0.003

0.104

ATTRIBUTABLE FRACTION (%)
45–59

2.4

0.2

4.5

60–64

2.6

0.2

4.9

65–69

2.5

0.2

4.9

70–74

2.4

0.2

4.9

75–79

2.3

0.2

4.9

80–84

2.3

0.1

4.8

85–89

2.3

0.1

4.8

90+

2.2

0.1

4.8

2.

BEIR VII/NCI-based risk and uncertainty assessment

D53.
The risk models from the third analysis of the NRRW cohort applied above to estimate risk forthe case of United Kingdom male workers exposed to 100 mGy do not have well-defined age-varying
terms and they are based on a population with a relatively short follow-up. It is of interest to estimate
risk for the same example case using risk models developed from longer follow-up of the Japaneseatomic bombing survivors (LSS cohort). The most recent, well-established risk assessment
methodology based on the LSS data has been developed by the United States National ResearchCouncil/National Academy of Science (NRC/NAS) BEIR VII committee [N19]. The BEIR VII
methodology includes risk models for 11 site-specific cancers: stomach, colon, liver, lung, breast,
uterus, ovary, prostate, bladder, thyroid and leukaemia, plus a risk model for all remaining solid
tumours (excluding non-melanoma skin cancer). This methodology has been further expanded by theUnited States National Cancer Institute [B7] to include risk models for seven additional cancer sites:
oral cavity and pharynx, oesophagus, gall bladder, pancreas, rectum, kidney, and brain/central nervous
system (CNS), plus a modified risk model for the new remaining solid tumours (still excluding nonmelanoma skin cancer). This section describes how the BEIR VII/NCI risk assessment methodology256 UNSCEAR 2012 REPORT

has been applied to assess the risk of cancer incidence for the example case of United Kingdom
workers exposed to 100 mGy.
D54.
The standard BEIR VII/NCI models for both the ERR and EAR of solid cancers other than ofηthe breast and thyroid have the form βS D exp [γ e*] (a*) where βS is the site-specific risk coefficient(for males or females), D is the dose in gray, γ is the age at exposure parameter, e* is (e - 30)/10 for eless than 30 and zero for e greater than or equal to 30, where e is age at exposure in years, η is theattained age parameter and a*=(a/60) where a is the attained age in years. The parameters were
estimated using the 1958–1998 cancer incidence data from the LSS and DS02 dosimetry [N17]. For
most cancer sites this dataset offers many advantages including its large size, high quality cancer
incidence data, wide range of doses and inclusion of all ages and both sexes. For breast and thyroid
cancer, detailed pooled analyses are available based on data from the LSS and medically exposed
populations. The risk of thyroid cancer is based on the ERR model derived from the pooled data ofseven studies described by Ron et al. [R3], as analysed by Land et al. [L5] and modified for sexdependency by the BEIR VII committee [N19]. The ERR thyroid model is similar in form to thestandard model for solid cancers, but depends only on age at exposure and not on attained age (i.e. η isequal to zero). The preferred model for breast cancer is the EAR model from the pooled analysis of fourcohorts by Preston et al. [P11]. That model has the same form as the standard model for solid cancers,
but e* is (e - 25)/10 for all ages e at exposures, and a* is (a/50). For leukaemia, models are based on the
LSS data for the period 1950–2000 and exclude chronic lymphocytic leukaemia (CLL). The ERR or
EAR BEIR VII models for leukaemia are linear–quadratic in dose and depend on sex, age at exposure(e) and time since exposure (t). The linear–quadratic model is applied for acute exposures, but only thelinear term can be applied for chronic exposure (meaning that the quadratic term can be dropped). To
account for the lower risk during the latency* period of cancers, S-shaped adjustment factors that varyfrom 0 to 1 were applied for all risk models, for the first few years after exposure, as described by
Kocher et al. [K7]. The uncertain latency adjustment is phased in between 4 and 11 years after exposure
for solid cancers, 0.4 and 4.1 years for leukaemia and 2.5 and 7.6 years for thyroid cancer.
D55.
The exposure was assumed to be chronic starting at age 30 and ending at age 44 and a total
dose of 100 mGy was assigned to each of the seventeen cancer sites and to the remainder cancergrouping. The excess risk of cancer incidence was calculated for each cancer site separately and a total
risk was estimated by summing across cancer sites. Leukaemia was not included in this summation, sothat the resulting risk is comparable to the estimates based on the NRRW cohort. Since the LSS cohort
was exposed acutely to (relatively) high doses of radiation, the risk for the assumed chronic exposure of
United Kingdom workers was adjusted by a dose and dose-rate effectiveness factor (DDREF) describedby a log-normal distribution with a geometric mean of 1.5 and a geometric standard deviation of 1.35
[N19]. The risk from radiation exposure for the United Kingdom worker population was projectedusing a risk transport model that linearly combines the ERR and EAR risk projections with 70% weight
for the ERR model and 30% weight to the EAR model (expect for lung cancer for which the weights
are reversed, thyroid cancer for which only an ERR model was used, and breast cancer for which only
an EAR model was used).
D56.
The United Kingdom baseline cancer incidence rates [O1] and life-tables [U5] for the year
2009 used in this calculation are the same as those used in the computation based on the NRRW cohort.
The baseline rates were adjusted to account for the “healthy worker effect” in the same way as in the
NRRW calculation; that is, a standardized mortality ratio (SMR) of 0.8 has been applied from up to
age 50, after which the SMR was allowed to increase linearly from 0.8 at age 51 to SMR90= 1.0 atage 90 and stay constant for the remainder of life. The SMR90 was considered to be uncertain anddescribed by a beta probability density function with parameters 1.5 and 0.5, scaled to range from
0.8 to 1.0.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 257

D57.
The estimated risk of cancer incidence was expressed as the rate of radiation-related cases, and
it is based on the “risk of exposure-induced death/cases” (REID/C) method [T3]. The uncertainty in therisk estimates was obtained using Monte Carlo methods (sample size of 500 with Latin Hypercube
Sampling) to propagate uncertainties in the risk model parameters, latency adjustment, transport
between population, DDREF, and healthy worker effect. Uncertainties associated with the assumed
dose of 100 mGy and with selection of competing dose–response models were not considered.
D58.
The BEIR VII/NCI [N19] methodology predicts a radiation-related risk from age 45 until theend of the remaining life of 0.81 (95% CI: 0.32, 1.6) cases per 100 exposed workers (table D3) and a
total expected rate of cases of 41.8 cases (95% CI: 38, 44) per 100, leading to a predicted attributablefraction of 1.9 (95% CI: 0.8, 3.7) per cent. The uncertainty in these estimates for all cancers combined
is dominated by the uncertainty in the DDREF. Age groups 70–74 and 75–79 seem to account for thelargest excess risk, each with about 16% of the total excess risk of 0.81 cases per 100. However, theattributable fraction is largest for age group 45–59 and it decreases with increasing age group up to
age 70 after which it remains relatively constant. The cancer-free life lost per person was estimated atabout 53 days, while the cancer-free life lost per cancer case is 129 days and the cancer-free life loss
per excess case is 16 years.
Table D3. Estimates of exposure-related risk of cancer incidence, based on the BEIR VII/NCI risk
assessment methodology, for United Kingdom nuclear workers who received an absorbed dose of
100 mGy between the ages of 30 and 44 with no additional occupational exposure
Statistic

Mean

95% credible interval
Lower

Upper

Total cancer cases

41.8

38.6

43.5

a

Excess cases

0.81

0.32

1.6

Attributable fraction (%)

1.9

0.8

3.7

a

NOTIONAL EXCESS CASES BY AGE AT DIAGNOSISAge at diagnosis

Mean

Lower

Upper

45–49

0.024

0.011

0.044

50–54

0.043

0.019

0.079

55–59

0.064

0.026

0.127

60–64

0.087

0.032

0.184

65–69

0.111

0.037

0.243

70–74

0.122

0.041

0.259

75–79

0.125

0.048

0.256

80–84

0.108

0.047

0.206

85–89

0.072

0.031

0.130

90+

0.050

0.019

0.101

258 UNSCEAR 2012 REPORT

Statistic

Mean

95% credible interval
Lower

Upper

ATTRIBUTABLE FRACTION (%) BY AGE AT DIAGNOSISAge at diagnosis

Mean

Lower

Upper

45–49

3.6

1.6

6.4

50–54

3.3

1.5

6.1

55–59

2.6

1.1

5.1

60–64

2.2

0.80

4.5

65–69

1.8

0.61

3.9

70–74

1.7

0.58

3.5

75–79

1.7

0.64

3.3

80–84

1.7

0.74

3.2

85–89

1.8

0.76

3.3

90+

2.0

0.76

3.9

a
Total cancer cases and excess cases are expected values for an assumed population of 100 workers with follow-up from age 45
through to the end of life. The number of cases includes all solid tumours, except non-melanoma skin cancer.

E. Summary
D59.
As detailed above, risk estimates for solid cancer after exposures in the order of 100 mGy canbe derived from a number of studies of diverse populations and exposure conditions. The group of solidcancers is made up of a large number of subgroups of individual cancer sites. In terms of statisticalpower, risk estimates for the combined group of solid cancers are usually based on comparatively large
numbers whereby the statistical uncertainty is reduced. However, in biological terms the group is madeup of rather diverse entities. Carcinogenic processes and causal associations with radiation as with otherimportant risk factors vary substantially between individual solid cancer sites. Thus, risk estimates forthe overall group need to be interpreted with caution even if detailed exposure, outcome, confounding
factor and other information are available.
D60.
Overall the body of evidence on solid cancer risks after external irradiation with cumulative
doses in the order of 100 mGy is established by highly sophisticated analyses of data from the atomic
bombing survivors on the one hand and a growing number of studies of persons externally irradiatedthrough their occupation or environment on the other hand.
D61.
In terms of sources of uncertainty beyond statistical sampling error, most work has focussed on
dosimetric errors, notably in the LSS but also in other studies, for example, the international workers
study. Uncertainty from other sources, be it from procedural aspects of conducting the study to absenceof or lack of precision of information on potential confounding factors, are frequently noted in terms ofa qualitative assessment, but usually not formally incorporated into risk estimation. Methods for
multiple bias modelling are under development, but since basic information is not available at times,
there will be limits to statistical treatment of biases also in the future.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 259

D62.
Crude risk estimates for solid cancer that do not take into account any uncertainty
considerations are presented in numerous studies. The statistical precision of such estimates is greatest
when estimated from LSS data, simply owing to the comparatively large power of the study and thewealth of information. On the other hand, the exposure situation and many other aspects limit theusefulness of LSS-based risks for describing the risks of solid cancers after protracted exposure at low
cumulative doses. Thus, direct risk estimates from studies of populations with low-dose-rate exposures,
even if less powerful and more prone to bias, need to be considered.
D63.
There is evidence of a positive dose response from these studies involving low-dose or lowdose-rate exposures (e.g. [K12, S12]), and the observed ERR per unit dose values are generally
consistent with those estimated from the LSS. An expected result of including additional uncertainties
into the risk estimation is the widening of the uncertainty range around the ERR central estimate.
D64.
The best estimates of the two approaches agree very well on a lifetime excess risk for cancer
incidence of 1% among United Kingdom radiation workers with a total dose of 100 mGy. Thus the new
study of cancer cases among members of the United Kingdom NRRW increases the confidence in thetransfer of all estimates of cancer risk from the Japanese survivors of the atomic bombings to otherpopulations. Although this approach took into account uncertainties due to the risk transfer from Japaneseto United Kingdom populations, and from exposures ranging from acute to protracted, the calculated 95%
credible interval (0.32% to 1.6%) is considerably smaller than the one derived from the NRRW study(0.07% to 1.97%). The large uncertainty in the latter approach is due to the limited statistical power which
the NRRW study had in spite of its large size (177,000 workers). Whether or not the uncertainty range
based on the risk transfer is too narrow cannot be answered at the present stage.

III. THYROID CANCER AFTER RADIATION EXPOSURE DURING
CHILDHOOD
D65.
Thyroid cancer after radiation exposure during childhood is a major concern after accidental
releases of radioactive isotopes of iodine from nuclear installations. A number of studies documented
that children are substantially more sensitive to radiation exposure than adults. Before the Chernobyl
accident, most of the knowledge on thyroid cancer risk in humans related to external exposures [R3]. A
major question was then how to transfer the risk from external exposures to that from internal
exposures to radioactive iodine. After the Chernobyl accident, direct knowledge on the effects of
exposure to 131I were gained by epidemiological studies of thyroid cancer among those in Belarus andUkraine, who were exposed during childhood or adolescence. The present section summarizes theknowledge on thyroid cancer after childhood exposures to ionizing radiation, and discusses
uncertainties for the hypothetical example of an 131I-exposure at age of 10 years with a thyroid dose of
200 mGy.

A. Summary from previous UNSCEAR reports
D66.
Annex A of the UNSCEAR 2006 Report summarized epidemiological studies of radiation andcancer [U12]. It concluded that the thyroid is highly susceptible to the carcinogenic effects of external
irradiation during childhood. A pooled analysis of thyroid cancer risk after external exposure during260 UNSCEAR 2012 REPORT

childhood resulted in an estimate of the ERR per unit dose of 7.7 (95% CI: 2.1, 28.7) Gy−1 and of theEAR per unit dose of 4.4 (95% CI: 1.9, 10.1) cases per 104 PY Gy. Thyroid cancer risks remain
elevated after such exposures for long times with some indication that the ERR begins to decline atabout 20 years after exposure. The dependence of the excess risk on sex was considered to be unclear.
The excess risk decreases strongly with increasing age at exposure.
D67.
Annex D of the UNSCEAR 2008 Report [U14] discussed health effects due to radiation fromthe Chernobyl accident. It concluded that the substantial increase in thyroid cancer incidence seenamong those exposed as children or adolescents in Belarus, the Russian Federation and Ukraine showedno signs of diminishing up to 20 years after exposure. The ingestion and inhalation of radioiodine
contributed substantially to the thyroid dose. A number of epidemiological studies had been performed
and resulted in consistent estimates of the ERR for thyroid cancer after an exposure during childhood oradolescence with a thyroid dose of 1 Gy. There was, however, conflicting evidence as to whether or not
iodine deficiency increased the risk from radiation exposure. It was emphasized that medical
surveillance of thyroid diseases increased in the affected countries after the accident leading to anincrease of the thyroid cancer cases reported in the registries. This factor has to be taken into account inmaking any kind of risk projection.

B. New evidence, not accounting for the impact of dose andmodel uncertainties
D68.
Gilbert et al. [G11] updated the analyses of thyroid cancer rates in the aftermath of the Nevada
atmospheric nuclear bomb tests. Data on thyroid cancer incidence from eight “Surveillance,
Epidemiology, and End Results” tumour registries were analysed for the period 1973–2004. The
calculation was based on the assumption that persons remained in the same county from 1951 to 2004.
Mean thyroid doses were estimated for each county, sex, and age in the calendar years 1951, 1952,
1953, 1955, 1957, 1958 and 1962 (representing 1961 and subsequent years). An increased thyroid
cancer risk was observed for mean thyroid doses in the range of 60 to 120 mGy received before one
year of age. The ERR per unit dose estimated for this age-at-exposure group was 1.8 (95% CI: 0.5,3.2) Gy−1. There was no evidence that this estimate declined with follow-up time. Furthermore there
was no evidence that the thyroid cancer risk increased after exposures at ages above 1 year. The authors
admit that the study results need to be interpreted in light of limitations and biases inherent in
geographical correlation studies, including large uncertainty in individual dose estimates and caseascertainment resulting from migration.
D69.
Bhatti et al. [B11] updated a study of second primary thyroid cancer among childhood cancer
survivors. Data were analysed for 12,547 of 5-year survivors of radiation therapy for childhood
leukaemia, Hodgkin lymphoma, non-Hodgkin lymphoma, central nervous system cancer, soft tissue
sarcoma, kidney cancer, bone cancer and neuroblastoma diagnosed between 1970 and 1986. In total,
there were 119 subsequent pathologically confirmed thyroid cancer cases. A maximum of the relativerisk for thyroid cancer of 14.6 (95% CI: 6.8, 31.5) was found for a thyroid dose of 20 Gy. For lower
doses, the risk increased linearly with increasing doses, and the ERR decreased with age at exposure.
The EAR was higher for females and increased with time after exposure.
D70.
Adams et al. [A1] analysed data on thyroid cancer among about 1,300 individuals, who hadradiation treatment of an enlarged thymus between 1926 and 1957, and among about 1,770 siblings.
Almost all of the exposed (96%) were treated at 1 year of age with a mean thyroid dose of 1.29 Gy.
Thyroid cancer occurred in 50 irradiated subjects, and in 13 non-irradiated siblings. Including theANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 261

lowest dose group receiving 0.01–0.24 Gy, thyroid cancer risk was increased in all dose groups except
one. Only the group receiving 0.25–0.49 Gy had low statistical power and no case occurred in thisgroup. The ERR per unit dose was 3.2 (95% CI: 1.5, 6.6) Gy−1, the EAR per unit dose was 2.2 (95% CI:
1.4, 3.2) per 10,000 person-year Gy. Thyroid cancer incidence appeared to decrease 40 years after
exposure and remained elevated up to 70 years after exposure.
D71.
Brenner et al. [B20] analysed thyroid cancer in a cohort of about 12,500 Ukrainians who were
under 18 years of age when the Chernobyl accident occurred and had individual radioactivity
measurements taken within the following two months. The arithmetic mean of the thyroid doses was
0.64 Gy, and the geometric mean was 0.20 Gy. Cohort members underwent up to four thyroid screening
examinations. While the first examination reflected cancer prevalence [T8], results of the last three
screenings between 2001 and 2007 could be used to calculate incidence risk [B20]. The ERR per unit
dose was 1.9 (95% CI: 0.4, 6.3) Gy−1, the EAR per unit dose was 2.2 (95% CI: 0.04, 5.8) per 10,000
person-year Gy. The ERR per unit dose varied significantly by oblast (region) of residence, but not bytime since exposure, use of iodine prophylaxis, iodine status, sex, age, or tumour size.
D72.
In summary, the two new analytical studies on external exposures confirmed earlier analyses
by deriving risk estimates either similar [B11] to the previous study of the same cohort, or a lower
estimate of the ERR per unit dose [A1]. The latter can probably be attributed to a decrease of risk withvery long follow-up times that had a median of 57.5 years in that cohort. The new study of thyroid
cancer after the Chernobyl accident was conducted over a longer time period after exposure than earlier
studies and tended to have a lower estimate of the ERR per unit dose.

C. Impact of dose and model uncertainties
D73.
Mallick et al. [M6] constructed Bayesian methods for modelling a monotonic regressionfunction when the dose estimates are subject to classical measurement errors, assignment errors, or a
mixture of the two (see also appendix B). They applied their method to the study of thyroid neoplasms
in relation to radioactive fallout from the Nevada Test Site (NTS). They showed that as the ratio ofclassical to assignment errors increases the estimated ERR per unit dose increases, as do the length andupper end of the corresponding 95% credible interval. Neglecting all errors, that is, working with thegeometric mean of the dose distribution for each of the individuals, resulted in an ERR per unit dose of
13 (95% CI: 1.5, 18) at 1 Gy. If, however, all errors were assumed to be random variability of true doseabout an assigned value, that is, to be assignment errors, then the result was 9.0 (95% CI: 2.1, 12). On
the other hand, if dose uncertainties were 100% classical measurement errors, then the ERR would be
18 (95% CI: 7.0, 32). Thus, in this case, neglecting the uncertainties in dose estimates would only be
misleading (a too low estimate, and a too narrow credible interval), if most of the uncertainty would be
due to classical measurement error.
D74.
Li et al. [L14] refined methodologies to deal with the complex error structure in the dosimetry
for the NTS Thyroid Disease Study. Their methods take account of the fact that assignment errors could
be shared within subgroups of the cohort. They assume further that the errors are a mixture of classicalmeasurement errors and assignment errors. They compare the results with an analysis, in which it isassumed that all errors are 100% due to unshared assignment errors and regression calibration is usedwith the expectation value of the individual dose. The point estimate and the upper limit of the 95%
credible interval of the ERR for thyroid neoplasms are found to increase by about a factor of 2–4
depending on assumptions made about the overall uncertainty in dose estimation. The authors conclude
that using regression calibration and expectation values for individual doses can lead to a substantial

262 UNSCEAR 2012 REPORT

underestimation of risk-per-unit-dose values, when sources of uncertainty include mixtures of classicalmeasurement error and shared sources of assignment error.
D75.
Kopecky et al. [K10] analysed data on thyroid cancer in the Bryansk oblast, Russia, amongindividuals, who were 0–19 years old at the time of the Chernobyl accident. The population-based
case–control study included 66 primary thyroid cancer cases diagnosed after the accident up to
September 1998. Thyroid dose estimates were based on a model for environmental concentrations andhad uncertainties assumed to be log-normally distributed (median geometric standard deviation of 2.2).
The authors assumed that all of the error in the doses was due to classical measurement error. No
consideration was made for shared sources of uncertainty. Correcting for such a kind of error resulted
in an increase of the estimated ERR per unit dose by a factor of three. However, the adjusted estimate is
likely to be too large, since not all of the random dose uncertainty arose from classical measurement
error. On the other hand, the effect of shared sources of dose uncertainty remains to be evaluated.
D76.
Walsh et al. [W3] analysed the impact of using different models for the estimate of the thyroid
cancer risk after exposure to ionizing radiation during childhood. They identified the modelling of thebaseline risk as the reason for contradictions in results that had been obtained previously by two
different papers [J2, L15] in analysing thyroid cancer incidence in Ukraine after the Chernobyl
accident. Different quality-of-fit criteria favoured parametric modelling of the baseline to various
stratified models of the baseline. Differences in ERR estimates amounted to more than a factor of 3 forages below 4 years old at exposure. EAR estimates are predicted to be very similar using the different
models. For thyroid cancer incidence at 12 years after exposure of the atomic bomb survivors, ERR
values predicted by a model with a parametric baseline risk were higher than a model with a stratified
baseline risk by more than a factor of 3 for ages below 7 years at exposure.
D77.
In summary, methods to correct thyroid neoplasm risk estimates for random dose errors havebeen implemented in two studies, both of which are characterized by large dose errors. In these cases,
corrected estimates of the ERR per unit dose are larger by a factor of about three than those in aregression calibration with mean values used for individual dose. The impact of shared sources of
uncertainty can influence the dose response further, but these shared errors remain to be evaluatedexplicitly. The Committee emphasizes that reliable risk estimates are normally derived from studies
with more certain dose estimates, and are thus less affected by dose uncertainties. The impact of the
choice of the model on estimates of thyroid cancer risk from exposure to radiation has been analysed
for two studies with more reliable dose estimates. For a time since exposure of 12 years, ERR estimatesfor young ages of exposure were strongly influenced by modelling of the baseline rates. EAR estimates
were more stable.

D. Selected risk evaluation
D78.
For this scenario the Committee considered a hypothetical group of Ukrainians aged 10 years
at the time of the Chernobyl accident. Their cumulative thyroid dose was 200 mGy. The dose wasnearly exclusively due to incorporation of 131I, so that short-lived radioiodines and external radiation do
not need to be considered. Surveillance of thyroid diseases in this hypothetical group should reflect thesituation in the higher contaminated parts of Ukraine about one to two decades after the accident. The
quantities of primary interest are the expected total rate of baseline and radiation-associated cases (per10,000 people) up to the end of April 2004 and up to the end of life of the group members.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 263

1.

