United Nations Scientific Committee on the Effects of Atomic Radiation

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 1

ATTACHMENT A-1

SOURCES AND ESTIMATION OF UNCERTAINTIES IN
MEDICAL EXPOSURE
UNSCEAR 2020/2021 Report, Annex A, Evaluation of medical
exposure to ionizing radiation

Contents
This electronic attachment provides supplementary information on overall uncertainty
determination in relation with total collective dose estimation from medical exposure.
Acknowledgements
The Committee would like to acknowledge the work conducted by E. Nekolla(Germany) with contributions from P. Thomas (Australia) and P. Shrimpton (United
Kingdom) in preparing this attachment.

Notes
©

United Nations, December 2022. All rights reserved, worldwide.

This publication has not been formally edited.

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 3

CONTENTS
I. TYPES OF ERROR ............................................................................................... 5
A. Systematic errors (bias) .................................................................................... 5
B. Random (statistical) errors................................................................................ 6
II. SOURCES OF ERROR IN FREQUENCY ESTIMATES .................................... 6
A. Incorrect counting due to problems in relating information (codes)
into actual numbers of examinations ................................................................ 7
B. Mistakes in the data recorded, e.g. no assessment of duplicate
examinations or typing errors ........................................................................... 8
C. Lack of frequency data from some important providers of radiology
services ............................................................................................................. 9
D. Unrepresentative sample................................................................................... 9
E. Invalid assumptions made when scaling up data to derive frequencies
for the whole country...................................................................................... 10
III. ESTIMATING UNCERTAINTIES IN FREQUENCY ESTIMATES ................ 10
A. Uncertainty in frequency measurements by counting .................................... 10
B. Uncertainty in frequency estimate for “sample survey” ................................. 11
C. Uncertainty in frequency estimate for “insurance data survey” ..................... 11
IV. ESTIMATING UNCERTAINTIES IN DOSE ESTIMATES ............................. 14
A. Uncertainties in basic dose measurements ..................................................... 14
B. Uncertainties due to variations in patient dose between imaging sites
and limited sample size of sites ...................................................................... 15
C. Uncertainties due to the conversion coefficients used to assess
effective doses ................................................................................................ 16
D. Overall uncertainties in mean effective dose estimates .................................. 16
V. OVERALL UNCERTAINTIES–PROPAGATION OF UNCERTAINTY ......... 17
REFERENCES ........................................................................................................... 23

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 5I.

TYPES OF ERROR

1.
In 2008, the report "Radiation Protection 154: European Guidance on
Estimating Population Doses from Medical X-Ray Procedures" (RP 154) of theEuropean Commission Dose Data Med project 1 (EC DDM 1) was published in theEuropean Commission's Radiation Protection series. This report discussed in detail theestimation of uncertainties associated with medical exposure assessments andidentified several important sources of uncertainty. In the following, frequent
reference is made to RP 154 [E1].
2.
An estimate of the population dose, i.e., the total collective dose from allradiological examinations in a country, is based on frequency data and typical dose
data for all examinations or categories of examinations considered. The overall
uncertainty in the population dose estimate must, therefore, be a combination of theuncertainties in the estimates of the frequency and the uncertainties in the estimates ofthe effective dose for each type or category of examination.
3.
There are many potential sources of systematic error (or bias) and random (orstatistical) error leading to uncertainties in frequency and dose estimates. In the first
instance, all major sources of error are to be identified and evaluated in order to derivea measure of the overall uncertainty.
A.

Systematic errors (bias)

4.
Systematic errors lead to estimates being systematically too high or too low.
All observations or measurements of X-ray examination frequency and patient doseare prone to bias. Systematic errors can be due to insufficient knowledge or evencomplete lack of knowledge. Therefore, assumptions will have to be made that will
not be completely valid. However, it is usually possible to make a rough assessment(educated guess) of the minimum (alow) and maximum (aupp) likely values of aquantity a such that the probability that the value lies between these limits is, for allpractical purposes, 100%. Provided that there is no contradictory information, thequantity can be treated as if it is equally probable for its value to lie anywhere within
the interval [alow, aupp], corresponding to a uniform (i.e., rectangular) probability
distribution. The best estimate of the value of the quantity is then:𝑎𝑎 =𝑎𝑎𝑢𝑢𝑢𝑢𝑢𝑢 − 𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙(A-1.1)𝑎𝑎(A-1.2)

2

with the standard uncertainty, u, being:(e.g. [T2]).