Risk estimation taking account of studies after the Chernobyl accident

D79.
In the recent analysis of the UkrAm cohort, excess risks for thyroid cancer incidence in the
period 2001 to 2007 were estimated for Ukrainians, who have been exposed during childhood oradolescence in 1986 to radioiodine released from the Chernobyl nuclear power plant [B20]. Two postaccident case–control studies in Belarus and Russia made estimates of the ERR at about 8 years after
exposure [C2, K10]. The time dependence of the ERR and of the EAR over a period of 4 to 15 years
after exposure has been assessed in a population study in Belarus and Ukraine [J2]. The results of thesefour studies agree within their ranges of uncertainty (figure D-I). They indicate a decreasing ERR
during the first 20 years of exposure whereas the EAR varied less with time after exposure.
D80.
The post-accident studies cover a period from 4 to 21 years after exposure. In order to makelifetime predictions, results from other studies are needed. The recent analysis of cancer incidence inthe LSS covers a period from 13 to 53 years after exposure [P14]. Figure D-I shows two kinds oftransfer of the LSS data (transfer of the ERR and transfer of the EAR) to the population of Ukraine
including an extrapolation to times after exposure shorter than the period for which incidence data are
available for the LSS. The extrapolation of the ERR in the LSS agrees within the uncertainty ranges foreach of the ERR results of the post-accident studies [B20, C2, J2, K10] (upper panel of figure D-I). On
the other hand, the post-accident studies indicate a time-since-exposure (TSE) effect (according to
Jacob et al. [J2]: the ratio of the ERR at TSE = 5 years to that at TSE = 15 years is 4) that is captured
better by the transfer of the extrapolated EAR than by the transfer of the extrapolated ERR (TSE effectof about 2). Also, the post-accident EAR results agree better with the transfer of the extrapolated EAR
than with the transfer of the extrapolated ERR (lower panel of figure D-I).
D81.
For the transfer of risk quantities for thyroid cancer from one population to another, generally
the ERR is used [N19, U12]. This is motivated by the pattern of thyroid cancer rates observed during
thyroid screening and surveillance, and the assumption that ERR estimates are less influenced by these
conditions. It is, however, noted that the estimates of the ERR per unit dose differed in four cohorts of apooled study by a factor of 13, whereas the estimates of EAR per unit dose differed only by a factorof 3 [R3]. A better agreement of EAR estimates was also found between the LSS data and results forthyroid cancer in Ukraine after the Chernobyl accident (figure D-I). In the present exercise, the ERR istransferred according to a generally adopted procedure, and results in:
ERRUkraine = ERRLSS; EARUkraine = ERRLSS × baselineUkraine(D.1)

and as an alternative, the EAR is transferred according to the relatively good agreement of EAR
estimates obtained in different studies, and results in:
ERRUkraine = EARLSS/baselineUkraine; EARUkraine = EARLSS

(D.2)

D82.
The upper parts of tables D4 and D5 summarize results of the calculations for the period 1986
to 2004. According to the thyroid cancer incidence in 2009 for the whole of Ukraine, which is notexpected to be significantly affected by the radiation exposure from the Chernobyl accident, about six
baseline thyroid cancer cases are expected among 10,000 females who were of age 10 at the time of theaccident. Independent of whether the ERR or the EAR are transferred from the LSS to this Ukrainian
population group, about nine additional thyroid cancer cases are expected to be induced by an 131I
exposure with a thyroid dose of 200 mGy. The baseline incidence among males who were of age 10 at
the time of the accident is more than a factor of four lower than among females. For males, the transferof the EAR model results in nearly twice as many predicted excess thyroid cancer cases than the ERR
model transfer.

264 UNSCEAR 2012 REPORT

Figure D-I. Estimates of excess risk of thyroid cancer after the exposure to 131I of Ukrainians at age 10
with a thyroid dose of 1 Gy
The upper panel gives results on the ERR, the lower panel results on EAR. The triangle with 95% confidence intervals gives
results for the UkrAm cohort [B20]; the circle and square results for two case–control studies [C2, K10]; the solid line results for
the Ukrainian population [J2]; the dashed line results for the transfer of the (extrapolated) EAR for the LSS [P14]; and thedashed-dotted line results for the transfer of the (extrapolated) ERR for the LSS [P14]ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 265

D83.
The lower parts of tables D4 and D5 summarize results of the calculations for lifetime risks.
According to the thyroid cancer incidence in 2009 for the whole of Ukraine, about sixty baseline
thyroid cancer cases are expected among 10,000 females who were of age 10 at the time of theaccident. According to the transfer of the EAR model, this number is doubled by an 131I exposure with athyroid dose of 200 mGy. A transfer of the ERR model results in a considerably lower number ofexcess cases. The baseline incidence during lifetime for males who were of age 10 at the time of theaccident is lower than for females by more than a factor of four. For males, the transfer of the EAR
results in more than twice as many predicted excess thyroid cancer cases than the ERR transfer. It may
be noted that the difference is here because of an uncertainty in the risk model, and not because of anuncertainty in the transfer model. If the EAR model estimate for the EAR is replaced by the product of
the ERR and the baseline in the LSS, then the difference of the lifetime risks of the two transfer models
is relatively small.
Table D4. Estimates of hypothetical number of thyroid cancer cases among 10,000 Ukrainians,
who were of age 10 years at the time of the Chernobyl accident and received a thyroid dose of
200 mGy from incorporation of 131I, using the ERR model for the transfer of the risk
Calculations took into account post-accident studies, and were based on LSS data

Period and sex

Baseline

Excess

Total

Males

1.3

1.4

2.7

Females

5.7

8.3

14

Males

13

5.6

3.9

Females

61

34

96

1986–2004

Lifetime

Table D5. Estimates of hypothetical number of thyroid cancer cases among 10,000 Ukrainians,
who were of age 10 years at the time of the Chernobyl accident and received a thyroid dose of
200 mGy from incorporation of 131I, using the EAR model for the transfer of the risk
Calculations took into account post-accident studies, and were based on LSS data

Period and sex

Baseline

Excess

Total

Males

1.3

2.6

3.9

Females

5.7

9.6

15

Males

13

13

26

Females

61

60

121

1986–2004

Lifetime

266 UNSCEAR 2012 REPORT

2. Risk estimation not taking account of studies after the Chernobyl
accident
D84.
The radiation-related excess risk was calculated using a risk model derived from the pooleddata of seven studies described by Ron et al. [R3], as analysed by Land et al. [L5] and modified for sexdependency by the BEIR VII committee [N19]. The pooled analysis included the LSS cohort ofJapanese survivors externally exposed to radiation from the atomic bomb detonations in Hiroshima andNagasaki, and cohorts of patients externally exposed to medical X-rays mostly in childhood.
D85.
The risk model is linear in dose, accounts for a decrease of risk with increasing age at
exposure, and does not depend on attained age. The mathematical form of the ERR model is βS D exp[γ e*] where βS is the ERR per unit dose, D is the dose in grays, γ is the age at exposure parameter, e*is (e-30)/10 for e less than 30 and zero for e greater than or equal to 30, where e is age at exposure inyears. Parameter βS has a value of 0.53 for males and of 1.03 for females and its uncertainty is
described by a log-normal probability density function with a GSD of 1.96 for both males and females.
The age-dependent parameter γ has the same value of -0.83 for both males and females.
D86.
The risk of thyroid cancer incidence was estimated by applying the risk model to the 2009baseline thyroid cancer incidence rates for Ukraine [N5] weighted by the survival function for Ukraine
determined from 2009 life-tables [U5]. The exposure scenario assumes males and females who were
10 years of age at the time of Chernobyl accident in 1986 received thyroid doses from intake of 131I
equal to 200 mGy. Doses from 131I are delivered as a chronic exposure, and thus the BEIR VII DDREF(log-normal distribution, GM = 1.5, GSD = 1.35) was applied. Given that only individuals of age 10 are
assumed to have been exposed and that, for thyroid cancer, mortality is very low compared toincidence, the survival function of the exposed population is virtually identical to the survival functionin the absence of exposure. Thus, for this exposure scenario, the lifetime attributable risk (LAR) is avery good approximation for the risk of exposure-induced deaths/cases (REID/C).
D87.
Uncertainties in all risk estimates were calculated using Monte Carlo uncertainty propagation(sample size of 500 with Latin Hypercube Sampling) and are presented as an arithmetic mean and a
95% credible interval. Uncertainties in the results include uncertainties in model parameters and in
DDREF. Uncertainty associated with the assumed dose of 200 mGy and with the selection ofcompeting dose–response models for estimating the excess risk per unit dose were not considered.
D88.
The upper part of table D6 summarizes results of the calculations for the period 1986 to 2004.
Of the total expected number of about 2 cases among 10,000 males, the mean value of the predictedexcess cases constitutes about 30%; and of the total number of 11 cases among 10,000 females, themean value of predicted excess cases constitutes about 50%. Baseline and relative risks from radiation
exposure are assumed to be larger for females than for males. Upper and lower bounds of the 95%
credible intervals for the radiation-associated cases differ by a factor of about 16. The uncertainty isdominated by the statistical uncertainty in the BEIR VII estimate of the ERR per unit dose (GSD =1.96), followed by the BEIR VII uncertainty in the DDREF (GM = 1.5, GSD = 1.35).
D89.
The lower part of table D6 summarizes results of the calculations for lifetime risks. Of the total
number of 20 cases among 10,000 males, the mean value of the predicted cases constitutes about 30%;and of the total number of about 120 cases among 10,000 females, the mean value of the predicted
cases constitutes about 50%. Baseline and relative risks from radiation exposure are assumed to belarger for females than for males. Upper and lower bounds of the 95% credible intervals for theradiation-associated cases differ by a factor of 18. Again, the uncertainty is dominated by theuncertainty in the ERR per unit dose and DDREF estimates.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 267

Table D6. Estimates of hypothetical number of thyroid cancer cases (best estimates and 95%
credible intervals) per 10,000 Ukrainians, who were of age 10 years at the time of the Chernobyl
accident and received a thyroid dose of 200 mGy from incorporation of 131I, using the BEIR VII
models [N19]Calculations did not take into account post-accident studies

Period and sex

Baseline

Excess

Total

Males

1.3 (–)

0.56 (0.11, 1.8)

1.9 (1.4, 3.1)

Females

5.8 (–)

5.2 (0.94, 15)

11 (6.7, 20)

1986–2004

Lifetime

3.

Males

14 (–)

6.6 (1.2, 21)

20 (15, 35)

Females62 (–)

59 (11, 210)

121 (73, 272)

Summary from the two risk estimations

D90.
The two calculations agree quite well on the estimates of the radiation-related thyroid cancer
risk during their lifetime of a hypothetical group of Ukrainians exposed after the Chernobyl accident to131
I. In the BEIR VII model, it is assumed that the ERR can be directly applied to the Ukrainian
population after the Chernobyl accident. A comparison with the results after the Chernobyl accident,
however, shows a better consistency with a transfer of the EAR from the LSS to the Ukrainian
population. The EAR transfer results in a predicted number of radiation-related thyroid cancer cases
during their lifetime that is higher than that derived using an ERR transfer by a factor of 3 for males andby a factor of 2 for females. The transfer of risk introduces an uncertainty additional to those discussed
in the last subsection.
D91.
The BEIR VII model assumes an ERR that is independent of time after exposure. Postaccident experiences, however, demonstrated higher ERR values for a few years after exposure than attimes after more than a decade. As a consequence, the predictions that take into account the experiencesof the Chernobyl accident result in higher risk estimates for the first two decades after the exposure
than the BEIR VII model. The difference is most expressed for males, for whom the EAR (ERR)
transfer results in a number of predicted excess cases larger than those in the BEIR VII approach by afactor of about 5 (2.5).

IV. LUNG CANCER AFTER RESIDENTIAL EXPOSURE TO RADON
DECAY PRODUCTS
D92.
Inhalation of radon gas and its progeny represents one of the main sources of radiation
exposure of the general population. The annual per caput dose resulting from this type of exposure
typically represents about half of the effective dose received by members of the public from all natural
sources of radiation exposure [U12].

268 UNSCEAR 2012 REPORT

D93.
The principal health effect from exposure to radon decay products is an increased risk of lungcancer. Review of available epidemiological data shows no consistent evidence for an association
between radon concentration and any cancer other than lung cancer [I17]. Prior to the past decade,estimates of this risk were based on studies of miners. Meanwhile, however, there is direct evidence
from studies of residential radon exposure for a causal relationship between indoor radon exposure andthe risk of lung cancer in the general population [U13, W8]. More than 20 analytical studies (mostly
case–control studies) of residential radon exposure and lung cancer have been published and reviewed
by the Committee [U13]. Most of the studies showed a positive association between radon exposureand risk of lung cancer; however, the estimated risk coefficients varied substantially between studies
and often did not reach statistical significance. For this reason, pooled analyses of the individual data of
13 European [D2, D3], 7 North American [K14, K15] and 2 Chinese studies [L30], respectively, were
performed by the three respective research groups. These pooled studies consistently showed an
approximately linear increase in the risk of lung cancer with increasing long-term radon exposure.

A. Uncertainties in radon exposure assessment
D94.
The greatest challenge in epidemiological studies of residential radon exposure is to assess
accurately the radon concentrations for the relevant period of interest, i.e. 3-5 years (represent aminimum latency period for lung cancer) to about 35 years before diagnosis of lung cancer or date ofinterview for the controls [L26]. Usually one-year radon measurements in one or two rooms of thecurrent home and all other dwellings inhabited by the cases and controls during the period of interest
were performed. Indoor radon concentrations in the population are considered to be log-normally
distributed. They vary considerably with time (day, season, year) and location. Sources of uncertainty
in the assessment of retrospective exposure to radon have been extensively discussed [B14, H10, L26,
S27, U13].
D95.
Uncertainty in the assessment of residential radon exposure arises from detector measurement
error, the use of current measurements of radon concentrations in air to reflect past levels of up to 30 ormore years ago, spatial variations within a home, gaps from missing radon concentration
measurements, failure to link radon concentrations with subjects’ mobility, and measuring radon gas
concentration as a surrogate for dose from radon progeny [B14, L26, W8]. The impact of formally
adjusting for uncertainties in the assessment of radon exposure has been investigated in a few studies ofresidential radon exposure [D1, D2, D3, L1, U13]. In the European pooled analysis of 13 studies ofresidential exposure to radon the adjusted linear excess relative risk for an increased concentration of
100 Bq/m3 was estimated to be 0.16 (95% CI: 0.05, 0.31) [D1]. In paragraph 4 of annex E of the
UNSCEAR 2006 Report the Committee considered this estimate as an appropriate, if possiblyconservative, estimate of the risk from residential exposure to radon [U13].
D96.
Heid et al. [H10] provided a comprehensive list of the sources of errors in the assessment ofradon exposure and classified them by type of error (classical or assignment) (see table D7). The
authors defined classical error as either repeated observations with values varying about the true value(such as detector measurement error), or if one measurement is used as proxy for the average, and if
repeated measurements would vary about the average (such as room-to-room or year-to-year variation).
In most studies of residential exposure to radon, one-year measurements of the radon concentration
were made by means of alpha-track detectors. The average radon concentration is estimated bycounting the number of etched tracks made on a plastic film by alpha particles. This process is subject
to error, which has been estimated to be about 15%–25% [L26]. Next to that, radon concentrations varywith placement of the detector in a specific room or between rooms. In most studies one measurement

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 269

was conducted in each of the main living room and the bedroom, while in the other occupied rooms no
measurements were performed; the values for these rooms were assumed to be equal to those rooms
with measurements. Seasonal variation is another source of error, if radon concentrations measured
over a period of less than one year are used to estimate the annual average. Thus most residential radonstudies perform one measurement over a year or two consecutive 6-month measurements to avoid thistype of error.
D97.
The major source of classical error in exposure assessment, however, is the use of current
measurements in order to reflect the conditions of previous years. Even if a person has lived only in one
home over the whole exposure period of interest, there are major year-on-year variations owing tostructural changes (such as insulation of windows), changes in living habits (more or less ventilation)and climate changes. Even more uncertainty may arise if the current home owner differs from the study
participant. The potential size of this type of error was investigated in a range of studies by conducting
measurements in the same dwelling in different years [D2, H21, L31, Z2]. Overall, considerable
variability was found, exhibiting a coefficient of variation on a linear scale of 40%–50% on average.
D98.
Based on measurement data of the West and East German residential studies, Gerken et al.
[G5] identified factors that determine the radon concentration in homes. These included fixed factors
such as type of house, and changeable factors (variates) such as the heating system (single oven versus
central heating), windows insulation (for example, single glazing versus double glazing) and ventilation
habits. Correction factors were developed by means of variance analyses in order to take into accountdifferences for current residents and former residents. Correction factors for single variates ranged
between 1.05 and 1.2. A maximum correction factor of 1.4 was reached in the rare case of changes inmore than variate. Applying such correction factors for structural and ventilation changes, but also forseasonal variation in the case of short-term measurements, results in assignment error [H10]. This typeof error occurs if a groups’ observation is assigned to each individual of the group, but the value forindividuals would differ within each group [H10].
D99.
Uncertainty also arises from gaps in the exposure history owing to demolished homes, homesthat cannot be located or were occupied briefly and not measured, or the current occupant refuses
measurements or died within the measurement period. Weinberg et al. [W7] compared several methods
for dealing with missing exposure values by imputation and evaluated the corresponding bias in risk
estimates. These methods included: (a) to substitute each missing value with the mean across allmeasured values in the study; (b) to substitute each missing value with the mean across all measured
exposure values of the controls; (c) to substitute each missing value of a case with the mean across themeasured values of all cases, and each missing value of a control with the mean across the measured
values of all controls; (d) to substitute the missing value with a concentration of zero; and (e) tosubstitute the missing value of a specific individual with the time-weighted average across all measured
periods for that individual. Assuming no other source of error, the method of assigning the arithmetic
mean across all measured control residences turned out to be the best method, inducing no bias in risk
estimate and no distortion in the confidence interval coverage. This method can even be improved by
imputation within strata of predictive information on the missing home (such as knowledge of thestorey).

270 UNSCEAR 2012 REPORT

Table D7. Sources and type of error in assessing residential radon exposure (adapted from [H10])
Type of error

Source of error

Classical error

Variability between
measurements

Deviation between measurements obtained repeatedly at thesame time and place; detector measurement error

Variability between
placements

Variation depending on the placement of the detector in a room

Variability between rooms

Radon concentrations in the rooms without measurements differ
from radon concentrations measured, e.g. in the living room as
proxy for the concentrations in other rooms

Variability between
seasons

There is strong seasonal variation in radon concentrations, withnearly twice as high radon concentration in the winter comparedto the summer. Error occurs if short-term measurements wereused to estimate the average one-year radon concentration

Variability between years

Variations over the years due to differences in the weather,structural changes and the habits of the occupants in a home

Variability between owners

Different ventilation habits and structural changes of the former
and current inhabitant of a home, which leads to conditions in
the home during measurement different from the conditions
during residency of the study subject

Differences in ventilation
habits by room and time ofday

The detector measures average radon concentration for the fullday, but the bedroom is occupied during the night and the otherrooms during the day. For example, if the bedroom is ventilated
more during the day than at night, the measured bedroom
concentration underestimates the concentration during the
bedroom’s occupancy

Variability between
environments

Radon concentrations in residential environments other than theprincipal home are not measured and assumed to be as high, on
average, as the principal home

False recall of occupancy or
residency

False recall of occupancy times for rooms and residency times for
homes

Imputation of missing
valuesGaps in the exposure history arise from demolished homes, nottraceable, homes outside the study area, and refusal to respondby or death of the current occupant. Missing measurement
values were imputed, e.g. by assigning the arithmetic mean ofmeasured homes of the controls to the missing values

Applying correction factors
for seasonal variation orprevious owners

A certain factor is assigned to all individuals with (1) the same
seasonal pattern, (2) the same house-alterations, or (3) the samechanges in ventilation habits between current house owner andstudy participantUsing exposure data as
surrogate for the lung dose

Error in the equilibrium factor and from variability between
persons. Lung doses of persons with the same radon and radon
progeny exposure vary owing to respiratory differences

Assignment
errorComments

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 271

B. Implications of exposure uncertainties on risk estimates
D100. Based on theoretical considerations Heid et al. [H10] investigated the effect of additive andmultiplicative classical and assignment error on the risk estimate derived from studies of residential
exposure to radon and described intuitive measures of the size of error. A non-differential randomhomoscedastic error model was assumed. The authors noted that the impact of both types of error on
the risk estimate differs substantially. The classical error could induce severe bias. It attenuated thedose–response curve and in the case of multiplicative error it could even distort the dose–response
curve. In contrast to this, no notable bias on the risk estimates was induced by assignment error. If at
all, multiplicative assignment error may lead to slightly increased risk estimates, while additive
assignment error induces no bias. However, assignment error weakened the precision of the risk
estimates. The resulting effects of multiplicative and additive classical and assignment error are
illustrated in figure D-II [H10]. The figure shows the theoretically observed dose–response curve when
the dose is measured with additive (standard deviation, SD = 50) or multiplicative error (GSD = e0.4) of
the classical or assignment type and a true relative risk of 1.12. The authors recommended conducting
repeated measurements (for example, more detectors in one room, or several measurements over many
years) in future epidemiological studies, in order to gain insight into the size of errors. Analyses ofGerman data on repeated measurements of radon, for example, provided evidence for a multiplicative
error owing to variabilities between measurements and between years in the West German study [H10].
Figure D-II. Theoretical observed dose–response curves when the dose is measured with additive(standard deviation = 50) or multiplicative (standard deviation on log-scale = 0.4) error of the classicalor assignment type and a true relative risk of 1.12 (see the line “none = add Berk”) (adapted from [H10])

272 UNSCEAR 2012 REPORT

D101. Investigators have addressed uncertainties in exposure assessment by formally adjusting risk
estimates using various models [D1, D2, D3, H11, L1, L31, R1], using glass-based measurements
instead of measurements in air [A5, L2], limiting participants to long-term residents by study design[F4], conducting sensitivity analyses limited to subjects with more accurate information [D3, K14, K15,
L30] or improving the exposure assessment through linkage with spatial and temporal mobility [F5].
Applying these methods, an increase in the order of 50% to 100% in the estimate of excess relative riskof lung cancer per unit dose was observed [B14]. The different methods of accounting for uncertainty
will be discussed in detail in the following paragraphs. Table D8 provides an overview of the results ofstudies of residential exposure to radon with formal adjustment for error in the exposure estimate.
D102. The Swedish radon study [L1] adjusted risk estimates for multiplicative classical error arisingfrom uncertainty in radon exposure assessment. The study included 1,360 lung cancer cases and 2,847
controls. Radon was measured in 8,996 dwellings that had been occupied at some time since 1947.
Overall, 27.4% of dwellings could not be measured. Empirical data from Sweden had been used toestimate uncertainty in the assessment of radon exposure using a Monte Carlo modelling technique.
Simulations included sources of errors related to the detector, extrapolation of three-monthmeasurements to one-year measurements, year-on-year variation due to structural and ventilation
changes, gaps in exposure history, and spatial and temporal (age-dependent) variation in occupancy
patterns. Adjusted risk estimates were obtained from regression analyses based on expected values fortrue time-weighted average of the radon concentration (TWA), conditional on the observed TWA. A
linear exposure–response, a log-normal distribution for the true TWA, and a log-normal distribution fora relative error with constant coefficient of variation were assumed. The estimated ERR per unit TWAof radon concentration was 0.10 (95% CI: 0.01, 0.22) per 100 Bq/m3 without adjustment for error. It
increased to about 0.15 to 0.20 Bq/m3 after adjustment. Assuming a best coefficient of variance ofabout 50%, the estimate for the ERR per unit TWA of radon concentration was 0.17 (95% CI: 0.03,
0.37) per 100 Bq/m3.
D103. Uncertainties in the assessment of radon exposure have also been formally taken into accountin the south-west England study [D1]. The study included 982 lung cancer cases and 3,185 controls.
Radon concentrations had been measured in homes occupied during the 30-year period ending 5 years
before interview. Two consecutive 6-monthly measurements had been performed in the living room andbedroom. The average annual radon concentration was estimated assuming an occupancy time of 45%
in the living area and 55% in the bedroom. The time-weighted average radon concentration over the
30-year period of interest was calculated. Missing radon concentrations were imputed by the arithmetic
mean in each geographical group of controls according to Weinberg et al. [W7]. The estimated ERR per
unit TWA of radon concentration without adjustment for uncertainties in exposure was 0.08 (95% CI:−0.03, 0.20) per 100 Bq/m3; this value became 0.14 (95% CI: 0.01, 0.29) per 100 Bq/m3, after
excluding subjects with incomplete coverage of measurements over the 30-year period. Uncertainties
were taken into account according the methodology of Reeves et al. [R1] for logistic regression. A
coefficient of variance on the original scale of 51% was assumed based on external data from a study
on repeated radon measurements. After accounting for error the estimated ERR per unit TWA of radon
concentration increased to 0.12 (95% CI: −0.05, 0.33) per 100 Bq/m3 for the full data set and to 0.24
(95% CI: −0.01, 0.56) per 100 Bq/m3 in the restricted group.

Table D8. Studies of residential exposure to radon that estimate risk before and after accounting formally for uncertainty in the assessment of radon exposure orcompare air-based with glass-based detectors (adapted from [B14])
Study location, author

Number of cases

Number of controls

ERR per 100 Bq/m3 (95% CI)

Comments

FORMAL ADJUSTMENT FOR MEASUREMENT ERROR
1 281

2 576

0.10
0.17

(0.01, 0.22)(0.03, 0.37)

No adjustment for uncertainty in radon exposure
Adjustment for uncertainty in radon exposure (CV of 50%)South-west England, United
Kingdom [D1]

982

3 185

484

1 637

0.08
0.12
0.14
0.24

(-0.03, 0.20)(-0.05, 0.33)(0.01, 0.29)(-0.01, 0.56)

All subjects, no adjustment for error
Adjustment for error in exposure according Reeves et al. [R1] (CV of 51%)
Complete coverage of 30 years with measurements, no adjustment for error
Adjusted for error in exposure according Reeves et al. [R1] (CV of 51%)

Gansu, China [W5]

768

1 659

0.16
0.29

(0.03, 0.40)(0.03, 1.04)

All subjects
Adjusted for error in exposure (CV of 43%)

Gansu, China [L31]

463

1 143

0.23
0.65

(0.06, 0.57)(0.16, 3.04)≥70% coverage of exposure time window with measurements
Adjusted for error in exposure (CV of 43%)

East Germany [H11]

1 053

1 667

0.04
0.11
0.16

(-0.04, 0.12)(-0.12, 0.42)(-0.04, 0.48)

No adjustment for uncertainty in radon exposure
Adjustment for error in radon exposure (size 0.4)
Adjustment for error in radon exposure (size 0.4) and smoking (error 0.5)West Germany [H11]

1 449

2 297

-0.03
0.02
0.12

(-0.19, 0.15)(-0.38, 0.68)(-0.32, 0.83)

No adjustment for uncertainty in radon exposure
Adjustment for error in radon exposure (size 0.4)
Adjustment for error in radon exposure (size 0.4) and smoking (error 0.5)

Europe [D2, D3]

7 148

14 208

0.08
0.16
0.16

(0.03, 0.16)(0.05, 0.31)(0.05, 0.31)

No adjustment for uncertainty in radon exposure
Adjustment for measurement error using regression calibration methods
Adjustment for measurement error using integrated likelihood methods

Europe [F2]COMPARISON OF AIR-BASED WITH SURFACE-BASED RADON DETECTORS
Missouri [A5]

247
372

299
471

0.04
0.63

(-0.13, 0.57)(0.07, 1.93)

Air-based measurements with alpha-track detectors
Glass-based detectors with surface monitors

Sweden II [L2]

109

229

0.33
0.75

(-0.12, 2.00)(-0.04, 4.30)

Air-based measurements with alpha-track detectors
Glass-based detectors with surface monitors

CV: Coefficient of variation on the original scale.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 273

Sweden [L1]

274 UNSCEAR 2012 REPORT

D104. Lubin et al. [L31] investigated sources of uncertainties in radon exposure assessment in a substudy of the residential exposure study in Gansu Province in China [W5]. Within this sub-study, 1,654
detectors were placed in between one and five rooms in 55 houses over three consecutive years. The
variations of radon concentrations within rooms, between rooms within a dwelling, between dwellings,
and over time were evaluated. Temporal variation turned out to be the single largest source of
uncertainty; however, substantial residual variation remained unexplained. The maximum likelihood
estimate of the total variation from sources other than the type of dwelling was 0.17 with a standard
deviation of 0.011, resulting in a geometric standard deviation for uncertainties from these factors of
1.50 (95% CI: 1.47, 1.55) or a coefficient of variance of 0.43 (95% CI: 0.40, 0.46). A modified
regression calibration approach was used to adjust risk estimates in the full study for uncertainty of
exposure. To exclude as far as possible additional assignment bias, through imputation of missing radonvalues using radon concentrations of the controls, risk analyses were performed using the full data set
and the data set restricted to subjects with 70% coverage of measurements in the 5–30 year period ofinterest. The unadjusted odds ratios at 100 Bq/m3 were 0.16 (95% CI: 0.02, 0.44) for the full data set
and 0.24 (95% CI: 0.06, 0.62) for the restricted data. After taking uncertainties into account, the odds
ratios increased to 0.29 (95% CI: 0.03, 1.04) and 0.65 (95% CI: 0.16, 3.04).
D105. Uncertainty may not only be present in the assessment of radon exposure, but also in theassessment of potential confounding factors. Heid et al. [H11] investigated the impact of measurement
error in radon exposure and of smoking on the risk estimate. She applied the regression calibration
method adopting a bivariate multiplicative error model of the classical type. By means of sensitivity
analyses the effects of various errors in exposure on the odds ratios were explored within the West andEast German residential radon study. Both variables were assumed to be log-normally distributed andthe error to be non-differential random and homoscedastic. A small negative correlation between radonand smoking was observed (−0.06). The original uncorrected odds ratios per average radon
concentration in air had been 0.97 (95% CI: 0.81, 1.15) per 100 Bq/m3 in the West study and 1.04 (95%
CI: 0.96, 1.12) per 100 Bq/m3 in the East study, respectively. The odds ratios increased after correction
for errors in radon exposure, for example to 1.02 and 1.11 respectively, assuming a measurement errorof 0.4 (explaining 40% of the variance of the log of radon exposures among controls) in radon exposureand accounting for the correlation between radon and smoking. Additionally accounting for an error of,for example, 0.5 in the smoking variable even increased the odds ratios to 1.12 (95% CI: 0.68, 1.83)
and 1.16 (95% CI: 0.91, 1.48) respectively, again after accounting for correlation of both variables.
Generally, adjustment for measurement error led to wider confidence intervals. The authors noted thatthe correlation between radon exposure and the smoking variable affects the correction even if thesmoking variable is error-free.
D106. So far the largest and most informative study on lung cancer and indoor radon is the pooled
analysis of 13 European case–control studies published by Darby et al. [D2, D3]. It included 7,148
cases and 14,208 controls, all with detailed information on smoking histories and radon measurements
in homes that the individual had occupied during the past 15 years or more. The available radonmeasurements covered a mean of 23 years in the relevant radon exposure period 5–34 years prior tointerview. Individual exposure to radon (called “measured” radon concentration) was calculated as thetime-weighted average of the radon concentrations in all the homes occupied over the past 5–34 years.
Missing radon values were substituted by the mean concentration of the controls in the specific study or
specific area strata [D3]. A linear regression model was used, with stratification for study, age, sex,
region or residence within each study, and detailed smoking history.
D107. Formal adjustment of the risk estimates for classical (year-on-year variability of measurements)
and assignment (imputation of missing values) measurement errors was performed. In order to accountfor classical measurement errors, a log-normal distribution of the “true” (or long-term average) radon

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 275

concentration within each geographical district was assumed. Next to that, it was assumed that, on alogarithmic scale, the variability associated with repeated measurements of radon concentrations in thesame dwelling was normally distributed about the true concentration for that dwelling [D3]. For thosecountries where repeated radon measurements had been made, these data were used to estimate acountry-specific coefficient of variation for the classical measurement errors. For all countries with nodata available the median of the estimated values for the other countries was used (CV = 40%). Two
different methods for correcting estimates of risk from residential radon exposure for errors were used
[D2, D3, F2]: the regression calibration method, and the method of integrated likelihood.
D108. Regression calibration was used to replace the measured radon concentrations by their
expected values. After correction, the mean of the TWA of radon concentration among cases andcontrols decreased: for cases from 104 Bq/m3 (observed) to 90 Bq/m3 (corrected); and for controls from
97 Bq/m3 (observed) to 86 Bq/m3 (corrected). The main effect of regression calibration is that thevalues for people exposed to high observed radon concentrations tended to be substantially lower after
correction, while for those exposed to low observed radon concentrations, the corrected values tended
to be somewhat increased. This can be seen in table D9, where for example, in the group of 181 persons(66 cases and 115 controls) with a measured concentration of more than 800 Bq/m3, the mean measured
value was 1,204 Bq/m3, whereas the mean corrected value was 678 Bq/m3. Similarly, among those
persons (566 cases and 1,474 controls combined) with a measured concentration of less than 25 Bq/m3,
the mean measured value was 17 Bq/m3, whereas the mean corrected value was 21 Bq/m3.
Table D9. Mean observed and corrected radon concentrations by categories of observed radon
concentration for the cases and controls [D3]
Observed radon
concentrations (Bq/m3)

Number ofcases

Number ofcontrols

Mean observed radon
concentrationa (Bq/m3)

Mean corrected radon
concentrationb (Bq/m3)

<25

566

1 474

17

21

25–49

1 999

3 904

39

42

50–99

2 618

5 033

71

69

100–199

1 296

2 247

136

119

200–399

434

936

273

236

400–799

169

498

542

433

≥800

66

115

1 204

678

a

Observed radon concentration for each address in the 30-year period ending 5 years prior to the index date, weighted
according to the length of time that the person lived there.

b

Corrected radon concentration, after uncertainties in the assessment of the radon concentrations were taken into account.

D109. In the European pooled study the estimate for the ERR per unit TWA of radon concentration
was 0.084 (95% CI: 0.03, 0.16) per 100 Bq/m3 without adjustment for measurement error. After
adjustment for uncertainty in the assessment of radon exposure the estimate increased to 0.16 (95% CI:
0.05, 0.30) per 100 Bq/m3 using regression calibration [D3]. A similar result was obtained when themethod of Monte Carlo integration of the likelihood was used (estimated ERR per unit TWA of radon
concentration was 0.16 (95% CI: 0.05, 0.31) per 100 Bq/m3. Figure D-III shows on the right the linear
relationship between the relative risk of lung cancer and TWA-corrected radon concentration. Also
shown on the right are relative risk estimates plotted against the mean corrected radon concentration for
persons in categories. Owing to the fact that the corrected mean in the highly exposed group is only
about half the mean observed value, the slope of the relationship is steeper after accounting for errors.

276 UNSCEAR 2012 REPORT

Figure D-III. Relative risk of lung cancer according to the TWA of observed radon concentration (onthe left) and the TWA-corrected radon concentration (on the right)
The relative risks and 95% CI are shown for the analyses by category, as are the estimated linear relationships (solid lines) with
95% CI (dashed lines). The risks were calculated after stratification by study, age, sex, region of residence, and smoking
history. On the right, the estimated linear relationship was calculated using the method of integrated likelihood, and therelative risks from the analysis based on categories of observed radon concentration were plotted against the mean
corrected radon concentration for each of these categories [D3]

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 277

D110. Analyses of effect modification by sex, age, smoking status and histological type of lungcancer gave similar results with and without correction for measurement errors, although the correction
had a proportionately greater impact on the ERR estimate for ex-smokers and lifelong non-smokers
than on the corresponding estimate for current smokers. Nevertheless, there was no statisticallysignificant heterogeneity in the ERR estimates between smoking categories, either with or without
adjustment for measurement errors. Furthermore, the ERR estimates and confidence intervals from theanalyses of effect modification were similar using the regression calibration and integrated likelihood
approaches. Fearn et al. [F2] suggested that regression calibration should perform very well in adjustingfor measurement errors in studies of residential exposure to radon and lung cancer and that moresophisticated approaches are not required.
D111. Table D10 summarizes the estimated ERR per unit measured radon concentration for the threepooled analyses in Europe [D2, D3], North America [K14, K15] and China [L30]. While the European
study was formally adjusted for uncertainties in radon exposure, no such adjustments have been madeso far in the pooled North American and Chinese studies. However, sensitivity analyses have been
performed by restricting subjects to those assumed to have more accurate exposure estimates, that is,complete or higher coverage of the period of interest with radon measurements or lower mobility(living in only 1 or 2 homes). Risk estimates increased with increasing assumed accuracy of dosimetry,leading to nearly doubling of the estimate.
Table D10. Estimates and 95% confidence intervals of excess relative risk per unit radon
concentration from pooled residential studies with and without restriction to more accurate exposure
Study, restrictions

Number ofcases

Number ofcontrols

ERR per unit radon
concentration(per 100 Bq/m3)

95% CI

0.08
0.09(0.03, 0.16)(0.03, 0.18)

EUROPE [D2, D3]
All subjects<3 residences, ≥20 years measured

7 148
4 221

14 208
8 371

NORTH AMERICA [K14, K15]
All subjects, no restriction to mobility

3 662

4 966

0.11

(0.00, 0.28)≥15 years measured

2 764

3 857

0.13

(0.00, 0.31)≥20 years measured

2 263

3 172

0.14

(0.01, 0.35)

25 years measured

1 621

2 323

0.21

(0.03, 0.50)≥15 years measured

2 171

3 009

0.17

(0.01, 0.41)≥20 years measured

1 910

2 651

0.18

(0.02, 0.43)

25 years measured

1 552

2 170

0.21

(0.03, 0.52)

1 050

1 995

0.13

(0.01, 0.36)

complete coverage of exposure
period

n.a.

n.a.

0.32

(0.09, 0.88)

subjects residing in one home

n.a.

n.a.

0.33

(0.08, 0.96)

Subjects residing in 1 or 2 houses only

CHINA [L30]
All subjects

278 UNSCEAR 2012 REPORT

D112. The pooled North American residential radon study [K14, K15] included a total of 3,662 cases
and 4,966 controls. Residential radon levels were measured for one year by alpha-track detectors. For
each individual the time-weighted average of the radon concentrations in the homes was calculated forthe period 5–30 years prior to the date of interview. The ERR per unit average radon concentration was
0.11 (95% CI: 0.00, 0.28) per 100 Bq/m3. Analyses restricted to individuals with presumed “moreaccurate dosimetry” resulted in increased risk estimates. For example, for individuals who lived in only
one or two homes in the 5–30 year period and for which alpha-track measurements covered 25 years of
this period, the ERR per unit average radon concentration was 0.21 (95% CI: 0.03, 0.52) per
100 Bq/m3. The Chinese pooled study [L30] included 1,050 cases and 1,996 controls. Similarly to theNorth-American pooled study, the time-weighted average of the radon concentration in the homes
within the exposure period 5–30 years was calculated. The ERR per unit increase in measured radon
concentration was 0.13 (95% CI: 0.01, 0.36) per 100 Bq/m3. When analyses were restricted to individuals
resident in only one home and with complete measurement coverage in the relevant period the estimate of
ERR per unit average radon concentration increased to 0.33 (95% CI: 0.08, 0.96) per 100 Bq/m3.
D113. Field et al. [F5] reported on the variation in risk estimates related to different exposure
scenarios within the Iowa Radon Lung Cancer Study [F4]. The study was restricted to individuals who
lived in their current home for at least 20 years. It included a total of 413 cases and 614 controls.
Information on the temporal and spatial occupancy pattern in the home, outside and in other buildings
was obtained via mailed questionnaire and face-to-face interviews. One-year radon measurements wereconducted in various areas in the home. In addition, data from regional outdoor radon measurements
were used and the subject’s exposure when in other buildings was assessed. Several methods were used
to calculate the cumulative radon exposure in the period 5 years to 20 years prior to interview. The
preferred model was based on radon measurements in the home, outdoors, and in another building withlinkage of these values to the individual’s spatial and temporal occupancy patterns. Other models usedradon measurements in either solely the basement, the living and/or bedroom, assuming a 70% standard
occupancy time for all subjects. Overall, the preferred radon-exposure model exhibited slightly higher
risk estimates and the lowest measurement error as compared with the other models that ignored theindividual mobility pattern. The findings were similar when the analyses were restricted to the subjects
still alive (283 cases and 614 controls) with presumably more accurate information on mobility andmore representative radon measurements. The lowest risk estimate and the highest measurement error
were found for the model using solely basement radon measurements. Here, misclassification of
exposure was expected to be high, because radon concentrations in the basement were particularly high,while occupancy was low. The authors argued that the improved dosimetry model reduced exposure
misclassification, and thus was likely to contribute to increased risk estimates.
D114. Heid et al. [H9] investigated how bias in risk estimates from additive and multiplicative
measurement error differs between groups with different parameter values of exposure. For example, in
the West German residential radon study [K11] higher risk estimates have been observed when data
were restricted to individuals living in radon-prone matching areas (365 cases and 565 controls) as
compared to the entire study (1,449 cases and 2,297 controls). The subgroup was characterized by alarger mean and standard deviation of observed radon exposure (59 Bq/m3 and 66 Bq/m3) compared tothe entire group (49 Bq/m3 and 47 Bq/m3), respectively. The effect of varying exposure parameters on
the bias from measurement error was investigated by means of theoretical considerations andsimulations, assuming a non-differential homoscedastic random error. Results showed that bias fromboth additive and multiplicative assignment error was independent of exposure distribution parameters.
In contrast to this, bias from additive classical error decreased with increasing exposure variance, but
was independent of the exposure mean. Bias from multiplicative classical error decreased withincreasing geometric standard deviation or increasing coefficient of variation of exposure, but was
independent of the geometric mean of exposure. The results indicate that the bias possibly differs

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 279

between groups where these parameters differ. Therefore, if groups with for example varying exposure
variance are compared, the bias on the estimates of the risk coefficient possibly differs between groups
even if the true underlying risk coefficient and the size of measurement error is assumed to be the sameacross groups and for all individuals.

C. Use of glass objects for radon dosimetry
D115. An innovative method to potentially improve retrospective assessment of radon exposure are
dosimetry techniques based on the 210Po surface activity on glass objects that have been in a subject’s
home through the whole or the major part of the exposure period of interest [B13, M5, S26, W6].
CR-39 alpha-particle detectors, so-called surface monitors, are made from an alpha-sensitive material,
allyl diglycol carbonate. They directly assess long-term (20-year or more) cumulative exposure byanalysing glass objects in the home. The surface monitors take advantage of the fact that the first longlived radon progeny, 210Pb (half-life 22 years), becomes embedded in glass surfaces in homes. The
alpha-activity of 210Po, a decay product of 210Pb, is measured in glass objects.
D116. A critical point in using glass-based monitors are factors affecting the deposition of radon
daughters on the surface of the object, such as the aerosol concentration, the relative extent of surface
areas compared to the volume of the room, the air-exchange rate and air motion in the room or the
position of the object [W1]. It was argued that tobacco smoke reduces the plate-out of radon progeny on
surfaces and that this could introduce bias [W6]. Bochicchio et al. [B13] compared air-based and glassbased measurements in a sample of 26 dwellings. The correlation between both methods was relatively
high (0.83) for objects exposed in non-smoky dwellings, while it vanished (−0.01) when the objects
were exposed in smoky dwellings. Other critical issues concern accuracy of estimates of the age of theglass objects, history of the glass before it was used in the homes, and in large-scale epidemiologicalstudies the existence of suitable glass objects to cover the exposure period.
D117. It has been discussed whether glass-based measurements can provide a better representation of
the cumulative radon exposure in the exposure period of interest than air-based measurements in thecurrent dwellings. Two residential radon studies used both methods of measurements [A5, L28]. In
both studies substantially higher risk estimates based on measurements on glass compared tomeasurements in air were observed (see table D8). Results indicate a presumably greater precision in
the estimation of past exposure when using surface monitors compared to air-based monitors. However,some unexplained bias that affects cases and controls differently cannot be ruled out completely.
D118. The Missouri residential radon study [A5] was the first epidemiological study that provided
risk estimates based on both types of dosimetry: air radon detectors and CR-39 surface monitors. The
study included 512 lung cancer cases and 553 controls. Indoor air dosimeters had been placed in thecurrent dwellings for one year, and the annual time-weighted average radon concentrations for the 5–25
years exposure period were calculated. Two glass objects for cumulative radon measurement by surface
monitors were identified by questionnaire and interview. The detectors were affixed for 4 weeks to theglass objects after being cleaned. The cumulative radon values from surface detectors were converted
into annual TWA of radon concentration by dividing the cumulative readings by the number of years
the subject owned the glass object. Correction factors were empirically derived [M5] to adjust fordifferential deposition rates among smokers and non-smokers and for window-glass or not. A
statistically significant excess odds ratio at 150 Bq/m3 of 0.95 (95% CI: 0.1, 2.9) for TWA of the radon
concentrations measured by surface monitors was found, while no elevated ERR was present whenmeasurements were based on indoor air detectors. Alavanja et al. [A5] argued that a possible
explanation for this result would be that surface monitors are less prone to random error than air-based

280 UNSCEAR 2012 REPORT

monitors. He demonstrated using a Monte Carlo simulation study that a year-on-year variability in therange, as estimated by Steck et al. [S26], could completely dilute a risk of the magnitude observed
using surface monitors when current measurements using air-based monitors are employed to reflect
the exposure period.
D119. Both glass-based and air-based measurements had also been performed in a Swedish case–control study on lung cancer among never-smokers [L2]. The study included 110 lung cancer cases and231 controls. Two air measurements were performed for 3 months in the heating period in all dwellings
occupied by the individual for at least 2 years in the 32-year period ending 3 years before interview,and the annual TWA of the radon concentration was calculated. Two surface-based measurements were
performed using glass objects that were preferably at least 20 years old, and new when present for the
first time in the subject’s home. Calibration factors were applied to translate surface activity into
average radon concentration for the exposure period of interest. The ERR per unit average radon
concentration was estimated to be 0.33 (95% CI: −0.12, 2.0) per 100 Bq/m3 for air-based radonmeasurements and 0.75 (95% CI: −0.04, 4.30) per 100 Bq/m3 for surface-based radon measurements.
Exposure to environmental tobacco smoke did not modify the relation between surface-based and airbased radon concentration estimates.

D. Evaluation of the risk and its uncertainty
D120. Overall the three major pooled analyses of residential radon exposure and lung cancer provide
consistent risk estimates (see table D11). Without adjustment for uncertainty in the assessment of radon
exposure, the estimate of ERR per unit TWA of radon concentration is 0.08 (95% CI: 0.03, 0.16) per
100 Bq/m3 in the European study [D2, D3], 0.11 (95% CI: 0.00, 0.28) per 100 Bq/m3 in the North
American study [K14, K15] and 0.13 (95% CI: 0.01, 0.36) per 100 Bq/m3 in the Chinese study [L30].
Risk estimates based on measured radon concentrations without accounting for error are likely tounderestimate the true risk. In the European pooled study, so far the largest study, the ERR per unit
TWA of radon concentration increased from 0.08 per 100 Bq/m3 to 0.16 per 100 Bq/m3 after taking into
account year-on-year variation. The joint risk estimate from the three pooled studies, when assuming asimilar effect of adjusting for year-on-year variation in the Chinese and North American studies as in
the European study, would be around 0.20 per 100 Bq/m3 [W8].
Table D11. Summary of risk estimates derived from pooled residential studies (adapted from [W8])
Number ofcases

Number ofcontrols

ERR per unit radon
concentration
3(per 100 Bq/m ) (95% CI)

Adjusted ERR per unit
radon concentration
3(per 100 Bq/m ) (95% CI)aEurope [D2, D3]

7 148

14 2080.08 (0.03, 0.16)

0.16 (0.05, 0.31)

North America [K14, K15]

3 662

4 966

0.11 (0.00, 0.28)-

China [L30]

1 050

1 995

0.13 (0.01, 0.36)

-

0.10

0.20b

Study

Weighted average of above
results of pooling studiesaAdjusted for year-on-year random variability in indoor radon concentrations.

b

Informal estimate, indicating the likely effect of removing the bias induced by random year-on-year variation in radon concentration.

D121. Sources of uncertainty in the assessment of past radon exposure include year-on-year variation,
detector measurement error, failure to link spatial and temporal mobility, gaps in exposure history, anduse of radon exposure as a proxy for radon progeny dose. Several methods have been applied toANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 281

account for these uncertainties in exposure assessment, such as using glass-based measurements insteadof air measurements [A5, L2], limiting participants to long-term residents by study design [F2],conducting sensitivity analyses with restriction to subjects with more accurate information [D3, K14,
K15, L30] or improving the exposure assessment through linkage, with spatial and temporal mobility[F5]. Applying these methods consistently led to an increase of the excess relative risk of lung cancer inthe order of 50% to 100%. In addition, uncertainty in the assessment of major confounding factors suchas smoking may be present, possibly leading to bias in the estimated risk [H11]. This indicates that thetrue ERR per unit TWA of radon concentration could be somewhat higher, even after correction for
year-on-year variation in measured radon concentrations [W8].
D122. The excess risk of lung cancer associated with indoor radon concentration is small, therefore
confounding is of particular concern. Most of the individual studies were matched by age and sex,
ensuring little confounding by these factors. The three pooled analyses were additionally stratified byage, sex and study. There was substantial negative confounding by smoking. In the European pooled
study much effort was spent to control adequately for smoking in the risk analyses [D2]. Detailed
sensitivity analyses suggested that it is appropriate to control for smoking by stratification into
20 groups: never-smokers, current cigarette smokers in 12 groups (subdivided by age at starting
smoking and cigarettes per day smoked), ex-smokers in six groups (subdivided by time since stoppingsmoking and cigarettes smoked per day), and smokers of pipe, cigars, and cigarillos. The ERR per unit
TWA of radon concentration stratified by age, sex and study without stratification for smoking
increased from 0.023 to 0.084 after additional stratification for smoking. Also restricting the risk
analyses to lifelong non-smokers led to a comparable statistical significant risk of 0.11 (95% CI: 0.003,
0.28) per 100 Bq/m3; for current cigarette smokers, a value of 0.07 (95% CI: −0.01, 0.22) per 100 Bq/m3
was obtained [D3]. It is interesting to note, that a similar result was obtained in a joint analysis of three
European case–control studies among uranium miners: The ERR per unit exposure was 0.012 (95% CI:
0.005, 0.026) per WLM among never smokers and long-term ex-smokers, while a value of 0.007 (95%
CI: 0.003, 0.013) per WLM was found for short-term ex-smokers and current smokers. Other potential
confounding factors such as social status or employment in an occupation with an established lungcancer risk have been investigated in the European radon indoor study as well [D3]. Inclusion of theserisk factors in the model, however, did not change the risk estimate.
D123. Misclassification of disease could be another issue of bias in the risk estimates. In most studies
lung cancer cases were collected from study clinics. Inclusion criteria for a case were a histological or
cytological confirmation of a primary lung cancer. In the pooled European analyses, fewer than 10% of
the cases and controls were based on death certificates only. The ERR per unit TWA of radon
concentration did not differ between studies with ascertainment of the cases based on clinicalinformation or death certificates only. Another issue is selection bias through the use of populationbased or hospital-based controls. Again, there were no significant differences in the estimated effect ofradon exposure. Similarly, there was no difference according to whether or not surrogate interviews
were accepted.
D124. There was little evidence of effect modification by age in the pooled European [D2] and North
American study [K14, K15]. In the European pooled study [D2], the ERR per unit observed TWA ofradon concentration were 0.11, −0.02, 0.14, 0.8 and 0.00 per 100 Bq/m3 for the age categories: younger
than 45, 45–54, 55–64, 65–74, older than 75 years, respectively (P value for trend test: 0.98). The same
held true for the risk estimates related to the corrected radon concentrations (P value for trend test: 0.28).
Here the corresponding risk estimates were −0.12, 0.13, 0.16, 0.16 and 0.57 per 100 Bq/m3, respectively.
D125. In the European pooled study, the effect of different measures of the radon concentration andof different models for the relationship between radon concentration and lung cancer were investigated[D2]. The published results are based on the time-weighted average of radon concentration in the282 UNSCEAR 2012 REPORT

30-year period of interest (5–35 years prior to interview). Using the time-weighted average of the 5–14
years, 15–24 years or 25–35 years in the past only, or the time-period weighting factors of the BEIR VI
model led to nearly similar results. When instead of linear relative risk model (RR = 1+β x), a linear–quadratic relationship (RR = 1 + β1 x + β2 x2) or a log-linear relationship (RR = exp(β x) was applied,there was no statistically significant improvement in the fit.
D126. The cumulative risk of death from lung cancer by age 75, 80 and 85 years for lifelong nonsmokers and continuing smokers of 15 to 24 cigarettes per day at various levels of observed radon
concentration and corrected radon concentrations was evaluated in the pooled European case–control
study [D2]. The authors assumed that the relative risk of lung cancer increases by 0.08 (95% CI: 0.03,
0.16) per increase of 100 Bq/m3 in the observed radon concentration regardless of smoking status. Thisoverall risk estimate was taken, because there was no heterogeneity between the estimated relative risks
for the three different smoking categories. The corresponding risk estimates had been 0.11 (95% CI:
0.003, 0.28) per 100 Bq/m3 for lifelong non-smokers, 0.08 (95% CI: 0.003, 0.21) per 100 Bq/m3 for exsmokers and 0.07 (95% CI: −0.01, 0.22) per 100 Bq/m3 for current smokers, respectively. The
cumulative risk was additionally calculated after adjustment for the effect of random uncertainties in
the assessment of radon concentration according the regression calibration method. It was assumed thatthe relative risk of lung cancer increases by 0.16 (95% CI: 0.05, 0.31) per increase of 100 Bq/m3
corrected radon concentration again regardless of smoking status. The corresponding risk estimates forlifelong non-smokers, ex-smokers and current smokers had been 0.20 (95% CI: 0.02, 0.53), 0.18 (95%
CI: 0.02, 0.47) and 0.09 (95% CI: <0.08, 0.37) per 100 Bq/m3. Again there was no evidence ofheterogeneity between these risk estimates. The authors assumed a relative risk of lung cancer forcontinuing smokers compared to lifelong non-smokers of 25, which refers to the overall estimate in the
study. The absolute risk of lung cancer for the lifelong non-smokers was taken from a prospective studyof the American Cancer Society [P3], because no comparable data had been available for Europe. A
comparable relative risk per unit TWA of radon concentration for smokers and non-smokers means thatthe excess absolute risk (number of cases per person years of risk) is considerably higher for smokers
than for non-smokers.
D127. Table D12 shows the results of the estimated cumulative risk of death from lung cancer by age
75 and 85 years in relation to observed and corrected radon concentrations for lifelong non-smokers
and current smokers. For lifelong non-smokers with no exposure to radon, the cumulative risk of deathfrom lung cancer was estimated to be 0.42% or 0.81% by the age of 75 or 85 years, respectively [D2].
For lifelong non-smokers with finite exposure to radon, the cumulative risks of death from lung cancer
were somewhat greater, for example, with values of 0.71% or 1.35% at 800 Bq/m3 by the age of 75 or
85 years, respectively. For continuing smokers of 15–24 cigarettes per day, not only was the cumulativerisk of death from lung cancer with no exposure to radon much higher (10.4% or 19.1% at age 75 or
85 years, respectively), but the increase in the cumulative risk with an increasing observed radon
concentration was also substantially higher. For example, with an observed radon concentration of
800 Bq/m3 the cumulative risks associated were evaluated as 16.8% or 29.8% by age 75 or 85 years,
respectively. It is important to note that the cumulative risks for ex-smokers who had quitted smoking
less than 10 years previously would be about 80% of those of continuing smokers. For those who
quitted smoking more than 10 years previously the risks would be lower [D2].
D128. When instead of observed radon concentrations, the corrected radon concentrations wereconsidered, a similar pattern of risk was observed, however, with consistently higher risk estimates (seetable D12). The cumulative risk of death from lung cancer for lifelong non-smokers with no radon
exposure was estimated to be 0.41% or 0.78% by the age of 75 or 85 years, respectively. For lifelong
non-smokers with finite exposure to radon, the cumulative risks were estimated to be somewhat higher,
for example, with a value of 0.91% or 1.78% by age 75 or 85 years for 800 Bq/m3, respectively. For
continuing smokers of 15–24 cigarettes per day, the cumulative risk of death from lung cancer

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 283

increased from 10.11% with no radon exposure to 21.6% at 800 Bq/m3 by age 75, and from 18.5% withno radon exposure to 37.3% at 800 Bq/m3 by age 85, respectively. As for the results on observed radon
concentrations, the cumulative risks for ex-smokers who gave up smoking less than 10 years previously
would be about 80% of the risk for continuing smokers.
Table D12. Cumulative risk of death from lung cancer by age 75 and 85 years for lifelong nonsmokers and continuing smokers of 15–24 cigarettes per day at various levels of observed andcorrected radon-concentration
From source ([D2], tables 29 and 38)

By ageRadon
concentration(Bq/m3)75 years

Lifelong non-smokers
Cumulative risk (%)

Continuing smokers of 15–24
cigarettes per day

95% CI

Cumulative risk (%)

95% CI

TIME-WEIGHTED AVERAGE OF OBSERVED RADON CONCENTRATION
0

0.42

-

10.43

-

100

0.46

0.42, 0.49

11.25

10.45, 11.97

200

0.49

0.43, 0.56

12.07

10.48, 13.49

400

0.56

0.43, 0.69

13.68

10.54, 16.45

800

0.71

0.43, 0.95

16.81

10.66, 22.06

TIME-WEIGHTED AVERAGE OF CORRECTED RADON CONCENTRATION
0

0.41

-

10.11

-

100

0.47

0.43, 0.54

11.63

10.59, 13.03

200

0.54

0.45, 0.66

13.12

11.06, 15.85

400

0.67

0.49, 0.91

16.03

12.00, 21.23

800

0.93

0.57, 1.42

21.57

13.86, 30.98

85 years

TIME-WEIGHTED AVERAGE OF OBSERVED RADON CONCENTRATION
0

0.81

-

19.06

-

100

0.88

0.81, 0.94

20.48

19.11, 21.72

200

0.95

0.81, 1.06

21.88

19.16, 24.29

400

1.08

0.82, 1.32

24.61

19.26, 29.18

800

1.35

0.83, 1.82

29.78

19.47, 38.04

TIME-WEIGHTED AVERAGE OF CORRECTED RADON CONCENTRATION
0

0.78

-

18.51

-

100

0.91

0.82, 1.03

21.13

19.34, 23.52

200

1.03

0.86, 1.27

23.67

20.16, 28.22

400

1.28

0.94, 1.75

28.51

21.77, 36.77

800

1.78

1.10, 2.70

37.29

24.91, 50.94- Absolute risk of lung cancer for the lifelong non-smokers taken from a prospective study of the American Cancer Society [P3].
- The relative risk of lung cancer for continuing smokers of 15–24 cigarettes per day was assumed to be equal to the overall
estimates in the study.
- The relative risk of lung cancer was assumed to increase by 0.08 (95% CI: 0.033, 0.158) per 100 Bq/m3 increase in the timeweighted-average (TWA) of observed radon concentrations and to increase by 0.16 (95% CI: 0.05, 0.31) per 100 Bq/m3 increasein the TWA of corrected radon concentrations regardless of smoking status.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 285

REFERENCES
A1

Adams, M.J., R.E. Shore, A. Dozier et al. Thyroid cancer risk 40+ years after irradiation for anenlarged thymus: an update of the Hempelmann cohort. Radiat Res 174(6): 753-762 (2010).

A2

AGIR. Review of risks from tritium. Advisory Group on Ionising Radiation. RCE-4. HealthProtection Agency, Chilton, 2007.

A3

Akaike, H. Information theory and an extension of the maximum likelihood principle. pp.267288 in: Proceedings of the 2nd International Symposium on Information Theory (B.N. Petrov
and F. Caski, eds.). Akademiai Kiado, Budapest, 1973.

A4

Akaike, H. A New Look at the Statistical Model Identification. IEEE Trans Autom Control
19(6): 716-723 (1974).

A5

Alavanja, M.C., J.H. Lubin, J.A. Mahaffey et al. Residential radon exposure and risk of lungcancer in Missouri. Am J Public Health 89(7): 1042-1048 (1999).

A6

Allodji, R.S., K. Leuraud, S. Bernhard et al. Assessment of uncertainty associated withmeasuring exposure to radon and decay products in the French uranium miners cohort. J
Radiol Prot 32(1): 85-100 (2012).

A7

Anderson, D.R. Model Based Inference in the Life Sciences: A Primer on Evidence. Springer,
New York, 2008.

A8

Annest, A., R.E. Bumgarner, A.E. Raftery et al. Iterative Bayesian Model Averaging: amethod for the application of survival analysis to high-dimensional microarray data. BMC
Bioinformatics 10: 72 (2009).

A9

Apostoaei, A.I., R.E. Burns, F.O. Hoffman et al. Iodine-131 releases from radioactive
lanthanum processing at the X-10 site in Oak Ridge, Tennessee (1944-1956) -- An assessmentof quantities released, off-site radiation doses, and potential excess risks of thyroid cancer.
Reports of the Oak Ridge Dose Reconstruction. Vols. 1 and 1A: Tennessee Department of
Health 1999.

A10

Apostoaei, A.I. and L.F. Miller. Uncertainties in dose coefficients from ingestion of 131I, 137Cs,
and 90Sr. Health Phys 86(5): 460-482 (2004).

A11

Apostoaei, A.I., B.A. Thomas, D.C. Kocher et al. Doses to the public from atmosphericreleases of radionuclides from the Idaho Chemical Processing Plant at the Idaho National
Engineering Laboratory (1957-1959). Final Report. Centers for Disease Control andPrevention, I. SENES Oak Ridge, Tennessee, 2005.

A12

Armitage, P. and R. Doll. The age distribution of cancer and a multi-stage theory ofcarcinogenesis. Br J Cancer 8(1): 1-12 (1954).

A13

Ashmore, J.P., N.E. Gentner and R.V. Osborne. Incomplete data on the Canadian cohort may
have affected the results of the study by the International Agency for Research on Cancer on
the radiogenic cancer risk among nuclear industry workers in 15 countries. J Radiol Prot
30(2): 121-129 (2010).

286 UNSCEAR 2012 REPORT

A14Astakhova, L.N., L.R. Anspaugh, G.W. Beebe et al. Chernobyl-related thyroid cancer inchildren of Belarus: a case-control study. Radiat Res 150(3): 349-356 (1998).

A15

Atkinson, W.D., D.V. Law, K.J. Bromley et al. Mortality of employees of the United Kingdom
Atomic Energy Authority, 1946-97. Occup Environ Med 61(7): 577-585 (2004).

B1

Barndorff-Nielsen, O.E. and D.R. Cox. Asymptotic Techniques for Use in Statistics. Chapman
and Hall, London, 1989.

B2

Bauer, S., B.I. Gusev, L.M. Pivina et al. Radiation exposure due to local fallout from Soviet
atmospheric nuclear weapons testing in Kazakhstan: solid cancer mortality in the
Semipalatinsk historical cohort, 1960-1999. Radiat Res 164(4 Pt 1): 409-419 (2005).

B3

Bäverstam, U. and G.A. Swedjemark. Where are the errors when we estimate radon exposurein retrospect? Radiat Prot Dosim 36(2/4): 107-112 (1991).

B4

Beebe, G.W. and M. Usagawa. The major ABCC samples. RERF TR/12-68 Radiation Effects
Research Foundation, 1968.

B5

Berhane, K., M. Hauptmann and B. Langholz. Using tensor product splines in modelingexposure-time-response relationships: application to the Colorado Plateau Uranium Miners
cohort. Stat Med 27(26): 5484-5496 (2008).

B6

Bernardo, J.M. and A.F.M. Smith. Bayesian Theory. Wiley, New York, 2007.

B7

Berrington de Gonzalez, A., M. Mahesh, K.P. Kim et al. Projected cancer risks from computed
tomographic scans performed in the United States in 2007. Arch Intern Med 169(22): 20712077 (2009).

B8

Berrington de Gonzalez, A., A. Iulian Apostoaei, L.H. Veiga et al. RadRAT: a radiation risk
assessment tool for lifetime cancer risk projection. J Radiol Prot 32(3): 205-222 (2012).

B9

Berry, D., J.K. Wathen and M. Newell. Bayesian model averaging in meta-analysis: vitamin E
supplementation and mortality. Clin Trials 6(1): 28-41 (2009).

B10

Beyreuther, E., W. Dorr, A. Lehnert et al. Relative biological effectiveness of 25 and 10 kV
X-rays for the induction of chromosomal aberrations in two human mammary epithelial celllines. Radiat Environ Biophys 48(3): 333-340 (2009).

B11

Bhatti, P., L.H. Veiga, C.M. Ronckers et al. Risk of second primary thyroid cancer afterradiotherapy for a childhood cancer in a large cohort study: an update from the childhood
cancer survivor study. Radiat Res 174(6): 741-752 (2010).

B12

Birchall, A., M. Puncher, J. Harrison et al. Plutonium worker dosimetry. Radiat Environ
Biophys 49(2): 203-212 (2010).

B13

Bochicchio, F., J.P. McLaughlin and C. Walsh. Comparison of radon exposure assessment
results: 210Po surface activity on glass objects vs. contemporary air radon concentration.
Radiat Meas 36(1): 211-215 (2003).

B14

Bochicchio, F. Radon epidemiology and nuclear track detectors: Methods, results andperspectives. Radiat Meas 40(2-6): 177-190 (2005).

B15

Boice, J.D., S.S. Cohen, M.T. Mumma et al. Mortality among radiation workers at Rocketdyne(Atomics International), 1948-1999. Radiat Res 166(1 Pt 1): 98-115 (2006).

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 287

B16

Boice, J.D., Jr., G. Engholm, R.A. Kleinerman et al. Radiation dose and second cancer risk inpatients treated for cancer of the cervix. Radiat Res 116(1): 3-55 (1988).

B17

Bolch, W.E., A.P. Shah, C.J. Watchman et al. Skeletal absorbed fractions for electrons in theadult male: considerations of a revised 50-microm definition of the bone endosteum. Radiat
Prot Dosim 127(1-4): 169-173 (2007).

B18

Bond, V.P., C.B. Meinhold and H.H. Rossi. Low-dose RBE and Q for x-ray compared to
gamma-ray radiations. Health Phys 34(5): 433-438 (1978).

B19

Box, G.E.P. Science and statistics. J Am Stat Assoc 71(356): 791-799 (1976).

B20

Brenner, A.V., M.D. Tronko, M. Hatch et al. I-131 dose response for incident thyroid cancers
in Ukraine related to the Chornobyl accident. Environ Health Perspect 119(7): 933-939 (2011).

B21

Breslow, N.E. Statistics in epidemiology: the case-control study. J Am Stat Assoc 91(433):
14-28 (1996).

B22

Breslow, N.E., T. Lumley, C.M. Ballantyne et al. Using the whole cohort in the analysis ofcase-cohort data. Am J Epidemiol 169(11): 1398-1405 (2009).

B23

Brugmans, M.J., S.M. Rispens, H. Bijwaard et al. Radon-induced lung cancer in French andCzech miner cohorts described with a two-mutation cancer model. Radiat Environ Biophys
43(3): 153-163 (2004).

B24

Buermann, L., M. Krumrey, M. Haney et al. Is there reliable experimental evidence fordifferent dicentric yields in human lymphocytes produced by mammography X-rays free-in-air
and within a phantom? Radiat Environ Biophys 44(1): 17-22 (2005).

B25

Burnham, K.P. and D.R. Anderson. Multimodel inference: Understanding AIC and BIC inmodel selection. Sociol Methods Res 33(2): 261-304 (2004).

C1

Cardis, E. and J. Estève. International Collaborative Study of Cancer Risk Among Nuclear
Industry Workers, II—Protocol. International agency for research on cancer, Lyon, 1992.

C2

Cardis, E., A. Kesminiene, V. Ivanov et al. Risk of thyroid cancer after exposure to 131I inchildhood. J Natl Cancer Inst 97(10): 724-732 (2005).

C3

Cardis, E., M. Vrijheid, M. Blettner et al. Risk of cancer after low doses of ionising radiation:
retrospective cohort study in 15 countries. Br Med J 331(7508): 77 (2005).

C4

Cardis, E., M. Vrijheid, M. Blettner et al. The 15-Country Collaborative Study of Cancer Risk
among Radiation Workers in the Nuclear Industry: estimates of radiation-related cancer risks.
Radiat Res 167(4): 396-416 (2007).

C5

Carpenter, L., V. Beral, P. Fraser et al. Health related selection and death rates in the United
Kingdom Atomic Energy Authority workforce. Br J Ind Med 47(4): 248-258 (1990).

C6

Carr, Z.A., R.A. Kleinerman, M. Stovall et al. Malignant neoplasms after radiation therapy for
peptic ulcer. Radiat Res 157(6): 668-677 (2002).

C7

Carroll, R.J., D. Ruppert, L.A. Stefanski et al. Measurement Error in Nonlinear Models: A
Modern Perspective. Second Edition. Chapman & Hall/CRC, Boca Raton, 2006.

C8

Chib, S. and E. Greenberg. Understanding the Metropolis–Hastings algorithm. Am Stat 49(4):327-335 (1995).

288 UNSCEAR 2012 REPORTC9CIRRPC. Neutron quality factor. ORAU 95/F-29. Committee on Interagency Radiation
Research and Policy Coordination, Washington D.C., 1995.

C10

Claeskens, G. and N.L. Hjort. Model Selection and Model Averaging. Cambridge University
Press, Cambridge, 2008.

C11

Clayton, D. and M. Hills. Statistical Models in Epidemiology. Oxford University Press,
Oxford, 1993.

C12

CNSC. Health Effects, Dosimetry and Radiological Protection of Tritium. INFO-0799.
Canadian Nuclear Safety Commission, Ottawa, 2010.

C13

CNSC. Verifying Canadian Nuclear Energy Worker Radiation Risk: A Reanalysis of Cancer
Mortality in Canadian Nuclear Energy Workers (1957-1994) Summary Report. INFO-0811.
Canadian Nuclear Safety Commission, Ottawa, 2011.

C14

Cohen, B.L. Test of the linear-no threshold theory of radiation carcinogenesis for inhaledradon decay products. Health Phys 68(2): 157-174 (1995).

C15

Cook, J.R. and L.A. Stefanski. Simulation-extrapolation estimation in parametric measurement
error models. J Am Stat Assoc 89(428): 1314-1328 (1994).

C16

Cox, D.R. Regression models and life-tables. J R Stat Soc 34(2): 187-220 (1972).

C17

Cox, D.R. and D.V. Hinkley. Theoretical Statistics. Chapman and Hall, London, 1974.

C18

Cristy, M. and K.F. Eckerman. Specific absorbed fractions of energy at various ages frominternal photon sources. ORNL/TM-8381/VI. Oak Ridge National Laboratory, USA, 1987.

C19

Crump, K.S., P. Duport, H. Jiang et al. A meta-analysis of evidence for hormesis in animalradiation carcinogenesis, including a discussion of potential pitfalls in statistical analyses todetect hormesis. J Toxicol Environ Health B Crit Rev 15(3): 210-231 (2012).

D1

Darby, S., E. Whitley, P. Silcocks et al. Risk of lung cancer associated with residential radon
exposure in south-west England: a case-control study. Br J Cancer 78(3): 394-408 (1998).

D2

Darby, S., D. Hill, A. Auvinen et al. Radon in homes and risk of lung cancer: collaborative
analysis of individual data from 13 European case-control studies. BMJ 330(7485): 223 (2005).

D3

Darby, S., D. Hill, H. Deo et al. Residential radon and lung cancer--detailed results of acollaborative analysis of individual data on 7148 persons with lung cancer and 14,208 persons
without lung cancer from 13 epidemiologic studies in Europe. Scand J Work Environ Health32(Suppl 1): 1-83 (2006).

D4

Davesne, E., P. Casanova, E. Chojnacki et al. Integration of uncertainties into internal
contamination monitoring. Health Phys 99(4): 517-522 (2010).

D5

Davesne, E., F. Paquet, E. Ansoborlo et al. Absorption of plutonium compounds in the
respiratory tract. J Radiol Prot 30(1): 5-21 (2010).

D6

Davis, S., K.J. Kopecky, T.E. Hamilton et al. Thyroid neoplasia, autoimmune thyroiditis, andhypothyroidism in persons exposed to iodine 131 from the hanford nuclear site. J Am Med
Assoc 292(21): 2600-2613 (2004).

D7

Deckbar, D., J. Birraux, A. Krempler et al. Chromosome breakage after G2 checkpoint release.
J Cell Biol 176(6): 749-755 (2007).

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 289

D8

Drozdovitch, V., E. Maceika, V. Khrouch et al. Uncertainties in individual doses in a casecontrol study of thyroid cancer after the Chernobyl accident. Radiat Prot Dosim 127(1-4): 540543 (2007).

D9

Drozdovitch, V., V. Khrouch, E. Maceika et al. Reconstruction of radiation doses in a casecontrol study of thyroid cancer following the Chernobyl accident. Health Phys 99(1): 1-16
(2010).

D10

Dunning, D.E., Jr. and G. Schwarz. Variability of human thyroid characteristics and estimatesof dose from ingested 131I. Health Phys 40(5): 661-675 (1981).

E1

Edwards, A.A. Relative biological effectiveness of neutrons for stochastic effects. Doc. NRPB
8(2) (1997).

E2

Edwards, A.A. Neutron RBE values and their relationship to judgements in radiologicalprotection. J Radiol Prot 19(2): 93-105 (1999).

E3

Eidemuller, M., E. Holmberg, P. Jacob et al. Breast cancer risk among Swedish hemangioma
patients and possible consequences of radiation-induced genomic instability. Mutat Res
669(1-2): 48-55 (2009).

F1

Farris, W.T., B.A. Napier, T.A. Ikenberry et al. Atmospheric pathway dosimetry report, 19441992. PNWD-2228 HEDR. Battelle Pacific Northwest Laboratories, Richland, 1994.

F2

Fearn, T., D.C. Hill and S.C. Darby. Measurement error in the explanatory variable of a binary
regression: regression calibration and integrated conditional likelihood in studies of residential
radon and lung cancer. Stat Med 27(12): 2159-2176 (2008).

F3

Feinendegen, L.E., M. Pollycove and R.D. Neumann. Low-dose cancer risk modeling must
recognize up-regulation of protection. Dose Response 8(2): 227-252 (2010).

F4

Field, R.W., D.J. Steck, B.J. Smith et al. Residential radon gas exposure and lung cancer: theIowa Radon Lung Cancer Study. Am J Epidemiol 151(11): 1091-1102 (2000).

F5

Field, R.W., B.J. Smith, D.J. Steck et al. Residential radon exposure and lung cancer: variationin risk estimates using alternative exposure scenarios. J Expo Anal Environ Epidemiol 12(3):197-203 (2002).

F6

Franco, N., J. Lamartine, V. Frouin et al. Low-dose exposure to gamma rays induces specificgene regulations in normal human keratinocytes. Radiat Res 163(6): 623-635 (2005).

F7Frankenberg, D., K. Kelnhofer, K. Bar et al. Enhanced neoplastic transformation bymammography X rays relative to 200 kVp X rays: indication for a strong dependence on
photon energy of the RBE(M) for various end points. Radiat Res 157(1): 99-105 (2002).

F8

Fritsch, P. Uncertainties in committed equivalent doses to the thyroid after ingestion or
inhalation of different chemical forms of 125-129-131I. Radiat Prot Dosim 127(1-4): 548-552(2007).

F9

Frome, E.L. and H. Checkoway. Epidemiologic programs for computers and calculators. Useof Poisson regression models in estimating incidence rates and ratios. Am J Epidemiol 121(2):309-323 (1985).

F10Fung, K.Y. and D. Krewski. On measurement error adjustment methods in Poisson regression.
Environmetrics 10(2): 213-224 (1999).

290 UNSCEAR 2012 REPORT

F11Furukawa, K., D.L. Preston, S. Lonn et al. Radiation and smoking effects on lung cancer
incidence among atomic bomb survivors. Radiat Res 174(1): 72-82 (2010).

G1

Gavrilin, Y., V. Khrouch, S. Shinkarev et al. Individual thyroid dose estimation for a casecontrol study of Chernobyl-related thyroid cancer among children of Belarus-part I: 131I,
short-lived radioiodines (132I, 133I, 135I), and short-lived radiotelluriums (131MTe and132Te). Health Phys 86(6): 565-585 (2004).

G2

Gavrilin, Y.I., V.T. Khrouch, S.M. Shinkarev et al. Chernobyl accident: reconstruction of
thyroid dose for inhabitants of the Republic of Belarus. Health Phys 76(2): 105-119 (1999).

G3

Gelman, A., J.B. Carlin, H.S. Stern et al. Bayesian Data Analysis. Chapman & Hall/CRC,
London, 2004.

G4

Geman, S. and D. Geman. Stochastic relaxation, gibbs distributions, and the bayesian
restoration of images. IEEE Trans Pattern Anal Mach Intell 6(6): 721-741 (1984).

G5

Gerken, M., L. Kreienbrock, J. Wellmann et al. Models for retrospective quantification ofindoor radon exposure in case-control studies. Health Phys 78(3): 268-278 (2000).

G6

Gilbert, E.S. Some confounding factors in the study of mortality and occupational exposures.
Am J Epidemiol 116(1): 177-188 (1982).

G7

Gilbert, E.S., J.J. Fix and W.V. Baumgartner. An approach to evaluating bias and uncertainty
in estimates of external dose obtained from personal dosimeters. Health Phys 70(3): 336-345(1996).

G8

Gilbert, E.S. Accounting for errors in dose estimates used in studies of workers exposed toexternal radiation. Health Phys 74(1): 22-29 (1998).

G9

Gilbert, E.S., N.A. Koshurnikova, M.E. Sokolnikov et al. Lung cancer in Mayak workers.
Radiat Res 162(5): 505-516 (2004).

G10

Gilbert, E.S., I. Thierry-Chef, E. Cardis et al. External dose estimation for nuclear worker
studies. Radiat Res 166(1 Pt 2): 168-173 (2006).

G11

Gilbert, E.S., L. Huang, A. Bouville et al. Thyroid cancer rates and 131I doses from Nevada
atmospheric nuclear bomb tests: an update. Radiat Res 173(5): 659-664 (2010).

G12

Gilks, W.R., S. Richardson and D.J. Spiegelhalter. Markov Chain Monte Carlo in Practice.
Chapman & Hall/CRC, London, 1996.

G13

Goggelmann, W., C. Jacobsen, W. Panzer et al. Re-evaluation of the RBE of 29 kV x-rays(mammography x-rays) relative to 220 kV x-rays using neoplastic transformation of human
CGL1-hybrid cells. Radiat Environ Biophys 42(3): 175-182 (2003).

G14

Gossner, W. Target cells in internal dosimetry. Radiat Prot Dosim 105(1-4): 39-42 (2003).

G15

Gössner, W., R. Masse and J.W. Stather. Cells at risk for dosimetric modelling relevant tobone tumour induction. Radiat Prot Dosim 92(1-3): 209-213 (2000).

G16Greenland, S. Multiple-bias modelling for analysis of observational data (with discussion). J R
Stat Soc Ser A 168(2): 267-305 (2005).

G17

Greenland, S. Introduction to Bayesian statistics. pp.328-344 in: Modern Epidemiology (K.J.
Rothman et al., eds.). Lippincott Williams & Wilkins, Philadelphia, 2008.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 291

G18

Greenland, S. and T.L. Lash. Bias analysis. pp.345-380 in: Modern Epidemiology (K.J.
Rothman et al., eds.). Lippincott Williams & Wilkins, Philadelphia, 2008.

G19

Griem, M.L., R.A. Kleinerman, J.D. Boice, Jr. et al. Cancer following radiotherapy for peptic
ulcer. J Natl Cancer Inst 86(11): 842-849 (1994).

G20

Grogan, H.A., W.K. Sinclair and P.G. Voillequé. Assessing risks of exposure to plutonium.
Part of Task 3: Independent analysis of exposure, dose and health risk to offsite individuals.
RAC Report No. 5-CDPHE-RFP-1998-FINAL. Radiological Assessment Corporation,
Neeses, 2000.

G21

Grogan, H.A., W.K. Sinclair and P.G. Voilleque. Risks of fatal cancer from inhalation of
239,240plutonium by humans: a combined four-method approach with uncertainty evaluation.
Health Phys 80(5): 447-461 (2001).

G22

Grogan, H.A., W.K. Sinclair and P.G. Voillequé. Risks of fatal cancer from inhalation of
239,240Pu by humans: a combined four-method approach with uncertainty evaluation;
Erratum. Health Phys. 82(3): 404 (2002).

G23

Group, T.J.U.-J.W. Reassessment of the Atomic Bomb Radiation Dosimetry for Hiroshima
and Nagasaki: Dosimetry System 2002. (R.W. Young and G.D. Kerr, eds.). Radiation Effects
Research Foundation, Japan, 2005.

G24

Grudzenski, S., A. Raths, S. Conrad et al. Inducible response required for repair of low-doseradiation damage in human fibroblasts. Proc Natl Acad Sci U S A 107(32): 14205-14210 (2010).

H1

Hall, P., A. Mattsson and J.D. Boice, Jr. Thyroid cancer after diagnostic administration ofiodine-131. Radiat Res 145(1): 86-92 (1996).

H2

Hamby, D.M. Uncertainty of the tritium dose conversion factor. Health Phys 77(3): 291-297(1999).

H3

Hamby, D.M. and R.R. Benke. Uncertainty of the iodine-131 ingestion dose conversion factor.
Radiat Prot Dosim 82(4): 245-256 (1999).

H4

Harrell, F.E.J. Regression Modelling Strategies: With Applications to Linear Models, Logistic
Regression, and Survival Analysis. Springer-Verlag, New York, 2001.

H5

Harrison, J. Biokinetic and dosimetric modelling in the estimation of radiation risks frominternal emitters. J Radiol Prot 29(2A): A81-A105 (2009).

H6

Harrison, J.D., A. Khursheed and B.E. Lambert. Uncertainties in dose coefficients for intakesof tritiated water and organically bound forms of tritium by members of the public. Radiat Prot
Dosim 98(3): 299-311 (2002).

H7

Hartge, P. and J. Cahill. Field methods in epidemiology. pp.492-510 in: Modern Epidemiology(K.J. Rothman et al., eds.). Lippincott Williams & Wilkins, Philadelphia, 2008.

H8

Harvey, R.P., D.M. Hamby and T.S. Palmer. Uncertainty of the thyroid dose conversion factor
for inhalation intakes of 131I and its parametric uncertainty. Radiat Prot Dosim 118(3): 296306 (2006).

H9

Heid, I.M., H. Kuchenhoff, J. Wellmann et al. On the potential of measurement error to induce
differential bias on odds ratio estimates: an example from radon epidemiology. Stat Med
21(21): 3261-3278 (2002).

292 UNSCEAR 2012 REPORT

H10Heid, I.M., H. Kuchenhoff, J. Miles et al. Two dimensions of measurement error: classical andBerkson error in residential radon exposure assessment. J Expo Anal Environ Epidemiol
14(5): 365-377 (2004).

H11

Heid, I.M., H. Kuchenhoff, A.S. Rosario et al. Impact of measurement error in exposures ingerman radon studies. J Toxicol Environ Health A 69(7): 701-721 (2006).

H12

Heyes, G.J. and A.J. Mill. The neoplastic transformation potential of mammography X rays
and atomic bomb spectrum radiation. Radiat Res 162(2): 120-127 (2004).

H13

Hildreth, N.G., R.E. Shore and P.M. Dvoretsky. The risk of breast cancer after irradiation of
the thymus in infancy. N Engl J Med 321(19): 1281-1284 (1989).

H14

Hill, A.B. The environment and disease: association or causation? Proc R Soc Med 58: 295300 (1965).

H15

Hoeting, J.A., D. Madigan and A.E. Raftery. Bayesian model averaging: a tutorial. Stat Sci
14(4): 382-417 (1999).

H16

Hofer, E. Hypothesis testing, statistical power, and confidence limits in the presence of
epistemic uncertainty. Health Phys 92(3): 226-235 (2007).

H17

Hofer, E. Correspondence: Response to Stram et al. Health Phys. 93(4): 327-328 (2007).

H18

Hofer, E. How to account for uncertainty due to measurement errors in an uncertainty analysis
using Monte Carlo simulation. Health Phys 95(3): 277-290 (2008).

H19

Hoffman, F.O., A.J. Ruttenber, A.I. Apostoaei et al. The Hanford Thyroid Disease Study: analternative view of the findings. Health Phys 92(2): 99-111 (2007).

H20

Huber, R., H. Schraube, U. Nahrstedt et al. Dose-response relationships of micronuclei inhuman lymphocytes induced by fission neutrons and by low LET radiations. Mutat Res
306(2): 135-141 (1994).

H21

Hunter, N., C.B. Howarth and J.C.H. Miles. Year-to-year variations in radon levels in asample of UK houses with the same occupants. pp.438-447 in: The Natural Radiation
Environment VII (J.P. McLaughlin et al., eds.). Elsevier Ltd., Oxford, 2005.

H22

Hwang, S.L., H.R. Guo, W.A. Hsieh et al. Cancer risks in a population with prolonged low
dose-rate gamma-radiation exposure in radiocontaminated buildings, 1983-2002. Int J Radiat
Biol 82(12): 849-858 (2006).

H23

Hwang, S.L., J.S. Hwang, Y.T. Yang et al. Estimates of relative risks for cancers in a
population after prolonged low-dose-rate radiation exposure: a follow-up assessment from1983 to 2005. Radiat Res 170(2): 143-148 (2008).

I1

IAEA. Evaluating the reliability of predictions made using environmental transfer models.
Safety Series No. 100. International Atomic Energy Agency, Vienna, 1989.

I2

IAEA. Cytogenetic analysis for radiation dose assessment: A manual. Technical Reports 405.
International Atomic Energy Agency, Vienna, 2001.

I3

IARC. IARC Monographs on the evaluation of carcinogenic risks to humans. Ionizing
radiation, Part 1: X- and gamma (γ)-radiation, and neutrons. IARC Monograph 75.
International Agency for Research on Cancer, Lyon, 2000.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 293

I4

IARC. IARC Monographs on the evaluation of carcinogenic risks to humans. Ionizing
radiation, Part 2: Some internally deposited radionuclides. IARC Monograph 78. International
Agency for Research on Cancer, Lyon, 2001.

I5

IARC. Cancer Incidence in Five Continents. IARC Publication No. 160, Volume IX (M.P.
Curado et al., eds.). International Agency for Research on Cancer, Lyon, 2009.

I6

ICRP. Biological effects of inhaled radionuclides. ICRP Publication 31. Annals of the ICRP
4(1-2). International Commission on Radiological Protection, Pergamon Press, Oxford, 1980.

I7

ICRP. 1990 Recommendations of the International Commission on Radiological Protection.
ICRP Publication 60. Annals of the ICRP 21(1-3). International Commission on RadiologicalProtection, Pergamon Press, Oxford, 1991.

I8

ICRP. Age-dependent doses to members of the public from intake of radionuclides: Part 2.
Ingestion dose coefficients. ICRP Publication 67. Annals of the ICRP 23(3-4). International
Commission on Radiological Protection, Pergamon Press, Oxford, 1993.

I9

ICRP. Human respiratory tract model for radiological protection. ICRP Publication 66. Annalsof the ICRP 24(1-3). International Commission on Radiological Protection, Pergamon Press,
Oxford, 1994.

I10

ICRP. Basic anatomical and physiological data for use in radiological protection: the skeleton.
ICRP Publication 70. Annals of the ICRP 25(2). International Commission on RadiologicalProtection, Pergamon Press, Oxford, 1995.

I11

ICRP. Relative biological effectiveness (RBE), quality factor (Q), and radiation weighting
factor (wR). ICRP Publication 92. Annals of the ICRP 33(4). International Commission on
Radiological Protection, Pergamon Press, 2003.

I12

ICRP. Low-dose extrapolation of radiation-related cancer risk. ICRP Publication 99. Annals of
the ICRP 35(4). International Commission on Radiological Protection, Elsevier Ltd., 2005.

I13

ICRP. Human alimentary tract model for radiological protection. ICRP Publication 100.
Annals of the ICRP 36(1-2). International Commission on Radiological Protection, Elsevier
Ltd., 2006.

I14

ICRP. The 2007 Recommendations of the International Commission on RadiologicalProtection. ICRP Publication 103. Annals of the ICRP 37(2-4). International Commission on
Radiological Protection, Elsevier Ltd., 2007.

I15

ICRP. Nuclear decay data for dosimetric calculations. ICRP Publication 107. Annals of the
ICRP 38(3). International Commission on Radiological Protection, Elsevier Ltd., 2008.

I16

ICRP. Adult reference computational phantoms. ICRP Publication 110. Annals of the ICRP
39(2). International Commission on Radiological Protection, Elsevier Ltd., 2009.

I17

ICRP. Lung cancer risk from radon and progeny and statement on radon. ICRP Publication
115. Annals of the ICRP 40(1). International Commission on Radiological Protection, Elsevier
Ltd., 2010.

I18

ICRU. The quality factor in radiation protection. ICRU Report 40. International Commission
on Radiation Units and Measurements, 1986.

I19

ICRU. Stopping powers and ranges for protons and alpha particles. ICRU Report 49.
International Commission on Radiation Units and Measurements, 1993.

294 UNSCEAR 2012 REPORT

I20

Ina, Y. and K. Sakai. Further study of prolongation of life span associated with immunologicalmodification by chronic low-dose-rate irradiation in MRL-lpr/lpr mice: effects of whole-life
irradiation. Radiat Res 163(4): 418-423 (2005).

I21

Inskip, P.D., R.R. Monson, J.K. Wagoner et al. Cancer mortality following radium treatment
for uterine bleeding. Radiat Res 123(3): 331-344 (1990).

I22

Ivanov, V.K., A.F. Tsyb, A.I. Gorsky et al. Leukaemia and thyroid cancer in emergency
workers of the Chernobyl accident: estimation of radiation risks (1986-1995). Radiat Environ
Biophys 36(1): 9-16 (1997).

I23

Ivanov, V.K., A.F. Tsyb and A.P. Konogorov. Case-control analysis of leukaemia among
Chernobyl accident emergency workers residing in the Russian Federation 1986-1993. J
Radiol Prot 17(3): 137-157 (1997).

I24

Ivanov, V.K., A.I. Gorski, M.A. Maksioutov et al. Mortality among the Chernobyl emergency
workers: estimation of radiation risks (preliminary analysis). Health Phys 81(5): 514-521(2001).

I25

Ivanov, V.K., A.I. Gorski, A.F. Tsyb et al. Solid cancer incidence among the Chernobyl
emergency workers residing in Russia: estimation of radiation risks. Radiat Environ Biophys
43(1): 35-42 (2004).

I26

Ivanov, V.K., K.A. Tumanov and V.V. Kashcheev. Mortality in Chernobyl clean-up workers:
analysis of dose-effect relationship. Radiation and Risk 15: 11-22 (2006). (Russian).

J1

Jablon, S. Atomic bomb radiation dose estimation at ABCC. ABCC-Technical Report 23:
ABCC, 1971.

J2

Jacob, P., T.I. Bogdanova, E. Buglova et al. Thyroid cancer risk in areas of Ukraine andBelarus affected by the Chernobyl accident. Radiat Res 165(1): 1-8 (2006).

J3

Jacob, P., R. Meckbach, M. Sokolnikov et al. Lung cancer risk of Mayak workers: modellingof carcinogenesis and bystander effect. Radiat Environ Biophys 46(4): 383-394 (2007).

J4

Jacob, P., L. Walsh and M. Eidemuller. Modeling of cell inactivation and carcinogenesis in theatomic bomb survivors with applications to the mortality from all solid, stomach and livercancer. Radiat Environ Biophys 47(3): 375-388 (2008).

J5

Jacob, P., W. Ruhm, L. Walsh et al. Is cancer risk of radiation workers larger than expected?
Occup Environ Med 66(12): 789-796 (2009).

J6

Jacob, P., R. Meckbach, J.C. Kaiser et al. Possible expressions of radiation-induced genomic
instability, bystander effects or low-dose hypersensitivity in cancer epidemiology. Mutat Res
687(1-2): 34-39 (2010).

J7

Jaynes, E.T. Probability Theory: The Logic of Science. Cambridge University Press,
Cambridge 2003.

J8

JCGM. Evaluation of measurement data – Guide to the expression of uncertainty inmeasurement. JCGM 100:2008 GUM 1995 with minor corrections. Joint Committee for
Guides in Metrology, 2008.

J9

JCGM. Evaluation of measurement data – Supplement 1 to the “Guide to the expression of
uncertainty in measurement” – Propagation of distributions using a Monte Carlo method.
JCGM 101:2008. Joint Committee for Guides in Metrology, 2008.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 295

J10

JCGM. Evaluation of measurement data – An introduction to the “Guide to the expression of
uncertainty in measurement” and related documents. JCGM 104:2009. Joint Committee for
Guides in Metrology, 2009.

J11

JCGM. International vocabulary of metrology – Basic and general concepts and associatedterms (VIM). JCGM 200:2012. Joint Committee for Guides in Metrology, 2012.

J12

Jeffreys, H. An invariant form for the prior probability in estimation problems. Proc R Soc
Lond A Math Phys Sci 186(1007): 453-461 (1946).

J13

Jewell, N.P. Statistics for Epidemiology. CRC Press, Florida, 2004.

J14

Jin, Y.W., Y.J. Na, Y.J. Lee et al. Comprehensive analysis of time- and dose-dependent
patterns of gene expression in a human mesenchymal stem cell line exposed to low-dose
ionizing radiation. Oncol Rep 19(1): 135-144 (2008).

J15

Johnson, C.J. Cancer incidence in an area of radioactive fallout downwind from the Nevada
Test Site. JAMA 251(2): 230-236 (1984).

K1

Kaiser, J.C. and W.F. Heidenreich. Comparing regression methods for the two-stage clonal
expansion model of carcinogenesis. Stat Med 23(21): 3333-3350 (2004).

K2

Kaiser, J.C., P. Jacob, R. Meckbach et al. Breast cancer risk in atomic bomb survivors frommulti-model inference with incidence data 1958-1998. Radiat Environ Biophys 51(1): 1-14
(2012).

K3

Kapur, J.N. and H.K. Kesavan. Entropy Optimization Principles with Applications. Academies
Press, Boston, 1992.

K4

Kaul, D.C., S.D. Egbert and W.A. Woolson. DS02 uncertainty analysis. pp.921-944 in:Reassessment of the Atomic Bomb Radiation Dosimetry for Hiroshima and Nagasaki:
Dosimetry System 2002. Report of the Joint US-Japan Working Group. Radiation Effects
Research Foundation, Japan, 2005.

K5

Kerber, R.A., J.E. Till, S.L. Simon et al. A cohort study of thyroid disease in relation to fallout
from nuclear weapons testing. J Am Med Assoc 270(17): 2076-2082 (1993).

K6

Kocher, D.C., A.I. Apostoaei and F.O. Hoffman. Radiation effectiveness factors for use incalculating probability of causation of radiogenic cancers. Health Phys 89(1): 3-32 (2005).

K7

Kocher, D.C., A.I. Apostoaei, R.W. Henshaw et al. Interactive RadioEpidemiological Program(IREP): a web-based tool for estimating probability of causation/assigned share of radiogenic
cancers. Health Phys 95(1): 119-147 (2008).

K8

Kopecky, K.J., S. Davis, T.E. Hamilton et al. Estimation of thyroid radiation doses for the
hanford thyroid disease study: results and implications for statistical power of theepidemiological analyses. Health Phys 87(1): 15-32 (2004).

K9

Kopecky, K.J., L. Onstad, T.E. Hamilton et al. Thyroid ultrasound abnormalities in persons
exposed during childhood to 131I from the Hanford nuclear site. Thyroid 15(6): 604-613(2005).

K10

Kopecky, K.J., V. Stepanenko, N. Rivkind et al. Childhood thyroid cancer, radiation dose from
Chernobyl, and dose uncertainties in Bryansk Oblast, Russia: a population-based case-control
study. Radiat Res 166(2): 367-374 (2006).

296 UNSCEAR 2012 REPORT

K11

Kreienbrock, L., M. Kreuzer, M. Gerken et al. Case-control study on lung cancer andresidential radon in western Germany. Am J Epidemiol 153(1): 42-52 (2001).

K12

Krestinina, L.Y., D.L. Preston, E.V. Ostroumova et al. Protracted radiation exposure andcancer mortality in the Techa River Cohort. Radiat Res 164(5): 602-611 (2005).

K13

Krestinina, L.Y., F. Davis, E. Ostroumova et al. Solid cancer incidence and low-dose-rateradiation exposures in the Techa River cohort: 1956 2002. Int J Epidemiol 36(5): 1038-1046(2007).

K14

Krewski, D., J.H. Lubin, J.M. Zielinski et al. Residential radon and risk of lung cancer: a
combined analysis of 7 North American case-control studies. Epidemiology 16(2): 137-145(2005).

K15

Krewski, D., J.H. Lubin, J.M. Zielinski et al. A combined analysis of North American casecontrol studies of residential radon and lung cancer. J Toxicol Environ Health A 69(7): 533597 (2006).

K16

Krumrey, M., G. Ulm and E. Schmid. Dicentric chromosomes in monolayers of human
lymphocytes produced by monochromatized synchrotron radiation with photon energies from1.83 keV to 17.4 keV. Radiat Environ Biophys 43(1): 1-6 (2004).

K17

Kukush, A., S. Shklyar, S. Masiuk et al. Methods for estimation of radiation risk inepidemiological studies accounting for classical and Berkson errors in doses. Int J Biostat 7(1):15 (2011).

K18

Kurpinski, K., D.J. Jang, S. Bhattacharya et al. Differential effects of x-rays and high-energy
56Fe ions on human mesenchymal stem cells. Int J Radiat Oncol Biol Phys 73(3): 869-877(2009).

L1

Lagarde, F., G. Pershagen, G. Akerblom et al. Residential radon and lung cancer in Sweden:
risk analysis accounting for random error in the exposure assessment. Health Phys 72(2): 269276 (1997).

L2

Lagarde, F., R. Falk, K. Almren et al. Glass-based radon-exposure assessment and lung cancer
risk. J Expo Anal Environ Epidemiol 12(5): 344-354 (2002).

L3

Land, C.E. Estimating cancer risks from low doses of ionizing radiation. Science 209(4462):
1197-1203 (1980).

L4

Land, C.E. Uncertainty, low-dose extrapolation and the threshold hypothesis. J Radiol Prot
22(3A): A129-135 (2002).

L5

Land, C.E., E. Gilbert, J.M. Smith et al. Report of the NCI-CDC Working Group to Revise the1985 NIH Radioepidemiological Tables. NIH Publication 03-5387. National Cancer Institute,
Bethesda, MD, 2003.

L6

Land, C.E., A. Bouville, I. Apostoaei et al. Projected lifetime cancer risks from exposure to
regional radioactive fallout in the Marshall Islands. Health Phys 99(2): 201-215 (2010).

L7

Langholz, B. and J. Jiao. Computational methods for case-cohort studies. Comput Stat Data
Anal 51(8): 3737-3748 (2007).

L8

Leggett, R.W. Reliability of the ICRP's dose coefficients for members of the public. 1. Sourcesof uncertainty in the biokinetic models. Radiat Prot Dosim 95(3): 199-213 (2001).

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 297

L9Leggett, R.W., L.R. Williams, D.R. Melo et al. A physiologically based biokinetic model for
cesium in the human body. Sci Total Environ 317(1-3): 235-255 (2003).

L10

Leggett, R.W., K.F. Eckerman, V.F. Khokhryakov et al. Mayak worker study: an improved
biokinetic model for reconstructing doses from internally deposited plutonium. Radiat Res
164(2): 111-122 (2005).

L11

Lehnert, A., W. Dorr, E. Lessmann et al. RBE of 10 kV X rays determined for the humanmammary epithelial cell line MCF-12A. Radiat Res 169(3): 330-336 (2008).

L12

Leuraud, K., M. Schnelzer, L. Tomasek et al. Radon, smoking and lung cancer risk: results ofa joint analysis of three European case-control studies among uranium miners. Radiat Res
176(3): 375-387 (2011).

L13

Li, W.B., M. Zankl, H. Schlattl et al. Impact on 141Ce, 144Ce, 95Zr, and 90Sr beta emitter
dose coefficients of photon and electron SAFs calculated with ICRP/ICRU reference adultvoxel computational phantoms. Health Phys 99(4): 503-510 (2010).

L14

Li, Y., A. Guolo, F.O. Hoffman et al. Shared uncertainty in measurement error problems, withapplication to Nevada Test Site fallout data. Biometrics 63(4): 1226-1236 (2007).

L15

Likhtarev, I., A. Bouville, L. Kovgan et al. Questionnaire- and measurement-based individual
thyroid doses in Ukraine resulting from the Chornobyl nuclear reactor accident. Radiat Res
166(1 Pt 2): 271-286 (2006).

L16

Lindberg, S., P. Karlsson, B. Arvidsson et al. Cancer incidence after radiotherapy for skinhaemangioma during infancy. Acta Oncol 34(6): 735-740 (1995).

L17

Little, M.P., D.G. Hoel, J. Molitor et al. New models for evaluation of radiation-induced
lifetime cancer risk and its uncertainty employed in the UNSCEAR 2006 report. Radiat Res
169(6): 660-676 (2008).

L18

Little, M.P. and B.E. Lambert. Systematic review of experimental studies on the relative
biological effectiveness of tritium. Radiat Environ Biophys 47(1): 71-93 (2008).

L19

Little, M.P., P. Vineis and G. Li. A stochastic carcinogenesis model incorporating multiple
types of genomic instability fitted to colon cancer data. J Theor Biol 254(2): 229-238 (2008).

L20

Lobrich, M., N. Rief, M. Kuhne et al. In vivo formation and repair of DNA double-strand
breaks after computed tomography examinations. Proc Natl Acad Sci U S A 102(25): 89848989 (2005).

L21

Lobrich, M. and P.A. Jeggo. The impact of a negligent G2/M checkpoint on genomic
instability and cancer induction. Nat Rev Cancer 7(11): 861-869 (2007).

L22

Loucas, B.D. and M.N. Cornforth. Complex chromosome exchanges induced by gamma raysin human lymphocytes: an mFISH study. Radiat Res 155(5): 660-671 (2001).

L23

Loucas, B.D., R. Eberle, S.M. Bailey et al. Influence of dose rate on the induction of simple
and complex chromosome exchanges by gamma rays. Radiat Res 162(4): 339-349 (2004).

L24

Lowe, X.R., S. Bhattacharya, F. Marchetti et al. Early brain response to low-dose radiation
exposure involves molecular networks and pathways associated with cognitive functions,advanced aging and Alzheimer's disease. Radiat Res 171(1): 53-65 (2009).

L25

Lubin, J.H., J.D. Boice, Jr., C. Edling et al. Radon-exposed underground miners and inverse
dose-rate (protraction enhancement) effects. Health Phys 69(4): 494-500 (1995).

298 UNSCEAR 2012 REPORT

L26

Lubin, J.H., J.D. Boice, Jr. and J.M. Samet. Errors in exposure assessment, statistical power
and the interpretation of residential radon studies. Radiat Res 144(3): 329-341 (1995).

L27

Lubin, J.H. and J.D. Boice, Jr. Lung cancer risk from residential radon: meta-analysis of eight
epidemiologic studies. J Natl Cancer Inst 89(1): 49-57 (1997).

L28

Lubin, J.H. The potential for bias in Cohen's ecological analysis of lung cancer and residential
radon. J Radiol Prot 22(2): 141-148 (2002).

L29

Lubin, J.H., D.W. Schafer, E. Ron et al. A reanalysis of thyroid neoplasms in the Israeli tinea
capitis study accounting for dose uncertainties. Radiat Res 161(3): 359-368 (2004).

L30

Lubin, J.H., Z.Y. Wang, J.D. Boice, Jr. et al. Risk of lung cancer and residential radon in
China: pooled results of two studies. Int J Cancer 109(1): 132-137 (2004).

L31

Lubin, J.H., Z.Y. Wang, L.D. Wang et al. Adjusting lung cancer risks for temporal and spatial
variations in radon concentration in dwellings in Gansu Province, China. Radiat Res 163(5):571-579 (2005).

L32

Lundell, M., A. Mattsson, T. Hakulinen et al. Breast cancer after radiotherapy for skinhemangioma in infancy. Radiat Res 145(2): 225-230 (1996).

L33

Lunn, D.J., N. Thomas, A. Best et al. WinBUGS - A Bayesian modelling framework:
concepts, structure, and extensibility. Stat Comput 10(4): 325-337 (2000).

L34

Lyon, J.L., S.C. Alder, M.B. Stone et al. Thyroid disease associated with exposure to the
Nevada nuclear weapons test site radiation: a reevaluation based on corrected dosimetry andexamination data. Epidemiology 17(6): 604-614 (2006).

M1

Machado, S.G., C.E. Land and F.W. McKay. Cancer mortality and radioactive fallout insouthwestern Utah. Am J Epidemiol 125(1): 44-61 (1987).

M2

MacMahon, B., P. Cole and J. Brown. Etiology of human breast cancer: a review. J NatlCancer Inst 50(1): 21-42 (1973).

M3

Madigan, D. and A.E. Raftery. Model selection and accounting for model uncertainty ingraphical models using Occam’s window. J Am Stat Assoc 89(428): 1535-1546 (1994).

M4

Madigan, D. and J. York. Bayesian graphical models for discrete data. Int Stat Rev 63(2):215-232 (1995).

M5

Mahaffey, J.A., M.A. Parkhurst, T.E. Hui et al. Factors affecting use of CR-39 surface monitor
technology to estimate past exposure to indoor radon. J Expo Anal Environ Epidemiol 6(4):425-437 (1996).

M6

Mallick, B., F.O. Hoffman and R.J. Carrol. Semiparametric regression modeling with mixturesof Berkson and classical error, with application to fallout from the Nevada test site. Biometrics
58(1): 13-20 (2002).

M7

Marsh, J.W. and A. Birchall. Sensitivity analysis of the weighted equivalent lung dose per unit
exposure from radon progeny. Radiat Prot Dosim 87(3): 167-178 (2000).

M8

Mattsson, A., B.I. Ruden, P. Hall et al. Radiation-induced breast cancer: long-term follow-up
of radiation therapy for benign breast disease. J Natl Cancer Inst 85(20): 1679-1685 (1993).

M9

McCulloch, C.E. Maximum likelihood algorithms for generalized linear mixed models. J Am
Stat Assoc 92(437): 162-170 (1997).

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 299

M10

Melintescu, A., D. Galeriu and H. Takeda. Reassessment of tritium dose coefficients for thegeneral public. Radiat Prot Dosim 127(1-4): 153-157 (2007).

M11

Mestres, M., M.R. Caballin, L. Barrios et al. RBE of X rays of different energies: acytogenetic evaluation by FISH. Radiat Res 170(1): 93-100 (2008).

M12

Mestres, M., L. Benkhaled, M.R. Caballin et al. Induction of incomplete and complex
chromosome aberrations by 30 kVp X rays. Radiat Res 175(2): 201-207 (2011).

M13

Mikhalskii, A.I., V.K. Ivanov and S.Y. Chekin. Accounting of heterogeneity in the estimationof radiation risks. Autom Remote Control 69(6): 1045-1050 (2008).

M14

Miller, G., H.F. Martz and T.T. Little. Bayesian graphical models for discrete data. Radiat Prot
Dosim 98(2): 191-198 (2002).

M15

Miller, G. Variability and uncertainty of biokinetic model parameters: the discrete empirical
Bayes approximation. Radiat Prot Dosim 131(3): 394-398 (2008).

M16

Miller, G., R. Guilmette, L. Bertelli et al. Uncertainties in internal doses calculated for Mayakworkers--a study of 63 cases. Radiat Prot Dosim 131(3): 316-330 (2008).

M17

Modan, B., E. Ron and A. Werner. Thyroid cancer following scalp irradiation. Radiology
123(3): 741-744 (1977).

M18

Moolgavkar, S.H. and D.J. Venzon. Two-event models for carcinogenesis: incidence curves
for childhood and adult tumors. Math Biosci 47(1-2): 55-77 (1979).

M19

Moolgavkar, S.H. and A.G. Knudson, Jr. Mutation and cancer: a model for humancarcinogenesis. J Natl Cancer Inst 66(6): 1037-1052 (1981).

M20

Muirhead, C.R., R. Cox and J.W. Stather. Estimates of late radiation risks to the UK
population. NRPB 4: 15-157 (1993).

M21

Muirhead, C.R., J.A. O'Hagan, R.G. Haylock et al. Mortality and cancer incidence following
occupational radiation exposure: third analysis of the National Registry for Radiation Workers.
Br J Cancer 100(1): 206-212 (2009).

M22

Muirhead, C.R., O’Hagan, J.A. and R.G.E. Haylock. Third analysis of the National Registryfor Radiation Workers: occupational exposure to ionising radiation in relation to mortality andcancer incidence. HPA-RPD-062 (2009).

N1

Nagasawa, H. and J.B. Little. Induction of sister chromatid exchanges by extremely low dosesof alpha-particles. Cancer Res 52(22): 6394-6396 (1992).

N2

Nair, R.R., B. Rajan, S. Akiba et al. Background radiation and cancer incidence in Kerala,
India-Karanagappally cohort study. Health Phys 96(1): 55-66 (2009).

N3

NCI. Estimated exposures and thyroid doses received by the American people from iodine-131
in fallout following the Nevada atmospheric nuclear bomb tests. DHHS/NIH/NCI, NIH
Publication No. 97-4264, National Cancer Institute, 1997.

N4

NCRP. The relative biological effectiveness of radiations of different quality. NCRP Report
No. 104. National Council on Radiation Protection and Measurements, 1990.

N5

NCRP. Limitation of exposure to ionizing radiation. NCRP Report No. 116. National Council
on Radiation Protection and Measurements, 1993.

300 UNSCEAR 2012 REPORTN6

NCRP. A guide for uncertainty analysis in dose and risk assessments related to environmental
contamination. NCRP Commentary No. 14. National Council on Radiation Protection andMeasurements, Bethesda, 1996.

N7

NCRP. Uncertainties in fatal cancer risk estimates used in radiation protection. NCRP Report
No. 126. National Council on Radiation Protection and Measurements, Bethesda, 1997.

N8

NCRP. Development of a biokinetic model for radionuclide-contaminated wounds andprocedures for their assessment, dosimetry and treatment. NCRP Report No. 156. National
Council on Radiation Protection and Measurements, 2006.

N9

NCRP. Uncertainties in the measurement and dosimetry of external radiation. NCRP Report
No. 158. National Council on Radiation Protection and Measurements, Bethesda, 2008.

N10

NCRP. Radiation dose reconstruction: Principles and practices. NCRP Report No. 163.
National Council on Radiation Protection and Measurements, 2010.

N11

NCRP. Uncertainties in internal radiation dose assessment. NCRP Report No. 164. National
Council on Radiation Protection and Measurements, Bethesda, 2010.

N12

NCRP. Uncertainties in the estimation of radiation risks and probability of disease causation.
NCRP Report No. 171. National Council on Radiation Protection and Measurements,
Bethesda, 2012.

N13

Neumaier, T., J. Swenson, C. Pham et al. Evidence for formation of DNA repair centers anddose-response nonlinearity in human cells. Proc Natl Acad Sci U S A 109(2): 443-448 (2012).

N14

Neyman, J. and E.S. Pearson. On the use and interpretation of certain test criteria for purposesof statistical inference, part II. Biometrika 20A(3-4): 263-294 (1928).

N15

Nikjoo, H. and D.T. Goodhead. Track structure analysis illustrating the prominent role of lowenergy electrons in radiobiological effects of low-LET radiations. Phys Med Biol 36(2): 229238 (1991).

N16

Nikjoo, H. and L. Lindborg. RBE of low energy electrons and photons. Phys Med Biol 55(10):R65-109 (2010).

N17

Nishizawa, S., S. Kojima, S. Teramukai et al. Prospective evaluation of whole-body cancer
screening with multiple modalities including [18F]fluorodeoxyglucose positron emission
tomography in a healthy population: a preliminary report. J Clin Oncol 27(11): 1767-1773(2009).

N18

NRC. Health effects of exposure to radon. Committee on Health Risks of Exposure to Radon,
BEIR VI. National Research Council, National Academy Press, Washington, D.C., 1999.

N19

NRC. Health risks from exposure to low levels of ionizing radiation. Committee to Assess
Health Risks from Exposure to Low Levels of Ionizing Radiation, BEIR VII - Phase 2.
National Research Council, The National Academies Press, Washington D.C., 2006.

O1

Office for National Statistics. Cancer statistics registrations. Registrations of cancer diagnosed
in 2009, England. MB1 40. London, UK, 2011.

O2

Ojima, M., N. Ban and M. Kai. DNA double-strand breaks induced by very low X-ray doses
are largely due to bystander effects. Radiat Res 170(3): 365-371 (2008).

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 301

O3

Omar, R.Z., J.A. Barber and P.G. Smith. Cancer mortality and morbidity among plutonium
workers at the Sellafield plant of British Nuclear Fuels. Br J Cancer 79(7-8): 1288-1301(1999).

P1

Pawel, D.J., R.W. Leggett and K.F. Eckerman. Uncertainties in cancer risk coefficients forenvironmental exposure to radionuclides. An uncertainty analysis for risk coefficients reported
in Federal Guidance 13. ORNL/TM-2006/583. Oak Ridge National Laboratory, USA, 2007.

P2

Pershagen, G., G. Akerblom, O. Axelson et al. Residential radon exposure and lung cancer in
Sweden. N Engl J Med 330(3): 159-164 (1994).

P3

Peto, R., A.D. Lopez, J. Boreham et al. Mortality from tobacco in developed countries:
indirect estimation from national vital statistics. Lancet 339(8804): 1268-1278 (1992).

P4

Pierce, D.A., D.O. Stram and M. Vaeth. Allowing for random errors in radiation dose
estimates for the atomic bomb survivor data. Radiat Res 123(3): 275-284 (1990).

P5

Pierce, D.A. and A.M. Kellerer. Adjusting for covariate errors with nonparametric assessmentof the true covariate distribution. Biometrika 91(4): 863-876 (2004).

P6

Pierce, D.A., M. Vaeth and J.B. Cologne. Allowance for random dose estimation errors inatomic bomb survivor studies: a revision. Radiat Res 170(1): 118-126 (2008).

P7

Portess, D.I., G. Bauer, M.A. Hill et al. Low-dose irradiation of nontransformed cells
stimulates the selective removal of precancerous cells via intercellular induction of apoptosis.
Cancer Res 67(3): 1246-1253 (2007).

P8

Posada, D. and T.R. Buckley. Model selection and model averaging in phylogenetics:
advantages of akaike information criterion and bayesian approaches over likelihood ratio tests.
Syst Biol 53(5): 793-808 (2004).

P9

Preston, D.L., H. Kato, K. Kopecky et al. Studies of the mortality of A-bomb survivors. 8.
Cancer mortality, 1950-1982. Radiat Res 111(1): 151-178 (1987).

P10

Preston, D.L., J.H. Lubin and D.A. Pierce. Epicure User’s Guide. Hirosoft International
Corporation, Seattle, Washington, 1993.

P11

Preston, D.L., A. Mattsson, E. Holmberg et al. Radiation effects on breast cancer risk: apooled analysis of eight cohorts. Radiat Res 158(2): 220-235 (2002).

P12

Preston, D.L., Y. Shimizu, D.A. Pierce et al. Studies of mortality of atomic bomb survivors.
Report 13: Solid cancer and noncancer disease mortality: 1950-1997. Radiat Res 160(4): 381407 (2003).

P13

Preston, D.L., D.A. Pierce, Y. Shimizu et al. Effect of recent changes in atomic bomb survivor
dosimetry on cancer mortality risk estimates. Radiat Res 162(4): 377-389 (2004).

P14

Preston, D.L., E. Ron, S. Tokuoka et al. Solid cancer incidence in atomic bomb survivors:
1958-1998. Radiat Res 168(1): 1-64 (2007).

P15

Preston, D.L., L.Y. Krestinina, M.E. Sokolnikov et al. How much can we say about sitespecific cancer radiation risks? Radiat Res 174(6): 816-824 (2010).

P16

Puncher, M. and A. Birchall. A Monte Carlo method for calculating Bayesian uncertainties ininternal dosimetry. Radiat Prot Dosim 132(1): 1-12 (2008).

302 UNSCEAR 2012 REPORT

P17Puncher, M., A. Birchall and R.K. Bull. Uncertainties on lung doses from inhaled plutonium.
Radiat Res 176(4): 494-507 (2011).

P18

Puncher, M. and J.D. Harrison. Uncertainty analysis of doses from ingestion of plutonium andamericium. Radiat Prot Dosim 148(3): 284-296 (2012).

P19

Puskin, J.S. Smoking as a confounder in ecologic correlations of cancer mortality rates withaverage county radon levels. Health Phys 84(4): 526-532 (2003).

R1

Reeves, G.K., D.R. Cox, S.C. Darby et al. Some aspects of measurement error in explanatory
variables for continuous and binary regression models. Stat Med 17(19): 2157-2177 (1998).

R2

Richardson, D., H. Sugiyama, N. Nishi et al. Ionizing radiation and leukemia mortality among
Japanese Atomic Bomb Survivors, 1950-2000. Radiat Res 172(3): 368-382 (2009).

R3

Ron, E., J.H. Lubin, R.E. Shore et al. Thyroid cancer after exposure to external radiation: apooled analysis of seven studies. Radiat Res 141(3): 259-277 (1995).

R4

Rothman, K.J. and S. Greenland. Causation and causal inference in epidemiology. Am J
Public Health 95 (Suppl 1): S144-150 (2005).

R5

Rothman, K.J., S. Greenland and T.L. Lash. Case-control studies. pp.111-127 in: Modern
Epidemiology (K.J. Rothman et al., eds.). Lippincott Williams & Wilkins, Philadelphia, 2008.

R6

Rothman, K.J., S. Greenland and T.L. Lash. Validity in epidemiologic studies. pp.128-147 in:Modern Epidemiology (K.J. Rothman et al., eds.). Lippincott Williams & Wilkins,
Philadelphia, 2008.

R7

Rothman, K.J., S. Greenland and T.L. Lash. Modern Epidemiology. Third edition. Lippincott
Williams & Wilkins, Philadelphia, 2008.

S1

Saccomanno, G., O. Auerbach, M. Kuschner et al. A comparison between the localization oflung tumors in uranium miners and in nonminers from 1947 to 1991. Cancer 77(7): 1278-1283(1996).

S2

Samet, J.M., J. Stolwijk and S.L. Rose. Summary: International workshop on residential Rn
epidemiology. Health Phys 60(2): 223-227 (1991).

S3

Sasaki, S. and N. Fukuda. Dose-response relationship for life-shortening and carcinogenesis inmice irradiated at day 7 postnatal age with dose range below 1 Gy of gamma rays. J Radiat
Res 47(2): 135-145 (2006).

S4

Sasaki, S. and N. Fukuda. Dose-response relationship for induction of ovarian tumors in mice
irradiated during prenatal, early postnatal and elder periods. J Radiat Res 49(6): 623-633(2008).

S5

Schafer, D.W., J.H. Lubin, E. Ron et al. Thyroid cancer following scalp irradiation: areanalysis accounting for uncertainty in dosimetry. Biometrics 57(3): 689-697 (2001).

S6

Schafer, D.W. and E.S. Gilbert. Some statistical implications of dose uncertainty in radiation
dose-response analyses. Radiat Res 166(1 Pt 2): 303-312 (2006).

S7

Schmid, E., D. Regulla, H.M. Kramer et al. The effect of 29 kV X rays on the dose response ofchromosome aberrations in human lymphocytes. Radiat Res 158(6): 771-777 (2002).

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 303

S8

Schmid, E., M. Krumrey, G. Ulm et al. The maximum low-dose RBE of 17.4 and 40 keV
monochromatic X rays for the induction of dicentric chromosomes in human peripheral
lymphocytes. Radiat Res 160(5): 499-504 (2003).

S9

Schneider, U. and L. Walsh. Cancer risk above 1 Gy and the impact for space radiation
protection. Adv Space Res 44(2): 202-209 (2009).

S10

Schwarz, G. Estimating the dimension of a model. Ann Stat 6(2): 461-464 (1978).

S11

Shagina, N.B., E.I. Tolstykh, T.P. Fell et al. In utero and postnatal haemopoietic tissue doses
resulting from maternal ingestion of strontium isotopes from the Techa River. Radiat Prot
Dosim 127(1-4): 497-501 (2007).

S12

Shilnikova, N.S., D.L. Preston, E. Ron et al. Cancer mortality risk among workers at the
Mayak nuclear complex. Radiat Res 159(6): 787-798 (2003).

S13

Shin, S.C., Y.M. Kang and H.S. Kim. Life span and thymic lymphoma incidence in high- andlow-dose-rate irradiated AKR/J mice and commonly expressed genes. Radiat Res 174(3): 341346 (2010).

S14

Shleien, B., L.A.J. Slaback and B.K. Birky. Handbook of Health Physics and Radiological
Health. Lippincott Williams & Wilkins, Baltimore, Maryland, 1998.

S15

Shore, R.E., N. Hildreth, E. Woodard et al. Breast cancer among women given X-ray therapy
for acute postpartum mastitis. J Natl Cancer Inst 77(3): 689-696 (1986).

S16

Shuryak, I., P. Hahnfeldt, L. Hlatky et al. A new view of radiation-induced cancer: integrating
short- and long-term processes. Part I: approach. Radiat Environ Biophys 48(3): 263-274(2009).

S17

Siegfried, T. Odds are, it's wrong: Science fails to face the shortcomings of statistics. Sci News
177(7): 26-29 (2010).

S18

Sigurdson, A.J., M.M. Doody, R.S. Rao et al. Cancer incidence in the US radiologic
technologists health study, 1983-1998. Cancer 97(12): 3080-3089 (2003).

S19

Silver, S.R., R.D. Daniels, T.D. Taulbee et al. Differences in mortality by radiation monitoring
status in an expanded cohort of Portsmouth Naval Shipyard workers. J Occup Environ Med
46(7): 677-690 (2004).

S20

Simon, S.L., L.R. Anspaugh, F.O. Hoffman et al. 2004 update of dosimetry for the Utah
Thyroid Cohort Study. Radiat Res 165(2): 208-222 (2006).

S21

Sinclair, W.K. Experimental RBE values of high LET radiations at low doses and theimplications for quality factor assignment. Radiat Prot Dosim 13(1-4): 319-326 (1985).

S22

Slonina, D., K. Spekl, A. Panteleeva et al. Induction of micronuclei in human fibroblasts andkeratinocytes by 25 kV x-rays. Radiat Environ Biophys 42(1): 55-61 (2003).

S23

Sokolnikov, M.E., E.S. Gilbert, D.L. Preston et al. Lung, liver and bone cancer mortality inMayak workers. Int J Cancer 123(4): 905-911 (2008).

S24

Spiegelhalter, D.J., N.G. Best and B.P. Carlin. Bayesian measures of model complexity andfit. J R Stat Soc Ser B 64(4): 583-639 (2002).

304 UNSCEAR 2012 REPORT

S25

Stayner, L., M. Vrijheid, E. Cardis et al. A Monte Carlo maximum likelihood method for
estimating uncertainty arising from shared errors in exposures in epidemiological studies ofnuclear workers. Radiat Res 168(6): 757-763 (2007).

S26

Steck, D.J., M.C. Alavanja, R.W. Field et al. 210Po implanted in glass surfaces by long term
exposure to indoor radon. Health Phys 83(2): 261-271 (2002).

S27

Steck, D.J. and R.W. Field. Dosimetric challenges for residential radon epidemiology. J
Toxicol Environ Health A 69(7): 655-664 (2006).

S28

Stepanenko, V.F., P.G. Voilleque, Y.I. Gavrilin et al. Estimating individual thyroid doses for acase-control study of childhood thyroid cancer in Bryansk Oblast, Russia. Radiat Prot Dosim
108(2): 143-160 (2004).

S29

Stevens, W., J.E. Till and D.C. Thomas. Assessment of leukemia and thyroid disease inrelation to fallout in Utah: Report of a cohort study of thyroid disease and radioactive fallout
from the Nevada test site. University of Utah, Salt Lake City, 1992.

S30

Stram, D.O., B. Langholz and M. Huberman. Measurement error correction of lung cancer risk
estimates in the Colorado Plateau cohort. Part I: Dosimetry analysis. Technical Report 126.
University of Southern California School of Medicine, 1998.

S31

Stram, D.O., B. Langholz, M. Huberman et al. Correcting for exposure measurement error in areanalysis of lung cancer mortality for the Colorado Plateau Uranium Miners cohort. Health
Phys 77(3): 265-275 (1999).

S32

Stram, D.O. and K.J. Kopecky. Power and uncertainty analysis of epidemiological studies ofradiation-related disease risk in which dose estimates are based on a complex dosimetry
system: some observations. Radiat Res 160(4): 408-417 (2003).

S33

Straume, T. and A.L. Carsten. Tritium radiobiology and relative biological effectiveness.
Health Phys 65(6): 657-672 (1993).

S34

Suzuki, K., H. Okada, M. Yamauchi et al. Qualitative and quantitative analysis ofphosphorylated ATM foci induced by low-dose ionizing radiation. Radiat Res 165(5): 499-504(2006).

T1

Telle-Lamberton, M., E. Samson, S. Caer et al. External radiation exposure and mortality in acohort of French nuclear workers. Occup Environ Med 64(10): 694-700 (2007).

T2

Thierry-Chef, I., M. Marshall, J.J. Fix et al. The 15-Country Collaborative Study of Cancer
Risk among Radiation Workers in the Nuclear Industry: study of errors in dosimetry. Radiat
Res 167(4): 380-395 (2007).

T3

Thomas, D., S. Darby, F. Fagnani et al. Definition and estimation of lifetime detriment fromradiation exposures: principles and methods. Health Phys 63(3): 259-272 (1992).

T4

Thompson, D.E., K. Mabuchi, E. Ron et al. Cancer incidence in atomic bomb survivors. Part
II: Solid tumors, 1958-1987. Radiat Res 137(2 Suppl): S17-S67 (1994).

T5

Tirmarche, M., D. Laurier and F. Bochicchio. Quantification of cancer and non-cancer risks
associated with multiple chronic radiation exposures: Epidemiological studies, organ dose
calculation and risk assessment. Final scientific report in the frame of the European project“Alpha Risk”. EUR Report 24599, 2010.

T6

Tosteson, T.D., L.A. Stefanski and D.W. Schafer. A measurement-error model for binary andordinal regression. Stat Med 8(9): 1139-1147; discussion 1149 (1989).

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 305

T7

Trabalka, J.R. and D.C. Kocher. Energy dependence of dose and dose-rate effectiveness factor
for low-let radiations: potential importance to estimation of cancer risks and relationship tobiological effectiveness. Health Phys 93(1): 17-27 (2007).

T8

Tronko, M.D., G.R. Howe, T.I. Bogdanova et al. A cohort study of thyroid cancer and otherthyroid diseases after the chornobyl accident: thyroid cancer in Ukraine detected during firstscreening. J Natl Cancer Inst 98(13): 897-903 (2006).

T9

Tubiana, M., L.E. Feinendegen, C. Yang et al. The linear no-threshold relationship isinconsistent with radiation biologic and experimental data. Radiology 251(1): 13-22 (2009).

T10

Turner, J.E., H.A. Wright and R.N. Hamm. A Monte Carlo primer for health physicists. Health
Phys 48(6): 717-733 (1985).

T11

Turner, M.C., D. Krewski, Y. Chen et al. Radon and lung cancer in the American Cancer
Society cohort. Cancer Epidemiol Biomarkers Prev 20(3): 438-448 (2011).

U1

U.S. EPA. Cancer risk coefficients for environmental exposure to radionuclides. EPA 402-R99-001. U.S. Environmental Protection Agency, Washington D.C., 1999.

U2

U.S. EPA. Estimating radiogenic cancer risks. Addendum: Uncertainty analysis. EPA Report
402-R-00-003. U.S. Environmental Protection Agency, 1999.

U3

U.S. EPA. EPA radiogenic cancer risk models and projections for the U.S. population. U.S.
Environmental Protection Agency, Washington, D.C., 2011.

U4

Uehara, Y., Y. Ito, K. Taki et al. Gene expression profiles in mouse liver after long-term lowdose-rate irradiation with gamma rays. Radiat Res 174(5): 611-617 (2010).

U5

University of California and Max Planck Institute for Demographic Research. The humanmortality database. Berkeley, USA, 2011.

U6

UNSCEAR. Sources and Effects of Ionizing Radiation. UNSCEAR 1977 Report. United
Nations Scientific Committee on the Effects of Atomic Radiation, 1977 Report to the General
Assembly, with annexes. United Nations sales publication E.77.IX.1. United Nations, New
York, 1977.

U7

UNSCEAR. Genetic and Somatic Effects of Ionizing Radiation. UNSCEAR 1986 Report.
United Nations Scientific Committee on the Effects of Atomic Radiation, 1986 Report to theGeneral Assembly, with annexes. United Nations sales publication E.86.IX.9. United Nations,
New York, 1986.

U8

UNSCEAR. Sources, Effects and Risks of Ionizing Radiation. UNSCEAR 1988 Report.
United Nations Scientific Committee on the Effects of Atomic Radiation, 1988 Report to theGeneral Assembly, with annexes. United Nations sales publication E.88.IX.7. United Nations,
New York, 1988.

U9

UNSCEAR. Sources and Effects of Ionizing Radiation. UNSCEAR 1993 Report. United
Nations Scientific Committee on the Effects of Atomic Radiation, 1993 Report to the General
Assembly, with scientific annexes. United Nations sales publication E.94.IX.2. United
Nations, New York, 1993.

U10

UNSCEAR. Sources and Effects of Ionizing Radiation. UNSCEAR 1994 Report. United
Nations Scientific Committee on the Effects of Atomic Radiation, 1994 Report to the General
Assembly, with scientific annexes. United Nations sales publication E.94.IX.11. United
Nations, New York, 1994.

306 UNSCEAR 2012 REPORTU11UNSCEAR. Sources and Effects of Ionizing Radiation. Volume II: Effects. UNSCEAR 2000
Report. United Nations Scientific Committee on the Effects of Atomic Radiation, 2000 Reportto the General Assembly, with scientific annexes. United Nations sales publication E.00.IX.4.
United Nations, New York, 2000.

U12

UNSCEAR. Effects of Ionizing Radiation. Volume I: Report to the General Assembly,
Scientific Annexes A and B. UNSCEAR 2006 Report. United Nations Scientific Committee
on the Effects of Atomic Radiation. United Nations sales publication E.08.IX.6. United
Nations, New York, 2008.

U13

UNSCEAR. Effects of Ionizing Radiation. Volume II: Scientific Annexes C, D and E.
UNSCEAR 2006 Report. United Nations Scientific Committee on the Effects of Atomic
Radiation. United Nations sales publication E.09.IX.5. United Nations, New York, 2009.

U14

UNSCEAR. Sources and Effects of Ionizing Radiation. Volume II: Effects. Scientific Annexes
C, D and E. UNSCEAR 2008 Report. United Nations Scientific Committee on the Effects ofAtomic Radiation. United Nations sales publication E.11.IX.3. United Nations, New York,
2011.

V1

Vasilenko, E.K., V.F. Khokhryakov, S.C. Miller et al. Mayak worker dosimetry study: an
overview. Health Phys 93(3): 190-206 (2007).

V2

Verhaegen, F. and A. Vral. Sensitivity of micronucleus induction in human lymphocytes to
low-LET radiation qualities: RBE and correlation of RBE and LET. Radiat Res 139(2): 208213 (1994).

V3

Vrijheid, M., E. Cardis, M. Blettner et al. The 15-Country Collaborative Study of Cancer Risk
Among Radiation Workers in the Nuclear Industry: design, epidemiological methods anddescriptive results. Radiat Res 167(4): 361-379 (2007).

W1

Walsh, C. and J.P. McLaughlin. Correlation of 210Po implanted in glass with radon gas
exposure: sensitivity analysis of critical parameters using a Monte-Carlo approach. Sci Total
Environ 272(1-3): 195-202 (2001).

W2

Walsh, L. A short review of model selection techniques for radiation epidemiology. Radiat
Environ Biophys 46(3): 205-213 (2007).

W3

Walsh, L., P. Jacob and J.C. Kaiser. Radiation risk modeling of thyroid cancer with special
emphasis on the Chernobyl epidemiological data. Radiat Res 172(4): 509-518 (2009).

W4

Walsh, L. and J.C. Kaiser. Multi-model inference of adult and childhood leukaemia excess
relative risks based on the Japanese A-bomb survivors mortality data (1950-2000). Radiat
Environ Biophys 50(1): 21-35 (2011).

W5

Wang, Z., J.H. Lubin, L. Wang et al. Residential radon and lung cancer risk in a high-exposurearea of Gansu Province, China. Am J Epidemiol 155(6): 554-564 (2002).

W6

Weinberg, C.R. Potential for bias in epidemiologic studies that rely on glass-based
retrospective assessment of radon. Environ Health Perspect 103(11): 1042-1046 (1995).

W7

Weinberg, C.R., E.S. Moledor, D.M. Umbach et al. Imputation for exposure histories withgaps, under an excess relative risk model. Epidemiology 7(5): 490-497 (1996).

W8WHO. WHO Handbook on indoor radon: A public health perspective (H. Zeeb and F.
Shannoun, eds.). World Health Organization, Geneva, 2009.

ANNEX B: UNCERTAINTIES IN RISK ESTIMATES FOR RADIATION-INDUCED CANCER 307

W9

Willett, W.C. Nutritional epidemiology. pp.580-597 in: Modern Epidemiology (K.J. Rothman
et al., eds.). Lippincott Williams & Wilkins, Philadelphia, 2008.

W10

Wing, S. and D.B. Richardson. Age at exposure to ionising radiation and cancer mortality
among Hanford workers: follow up through 1994. Occup Environ Med 62(7): 465-472 (2005).

W11

Wintle, B.A., M.A. McCarthy and C.T. Volinsky. The use of Bayesian model averaging tobetter represent uncertainty in ecological models. Conserv Biol 17(6): 1579-1590 (2003).

W12

Wykes, S.M., E. Piasentin, M.C. Joiner et al. Low-dose hyper-radiosensitivity is not caused bya failure to recognize DNA double-strand breaks. Radiat Res 165(5): 516-524 (2006).

Y1

Yamada, Y., S. Tokonami and W. Zhuo. Rn-Tn discriminative measurements and their dose
estimates in Chinese loess plateau. International Congress Series 1276: 76-80 (2005).

Y2

Yang, Y. Can the strengths of AIC and BIC be shared? A conflict between model
indentification and regression estimation. Biometrika 92(4): 937-950 (2005).

Y3

Young, S.S. and A. Karr. Deming, data and observational studies. Significance 8(3): 116-120(2011).

Z1

Zankl, M., N. Petoussi-Henss, U. Fill et al. The application of voxel phantoms to the internal
dosimetry of radionuclides. Radiat Prot Dosim 105(1-4): 539-548 (2003).

Z2

Zhang, Z., B. Smith, D.J. Steck et al. Variation in yearly residential radon concentrations in
the upper midwest. Health Phys 93(4): 288-297 (2007).

GLOSSARY 309

GLOSSARY
Abscopal effect: A biological consequence induced by radiation that is observed at a distance from theirradiated tissue (see annex C of [U2]).
Absorbed dose, D: The fundamental dose quantity given by
D=

dε
dm

where dε is the mean energy imparted to matter of mass dm by ionizing radiation. The SI unit for
absorbed dose is joule per kilogram (J/kg) and its special name is gray (Gy).
Acute exposure: Exposure received within a short time period. (See also: Chronic exposure).
Adaptive response: Refers to the phenomenon by which cells irradiated with a sublethal dose ofionizing radiation (an “adaptive” dose of a few centigrays) become less susceptible to subsequent
exposure to high doses of radiation (a “challenge” dose of several grays).
Akaike Information Criterion (AIC): The AIC is a relative measure of goodness of fit taking into
account the “likelihood” of the data being observed given an assumed model and number of model
parameters. It is a concept derived from information theory, and is defined as AIC = −2 ln(L) + 2p,
where ln(L) is the natural logarithm of the maximized “likelihood” for the model of interest and p is thenumber of free parameters in the model. For a given set of observed data and two models assumed to
explain the observations, the model with the lower AIC is considered to have the higher probability of
being correct. See “Bayesian Information Criterion” for an alternative approach to judge the probabilityof one model being correct over another.
Aleatory uncertainty (Type A uncertainty): Uncertainty due to stochastic variability in observations,
measurements, or true values of the quantity of interest. For a cohort of individuals, some portion of theinter-individual variability of true values will be due to stochastic or aleatoric processes. Aleatory
uncertainty (i.e. natural or random variability) can be characterized through research, if additional
factors and conditions can be identified that explain the observed variability in the quantity of interest.
Assigned share: Assigned share is the probability that an observed health effect in an individual wascaused by a specific radiation exposure. It is equal to the fraction of the total number of cases of a
specific type of cancer diagnosed among individuals which is in excess to the baseline number of cases
for persons who share the same attributes, such as absorbed organ dose, age, time since last exposure,sex, smoking history, etc. The assigned share (AS) is quantified as
AS =excess relative risk
relative risk

The AS is often referred to as the “attributable fraction” or “probability of causation” assuming that thecalculated excess relative risk represents the net consequences of mechanisms of disease manifestation
for a given individual diagnosed with disease.

310 UNSCEAR 2012 REPORTAssignment error (“Berkson error”): Assignment error is relevant in situations where the difference(or ratio) of the assigned and true values of quantity of interest (e.g. a radiation dose) is independent of
the assigned value. Such errors typically arise as the result of some sort of grouping in which all
members of a defined subgroup are assigned a single representative value (e.g. an unbiased expectedvalue of dose for each member of a subgroup, where the subgroup is identified by exposure
characteristics, such as age, sex, location, diet, residence history and shielding). A fundamental
characteristic of assignment error is that true values vary at random about the assigned value. Thus, thevariance of true values will be larger than the variance of assigned values. Furthermore, the assigned
value will equal (or closely approximate) the true mean value for the subgroup. In linear regression, thepresence of additive assignment error in the independent variable does not lead to bias in the estimate of
the regression slope. Assignment error can be contrasted with “measurement error” and “shared error”.
Attribution: The ascribing of an actual or manifest outcome to a cause. In the context of this report,
attribution refers to the ascribing of an outcome—in particular a health effect—to radiation exposure.
(a) An outcome may be an individual outcome (such as the occurrence of a health effect in an
individual);(b) An outcome may also be a collective outcome (such as a change in the frequency ofoccurrence of health effects in a population or a group);(c) Attribution may require expert assessment (or the consensus of a number of expert
assessments), which may be made on the basis of a combination of evidence (facts) and argument(explanation).
Attributability: The ability to attribute a cause to an outcome.
(a) In the context of this report, attributability refers whether or not a manifest health effect in an
individual or a manifest change in frequency of health effects in a population is capable of being
ascribed as having being induced by radiation exposure;(b) Attributability can be expressed qualitatively as a level of confidence in attribution (such as
unequivocally, confidently, reliably, and plausibly), based on evaluation of the type, amount,quality and consistency of evidence, and the degree of scientific consensus.
Attributable fraction (proportion): See “Assigned share”.
Baseline (hazard) rate (frequency): (Age-specific) disease rates for a population of interest in theabsence of exposure or at some reference exposure level. See also “Hazard rate (function)” and “Excess(absolute) rate”.
Baseline risk: Baseline risk refers to the probability that an event of interest (e.g. diagnosis of cancer)
will occur in an individual among an unexposed population over a given time period (e.g. lifetime
following exposure). See “Risk”.
Bayesian inference: The method of inference that quantifies the degree of belief (or the analyst’s stateof knowledge) of a true value or sets of values of a quantity of interest by combining their priorknowledge about these quantities with recent measurements, observations, or estimates. The degree ofbelief of the quantity of interest is often described by a subjective probability distribution representing
possibly true values for that quantity. The distribution resulting from Bayesian inference is called aposterior distribution.

GLOSSARY

311

Bayesian Information Criterion (BIC): The BIC is a relative measure of goodness of fit taking into
account the “deviance” of the observed data from the assumed model and the number of model
parameters. The BIC is a measure derived from Bayesian statistics. For a given set of observed data andtwo assumed models, the model with the lower BIC is considered to have the higher probability of
being correct. The BIC is given by the difference between (1) the product of the number of model
parameters and the natural logarithm of the sample size, and (2) twice the natural logarithm of the“likelihood”. See “Akaike Information Criterion” for an alternative approach to judge the probability of
one model being more correct over another.
Berkson error: See “Assignment error”.
Bias: A statistical estimation procedure is “biased” if the expected value of the estimate of the quantityof interest is not equal to the true value of the quantity. The “bias” of the procedure is the difference
between the expected and true values.
Bystander effect: A non-targeted cellular action of radiation exposure meaning that not only the cellthat was actually hit shows radiation consequences, but also neighbouring cells (see annex C of [U2]).
Causation: The relationship between cause (here, radiation exposure) and outcome (radiogenic healtheffect or associated risk). The term can also mean the action of causing something.
Chronic exposure: Exposure persisting in time. (See also: “Acute exposure” and “Protracted exposure”.)
Classical error: Classical error, or more precisely classical measurement error, applies in situations inwhich the difference between the measured or estimated value and the true value of a quantity ofinterest (e.g. a radiation dose) is independent of the true value. Classical measurement error is a type ofrandom error; it arises when measured or estimated values of a quantity of interest are determined byimprecise measurements or by estimates of quantities used as independent variables in a regression
analysis. A fundamental characteristic of classical measurement error is that the variance of measured
or estimated values is larger than the variance of true values. The mean of the measured or estimatedvalues is unbiased with respect to the true mean. In linear regression, the presence of classicalmeasurement error in the independent variable biases the estimate of the regression slope toward zero.
Classical measurement error can be contrasted with “assignment error” and with “shared error”.
Confidence interval: In “frequentist inference”, a confidence interval is an interval defined in terms of
the sampling distribution of a statistic of interest (i.e. the distribution of estimates of the statistic thatwould arise from repeated—generally hypothetical—realizations of data generated from the sameunderlying distribution as the observed data) such that, for example, the probability that a 95%
confidence interval for a given parameter contains the true value of that parameter is 0.95. (Compare
this with “Credible intervals” used in “Bayesian inference”.)
Confounding factor or confounder: In statistics, a confounding factor is a variable that is correlatedwith both the dependent variable (e.g. radiation exposure or dose) and the independent (outcome)variable (e.g. risk of lung cancer) and, if not controlled for analytically may distort the conclusions. For
example, occupation may be a confounding factor in a study of the relation between lung cancer
incidence among non-smokers (dependent variable) and medical radiation exposure (independent
variable). For instance, air crew are exposed to higher levels of radiation due to their employment(correlation with independent variable) while staff working in certain recreation industries are often
occupationally exposed to cigarette smoke (correlation with dependent variable). This confounding
might be controlled by introducing into the analysis an indicator for the occupational group. See also
“Effect modification”. A variable may, but need not, be both a confounding factor and an effect312 UNSCEAR 2012 REPORT

modifier in which case dose–response analyses need to allow for influence of the factor on the outcomeof interest and for the interaction between dose and the factor.
Counterfactual analysis: Counterfactual analysis approaches causal hypotheses by considering a(counterfactual conditional) proposition of the form “If A had not occurred, would B not have occurred(at the same time and nature with which it was observed)?”Credible interval: This term is used in Bayesian inference to refer to an interval defined from the
distribution of the degree of belief of the value of the quantity of interest within which a certain
probability is assigned (e.g. 90%) representing the assessor’s degree of belief that the true value of aquantity of interest falls within the interval. Credible intervals are sometimes called Bayesian credibility
intervals or subjective confidence intervals. The interpretation of credible intervals is subtly different
from that of frequentist confidence intervals (see “Confidence interval”).
Deterministic (health) effect: See “Health effects”.
(Radiation) Detriment: The total harm that would eventually be experienced by an exposed group andits descendants as a result of the group’s exposure to radiation from a source [I1].
Deviance: Deviance is a measure of the goodness of fit of a statistical model for a set of data. Deviance
was originally defined for the class of generalized linear models (which includes ordinary linear
regression, Poisson regression, logistic regression, and many other commonly used models) as a“likelihood ratio test”, which compares a specific fitted model (in which parameters were estimatedusing maximum likelihood methods) to a “saturated” model in which there is one parameter for eachobservation. If ℓM is the logarithm of the maximum likelihood for the model of interest withp parameters and ℓS is the logarithm of the likelihood for the saturated model with n parameters, thedeviance is defined as −2 (ℓM − ℓS ) and can, under certain conditions, be treated as the difference
between the true value of a quantity of interest and a measurement of that value.
EAR: See “Excess absolute rate/risk”.
Effect modification: Effect modification (also called statistical “interaction”) occurs when themagnitude of the influence of the dependent variable of interest (e.g. radiation dose or exposure) on an
independent (outcome) variable (e.g. lung cancer) depends upon the magnitude of some other factor(the effect modifier). For example, analyses of the atomic bombings survivors suggest that themagnitude of the outcome of ionizing radiation exposure on the excess relative risk of lung cancer
depends on smoking intensity, with a larger outcome from unit dose among moderate smokers andmuch smaller outcome among heavy smokers. An effect modifier may or may not be a confounding
factor, depending on whether or not there is a correlation between the dependent variable of interestand the effect modifying factor.
Epistemic uncertainty (Type B uncertainty): The subjective degree of belief about the true, fixed but
unknown value for a given quantity of interest. Epistemic uncertainty for a fixed quantity can becontrasted with aleatory uncertainty (random variability of repeated measurements, observations, or oftrue values for the individuals within a population of interest). Epistemic uncertainty is often quantified
using Bayesian inference. In principle, and in contrast to aleatory uncertainty, epistemic uncertainty canbe reduced through research.
ERR: See “Excess relative risk/rate”.

GLOSSARY

313

Error: The difference between an observed or estimated value and the true (but unknown) value. Since
the true value is unknowable, error cannot be quantified. Error can be contrasted with uncertainty,
which can be estimated by repeated measurements or Bayesian inference.
Excess absolute risk/rate (EAR): The difference between the hazard rate in an exposed population andthe “baseline rate” in that population. This is often a function of dose, age (or some other measure oftime) and other factors (effect modifiers). Excess absolute rate is often called “excess absolute risk” or“excess rate”. Strictly risk would apply to a prospective estimate inferred from the data and reasoning,
while rate would be the direct statistic calculated from the data.
Excess relative risk/rate (ERR): The “relative risk/rate” minus one. The excess relative rate is strictlya statistic calculated from observed frequencies/rates, while the excess relative risk is a prospective
estimate inferred from the data and reasoning. The ERR is often considered as a function of dose andother factors.
Excess risk/rate: A measure of the statistical relationship between a given risk factor and a specificoutcome. Depending on the context it can refer to some characterization of the influence on rates suchas the “relative risk”, “excess relative risk”, or “excess (absolute) rate”, or, perhaps most appropriately,
to estimates of the risk over some period of time (lifetime risk) associated with an exposure of interest.
The excess rate is strictly a statistic calculated from observed frequencies/rates, while the excess risk is
a prospective estimate inferred from the observations and reasoning.
Falsifiable: In the context of this annex, falsifiable means being able to be shown to be false (here it
does not mean being able to alter information so as to mislead). According to critical rationalism as
advanced by Popper and dominating the empirical sciences, only hypotheses that can be falsified with asevere empirical test belong to the field of science proper [P1]. The approach used for testing falsifiablehypotheses is in principle relatively straightforward. A question is formulated and a study is designed toprovide an answer. The question is usually framed in the form of a hypothesis, such as “children
exposed to low level radiation are more likely to develop cancer than children not exposed”. Most
commonly the hypothesis is expressed in the negative (i.e. is falsifiable), such as “children exposed to
low level radiation are no more likely to develop cancer than children not exposed”. This is termed the"null hypothesis" and research is conducted to prove that it is wrong (in epidemiological parlance, “toreject the null hypothesis of no effect”). After a hypothesis is developed and a study is designed, data
are collected (something is measured or counted) and analysed, and then conclusions are drawn.
Frequency (of occurrence of disease): The number of new cases of the disease under study divided by
the number of people in a population over a defined time period.
Frequentist inference: A method of inference in which parameter estimates, hypothesis tests, andconfidence intervals for some quantities of interest are based on the chances of obtaining the observed
data in repeated (hypothetical) realizations of the data given an assumed state of nature. The main
alternative approach to frequentist inference is “Bayesian inference”.
Genomic instability: An all-embracing term to describe the increased rate of acquisition of alterationsin the genome. As compared with the direct actions of radiation, i.e. those consequence directly induced
by energy deposition, radiation-induced instability is observed in cells at delayed times after irradiationand manifests in the progeny of exposed cells multiple generations after the initial insult.
Hazard rate (function): A hazard rate refers to the limiting probability of occurrence of an event ofinterest in a short time interval (t, t + ∆t) as the length of the interval approaches 0 given that the event
can occur after time t. In radiation risk estimation, t generally refers to age or time since exposure.

314 UNSCEAR 2012 REPORT

Since hazard rates generally vary with time and other factors (e.g. sex or dose), the concept of a hazard
function is often used.
Health effects (of radiation) (also radiogenic health effects):
Deterministic (health) effect: A health effect of radiation for which generally a thresholdlevel of dose exists, which varies with person and circumstance, above which the severity of
the health effect is greater for a higher dose. The ICRP has introduced a term “tissue reactions”
to describe a group of health effects comprising deterministic effects and some health effects(such as cataracts and fibrosis) that are not determined solely at the time of irradiation but canbe modified after radiation exposure [I1, I2].
Stochastic (health) effect: A radiation-related health effect, the probability of occurrence of
which depends on radiation dose and the severity of which (if it occurs) is independent ofdose. In radiation protection the so-called LNT-model is used (linear non-threshold) meaningthat the assumption is made that one can linearly extrapolate from moderate/high doses to low
and very low doses without a threshold. Note that this should not be confused with thestochastic actions or processes of radiation interaction at the molecular or cellular level.
Inference: The process of drawing conclusions from scientific observations, evidence and reasoning in
the presence of uncertainty. While this report is focussed on prospectively inferring risk, note that
estimating an assigned share (or probability of causation) is also inference, but retrospective.
Interaction: Refers to the situation in which the magnitude of the influence of one risk factor on
disease rates depends upon the magnitude of one or more other risk factors (see “Joint effects”).
Joint effects: Refers to the combined influence of two or more risk factors (e.g. radiation exposure andsmoking) on disease rates. Simple common types of joint effects include additive and multiplicative
effects. If two risk factors, D and S, are additive, the excess rate ρ(D) associated with factor D does notdepend on the excess rate ψ(S) for factor S, and the total rate is λ0 + ρ(D) + ψ(S), where λ0 is the rate in
the absence of exposure (baseline rate). This additive model can also be written in terms of “excess
relative risks” as λ0 (1 + ρ´ (D) + ψ´ (S)), where ρ´ (D) = ρ (D) / λ0 and ψ´ (S) = ψ (S) / λ0 are excess
relative risk functions. In the case of a (simple) multiplicative interaction, the magnitude of the excess
rate associated with one risk factor depends on the level of the other risk factor; for example, risk isrepresented by λ0 + ρ (D) + ψ (S) + ρ (D) ψ (S) or, in terms of excess relative risk, risk =λ0 (1 + ρ´ (D))(1 + ψ´ (S)). A somewhat more general interaction model can be written (in terms ofexcess relative risks) as λ0 (1 + ρ´ (D) + ψ´ (S) + θ ρ´ (D) ψ´ (S)), where θ is a parameter such that thejoint effects are additive if θ = 0, multiplicative if θ = 1, sub-additive if θ < 0, sub-multiplicative if
0 < θ < 1 and super-multiplicative if θ > 1. More general interactions can also be considered.
Latency (period): The period between exposure and manifestation of a health effect. This is also theperiod after which statistically significant increases in frequency of occurrence of the health effect in a
population have been seen; theoretically, there might be an undetectable increased frequency ofoccurrence of the health effect in an exposed population during the presumed latency period, but thispossibility becomes vanishingly small in the period shortly after exposure because there is a finite timerequired for damaged cells to replicate in an uncontrolled manner and manifest as a cancerous growth.
LET (linear energy transfer): The average linear rate of energy loss of charged particle radiation in a
medium, i.e. the radiation energy lost per unit length of path through a material. That is, the quotient ofdE by dl where dE is the mean energy lost by a charged particle owing to collisions with electrons intraversing a distance dl in matter.

GLOSSARY

L=

315

dE
dl

The unit of L is J/m, often given in keV/µm.
Lifetime risk: An estimate of the risk associated with an exposure of interest over the (remaining)
lifetime of an exposed population. Technically, the lifetime risk associated following an exposure todose D is given by∞∫ h (u, D) S (u, D) dut0c

where hc (u, D) is the assumed (hazard) rate for the cause of interest at time u given exposure to dose D
and S (u, D) is the probability of still being alive and at risk of having the event at time u given dose D.
The excess lifetime risk is defined as∞∫ [h (u, D) − h (u, 0)] S (u, D) du
c

t0

c

In the literature on radiogenic health effects and radiation protection, this quantity is often called the
REID or REIC (risk of exposure-induced excess deaths or cases). It is sometimes approximated by the(LAR) (lifetime attributable risk), which is defined as∞∫ [h (u, D) − h (u, 0)] S (u, 0) du
t0

c

c

or the ELR (excess lifetime risk) which is defined as∞∞∫ h (u, D) S (u, D) du − ∫ h (u, 0) S (u, 0) du
t0

c

t0

c

If hc (u, D) > hc (u, 0), the ELR understates the impact of the exposure because it does not account for
deaths (cases) that might occur earlier than they would have in the absence of exposure, while the LAR
tends to overestimate the number of exposure-related events at higher doses. By limiting the range of
integration in the above expressions, excess risks for periods of interest other than the full lifetime after
exposure can be computed.
Likelihood: Generally, the state or fact of being likely or probable. The term may also be used toexpress a defined statistical concept. Specifically, given a set of data and a statistical model that
describes the distribution of the data in terms of some parameters, the statistical concept of “likelihood”
is a function of the model parameters that is proportional to the probability density function for the data
(given the parameter values). For independent observations, the likelihood of the data is the product of
the likelihood values for each observation. Likelihood functions play a central role in both “frequentist
inference” and “Bayesian inference” (albeit with different interpretations). Frequentist inference often
proceeds by finding parameters that maximize the likelihood given the data (maximum likelihood
estimation) and using (asymptotic) properties of the maximized (log-) likelihood as the basis for
inference.
Low dose rate: The Committee has defined “low dose rate” as 0.1 mGy per minute, averaged over one
hour or less, for radiations such as external X-rays and gamma rays [U1, U3].

316 UNSCEAR 2012 REPORT

Measurement error: The difference between the true value of a quantity of interest and a measurementof that value. Measurement error can be random (see “Assignment error” and “Classical error”) or
systematic (see “Shared error”).
Meta-analysis: In statistics, a meta-analysis combines the results of two or more studies that address a
set of related research hypotheses, for example by estimating a certain unknown parameter orparametric function common to two or more data sets, while controlling or adjusting for differences inother parameters unrelated to those of immediate interest. The purpose is to obtain an estimate that ismore informative than any obtainable from a single study, while ensuring that other data do not corrupt
or bias the result. The term “meta-analysis” is also used for statistical pooling of results available inpublished form, in contrast with a pooled analysis of original data from two or more studies.
Model: An analytical or physical representation or quantification of a real system and the ways inwhich phenomena occur within that system, used to predict or assess the behaviour of the real system
under specified (often hypothetical) conditions. This is in contrast to a relationship, which is simply theway two or more factors are connected or related (i.e. relationships include causal relationships, those
based on models, and those that simply fit the observed data).
Model uncertainty: The value of a quantity of interest derived from a data set of observations depends
in general on the model that has been assumed to analyse the data. The related uncertainty of that value(i.e. the range of values for a quantity of interest that is obtained from analysing the data with different
assumed models) is called model uncertainty.
Molecular epidemiology: This epidemiological approach uses the currently available biomarkers (notradiation-specific) combined with classical epidemiological methods. Central to this are the –omics(genomics, transcriptomics, proteomics, metabolomics and others) which allow the detection ofindividual characteristics on various molecular levels (genes, transcripts, proteins, metabolism andothers). The frequency of occurrence of these individual characteristics in exposed populations are thenstudied using classical epidemiological methods.
Monte Carlo uncertainty propagation: Computation of a probability distribution of an output of amodel on the basis of repeated calculations using random sampling of values of uncertain input
variables specified as probability distributions. The numerical sampling strategy used may be Simple
Random Sampling, or a form of stratified sampling such as Latin Hypercube Sampling.
Multi-model inference: Multi-model inference derives the probability density function of a quantity ofinterest by accounting for results of more than one model applied to the same set of data.
Norms: A required or acceptable standard.
(a) Internal. Norms from within the scientific community (such as truthfulness, consistency,
coherence, testability, reproducibility, validity, reliability, openness, impartiality and transparency).
(b) External. Norms from outside the scientific community that guide and justify scientificactivities (such as social responsibility, ethics, utility, prudence, precaution and practicality of
application).
Observed value: The often imprecisely determined and possibly biased value of a quantity of interest(e.g. a radiation dose). Observed values may include combinations of various types of classicalmeasurement and assignment error. Errors may be shared between groups of individuals.

GLOSSARY

317

Plausible: This relates to an argument or statement that seems reasonable or probable, without it
necessarily being so. For the purposes of this annex, the term is used to constrain the number ofpossibilities to those that currently appear to be supported by sound scientific reasoning, e.g. in the caseof health effects and inferred risks, those that can be reasonably supported by arguments based on
observed or known radiation action and response in biological systems. Other responses not supported
by mechanistic reasoning or other observations may be possible, but without such reasoning are notconsidered plausible.
Pooled analysis: A combined analysis of original data from two or more data sets bearing on acommon question of interest. The analysis may include parameters that distinguish between the
different data sets. (Contrast with “meta-analysis”.)
Prediction – well-founded and conditional: The conventional meaning relates to foretelling that a
specified outcome will occur in the future or will be a consequence of an action, event or set of
conditions. In this report, a distinction is made between well-founded prediction and conditional
prediction, both being included within the concept of science-based inference. A well-foundedprediction is one that is based on a hypothesis that is deemed proven by the application of scientificmethod; a conditional prediction is one that is based on a hypothesis that is currently not deemed
proven, but is based on scientific reasoning including the use of models and assumptions.
Probability density function (pdf): Function that describes the relative probability for a randomvariable to take on a given value. The probability of a random variable being in a specific range is equal
to the integral of the pdf over that range. For discrete distributions the probability function (which gives
the probability of the realization of specific values) is the analogue of the pdf.
Protracted exposure: Exposure received over a long time period (compare with “Acute exposure” and“Chronic exposure”).
Quantity of interest: The true but unknown value being estimated, measured, or observed (also known
formally as the “measurand”). It can be a single value, such as the dose or risk to a specific individual,
or a set of true values, such as the set of doses to each individual in a defined cohort.
Radiogenic health effects: See “Health effects (of radiation)”.
Random error: An error in which the difference between the true value and an estimated value occurs
at random. Random error implies the absence of systematic bias in the central or mean value. Random
error gives rise to classical measurement errors if each individual’s true dose is estimated using
information obtained independently from each individual in a cohort. Random error gives rise to
assignment errors when expected values of dose estimates are assigned to every individual having thesame exposure characteristics, such as age, gender, occupation, residence history, and diet, and when
the assigned dose to an individual is equal to the true mean dose for the exposure subgroup.
Rate: In general, the ratio of two quantities, where the denominator is usually a function of the periodeof time at risk. Rates of interest in epidemiology (and radiation risk estimation) are of the form,
PY
where e is the number of events over some time period of interest in a study population and PY(expressed as person-years) is the sum of time at risk during this time period for each person in the
study population. Rates for an event of interest can vary with such factors as age, sex, and dose.
Characterization of how rates depend on dose (or exposure) is central to radiation risk estimation. See also
“Hazard function”, “Risk”, “Relative risk”, “Excess rate”, and “Relative risk”, and “Excess relative risk”.
RBE: See “Relative biological effectiveness”.

318 UNSCEAR 2012 REPORTRegression calibration: Usually refers to a method used to adjust quantities measured with (classical)
measurement error to reduce the bias in dose–response estimates derived from the estimated doses.
More generally, regression calibration involves replacing the estimated dose by its expected value given
the estimated dose, and using what is known about the magnitude of the measurement error and the
distribution of true doses in the population of interest. As a further generalization, samples from theconditional distribution of dose given the estimated dose, and what is known about the measurement
error and the distribution of true doses in the population could be used. In principle, complex (Monte
Carlo) simulation systems are intended to provide such sets of dose realizations.
Relationship: The way two or more factors are connected or related (i.e. relationships include causal
relationships, those based on models, and those that simply fit the observed data).
Relative biological effectiveness (RBE): For a specified radiation, RBE is the ratio of the (a) absorbed
dose of a reference radiation required to produce a specific level of a response in a biological system tothe (b) absorbed dose of the specified radiation required to produce an equal response, with all physicaland biological variables, except radiation quality, being held as constant as possible. The reference
radiation with a defined RBE of unity normally is gamma rays (often those from 60Co) or X-rays (mostcommonly 180–250 kVp X-rays). RBE generally depends on dose, dose per fraction (if the dose isfractionated), dose rate, and biological end point. Note that RBE is an experimentally determined
quantity and is not appropriate for the inference of risk and risk assessment, where a modifying factor
that quantifies differences in risk for the same value of dose for a high-energy gamma ray comparedwith other types of radiation is more appropriate. (See also annex B, paragraphs C51-C58).
Relative risk/rate ratio: The ratio of disease rates in different groups (e.g. an exposed and unexposedgroup) or for different exposure conditions (e.g. people exposed at high dose rates and people exposedat low dose rates). It is often useful to view the relative risk as a function of variables, such as dose, sex,
or age. Note that while this ratio is commonly called a relative risk, this is a misnomer; it is actually aratio of rates, as are statistics derived from it (such as excess relative risk).
Risk: In the context of (radiation-related) health effects, risk refers to the probability that an event ofinterest (e.g. onset of cancer) will occur (i.e. it is prospective) during a given time period (e.g. the restof life following an exposure). Risks can be estimated using evidence from epidemiologicalinvestigations of disease rates in previously exposed populations (i.e. based on past observations). The
results from such retrospective analyses often are used, with appropriate modifying and adjustment
factors, to make inferences about the risk for other exposure situations involving different populations
for which direct epidemiological data on the dose–response relationship are not available.
Scientific method: A method of procedure that has characterized natural science since the 17th
century, consisting in systematic observation, measurement, and experiment, and the formulation,
testing, and modification of hypotheses.
Shared error: An error common to some or all members of a cohort or cohort subgroup. Shared error
is a form of systematic error, which influences the direction and magnitude of the difference between
the estimated value of the true value of a quantity of interest for individual members of a cohort orcohort subgroup. Uncertainty in the estimate of a true value for a model parameter used to quantify
dose to a group of individuals is a common source of shared errors in dosimetry. Being a form ofsystematic error, shared errors should be distinguished from independent random errors such as“assignment errors” and “classical errors”. This distinction is especially important when estimates ofthe dose to an individual dose are used in an analysis of the dose–response relationship.
Stochastic (health) effect: See “Health effects”.

GLOSSARY

319

Systematic error: A systematic error affects bias in a group of measurements or in estimates of aquantity of interest. This bias will be in a given direction, but may apply to varying degrees for different
cohort subgroups. As mentioned above, systematic error is related to “Shared error”.
Tissue reaction: See “Health effects”
True dose: The true but unknown value of dose for a specific individual. The state of knowledge about
this unknown true value can be characterized by measurements and estimates that produce a
distribution representing state of knowledge about possibly true values. In an epidemiological cohort,there will be a unique set of unknown true doses.
Type A uncertainty: Stochastic variability of true values of the quantity of interest (see aleatory
uncertainty). Type A uncertainty as used in this report differs from “Type A evaluation of uncertainty”
as defined in metrology. In metrology, “Type A evaluation of uncertainty” applies to situations inwhich statistical methods are used to address random variability of repeated measurements orobservations to evaluate the uncertainty in a quantity of interest for which there is a single true but
unknown value.
Type B uncertainty: Uncertainty about a true but unknown fixed value for a quantity of interest (seeepistemic uncertainty). In the absence of data obtained from an appropriate experimental design, theestimation of Type B uncertainty relies on subjective approaches and Bayesian inference to characterize
the state of knowledge about this true value. This state of knowledge or degree of belief is typically
represented as a subjective probability distribution of possibly true values for the quantity of interest.
Type B uncertainty in parameters of a model used to estimate dose to groups of individuals in a cohort
is a source of shared errors. This shared error can result in systematic bias in the dose estimate because
only one value for the parameter can be the true value and this true value could be substantially higher
or lower than the central estimate of the unknown true value. Type B uncertainty as used in this report
differs from “Type B evaluation of uncertainty” which, in metrology, applies to situations in which
methods other than statistical are used to characterize uncertainty in a quantity of interest. In this report,
both statistical and non-statistical methods can be used to characterize uncertainty about true fixedvalues for a quantity of interest.
Uncertainty: Expression of having doubt, or being unsure about study results, hypotheses, modelbased estimations or results of measurements, and specifically the true value of a quantity of interest.
This may be due to lack of complete knowledge about true values for an individual or to a lack ofcomplete knowledge of factors explaining the inter-individual variability of true values in a defined
subgroup or population. Unlike error, uncertainties can be quantified. Estimates of uncertainty represent
the amount or percentage by which an observed or calculated value might differ from its true value. Fora quantity of interest that has a true fixed value, uncertainty is defined here as a degree of belief
probability distribution comprising many realizations of possibly true values. For a quantity of interest
that is a group or population of true values, uncertainty can be characterized as many alternative
realizations of sets of true values.
Uncertainty propagation: A method used to evaluate the uncertainty in the result of a calculation
resulting from uncertainty in all inputs to the calculation. Uncertainty propagation can be carried out(a) using a closed-form algebraic solution if uncertainties are described as means, variances, or ranges
in inputs to simple equations, or (b) by numerical methods with the aid of a computer. The mostcommon method for evaluating the uncertainty in estimates made using complex models is Monte
Carlo uncertainty propagation.

320 UNSCEAR 2012 REPORT

Unshared errors: Errors that are independent among individual members of a cohort. “Random
aleatory uncertainty” is often considered a source of unshared error, when measurements are specific toan individual. “Classical errors” and “assignment errors” are considered sources of unshared errors.
Variability: Heterogeneity, diversity or a range which characterizes variation in estimated, measured,or true values of a quantity of interest. The term variability is often used to describe differences inmeasured or true values among individuals in a population or cohort. Examples include inter-individual
differences in body weight and/or dose or inter-cohort differences in exposure–response due todifferences in sensitivity to a hazardous agent. Further study cannot reduce variability, but may provide
additional information to explain reasons why some of this variability occurs. This additional
information can reduce the fraction of inter-individual variability initially treated as stochastic.

REFERENCES
I1

ICRP. The 2007 Recommendations of the International Commission on RadiologicalProtection. ICRP Publication 103. Annals of the ICRP 37(2-4): International Commission on
Radiological Protection, Elsevier Ltd., 2007.

I2

ICRP. ICRP statement on tissue reactions / Early and late effects of radiation in normal tissues
and organs – Threshold doses for tissue reactions in a radiation protection context. ICRP
Publication 118. Annals of the ICRP 41(1-2): International Commission on RadiologicalProtection, Elsevier Ltd., 2012.

P1

Popper, K.R. The Logic of Scientific Discovery. Basic Books, New York, 1959.

U1

UNSCEAR. Sources and Effects of Ionizing Radiation. UNSCEAR 1993 Report. United
Nations Scientific Committee on the Effects of Atomic Radiation, 1993 Report to the General
Assembly, with scientific annexes. United Nations sales publication E.94.IX.2. United
Nations, New York, 1993.

U2

UNSCEAR. Effects of Ionizing Radiation. Volume II: Scientific Annexes C, D and E.
UNSCEAR 2006 Report. United Nations Scientific Committee on the Effects of Atomic
Radiation. United Nations sales publication E.09.IX.5. United Nations, New York, 2009.

U3

UNSCEAR. Report of the United Nations Scientific Committee on the Effects of Atomic
Radiation 2010. Fifty-seventh session, includes Scientific Report: Summary of low-doseradiation effects on health. UNSCEAR 2010 Report. United Nations Scientific Committee on
the Effects of Atomic Radiation. United Nations sales publication M.II.IX.4. United Nations,
New York, 2011.