𝑢𝑢 =

√3

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 6

B.

Random (statistical) errors

5.
Random errors are present in all sampling procedures due to statisticalfluctuations. They are equally likely to be positive or negative about the true value,
usually following a normal distribution. They can arise from precision limitations inpatient dose measurement devices or from surveys where data are collected from asample of sites. Random errors can be reduced by increasing the number ofobservations.
� is the arithmetic mean of m values 𝑁𝑁𝑖𝑖 ,If 𝑁𝑁∑𝑚𝑚 𝑁𝑁𝑁𝑁¯ = 𝑖𝑖=1 𝑖𝑖 ,𝑚𝑚

the standard deviation, s, is given by∑𝑚𝑚 (𝑁𝑁𝑖𝑖 − 𝑁𝑁¯ )2

𝑠𝑠 = � 𝑖𝑖=1𝑚𝑚−1(A-1.3)(A-1.4)the standard uncertainty of the mean (also: “standard error of the mean SEM”), u, isthen given by the standard deviation, s, divided by the square root of the number, m,of values Ni (e.g., [T2])𝑠𝑠𝑢𝑢 =(A-1.5).
√𝑚𝑚

II.

SOURCES OF ERROR IN FREQUENCY ESTIMATES

6.
There are basically two types of sources for deriving examination frequency
data. Numbers are obtained either directly from a representative sample (“sample
survey”) of health care providers (e.g., hospitals) or from central statistics held bygovernmental departments or provided by health insurance companies (“insurance
data survey”). In the case of a sample survey, an algorithm for scaling up to the wholecountry is needed. In the case of governmental central statistics or an insurance data
survey, numbers are usually given for a large proportion or even the total of the
population and might therefore be representative of radiology practice in the country
without any need of scaling. Some countries apply a “mixed” approach, combining
health insurance data with supplementary information from sample surveys [N1].
Insurance data from a representative sample of patients can also be used. In a study on
population exposure from medical diagnostic procedures in France in 2012, theexamination frequency was estimated from a permanent representative sample of the
population protected by French health insurance, the Échantillon Généraliste deBénéficiaires (EGB). The EGB is based on a survey of about 1% of the beneficiaries
from the three main French health insurance schemes, whether these beneficiaries
have received healthcare reimbursements or not (representing a coverage of around
85% of beneficiaries of all French social security schemes) [D1]. In the EC DDM 1
project [E1], some countries had sample sizes close to 100% (usually based oncomprehensive national health insurance statistics) whereas others had to rely on
limited surveys restricted to <20% of the total national practice.

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 7

7.
There are several sources of error which can lead to significant uncertainties infrequency estimates [E1]:A.

Incorrect counting due to problems in relating information(codes) into actual numbers of examinations

8.
Especially if health insurance data are used to estimate examination
frequencies, there might be problems in assigning a specific code to a specificexamination. Primarily, health insurance code systems are designed forreimbursement, and might therefore not be fully appropriate for a survey onradiological procedures. There might, for example, be insufficiently differentiatedcodes, that is, single codes which refer to X-ray examinations of different sites (e.g.,
only one code for knee joint and shoulder joint).
9.
It is important to have an adequate definition of the term “examination”, whichis to be used consistently. The EC DDM 1 project [E1] definition of an examination
was as follows: “An X-ray examination or procedure is defined as one or more(a series of) X-ray exposures of one anatomical region/organ/organ system using asingle imaging modality, needed to answer a specific diagnostic problem or clinicalquestion during one visit to the radiology department or medical practice”, i.e. one
radiological examination may consist, for example, of:− Several X-ray images (e.g., radiographs of thoracic spine in anteroposterior
and lateral projections);− One X-ray image combined with some fluoroscopy (e.g., plain radiography ofchest organs with fluoroscopy);− A prone plus a supine computer tomography (e.g., colonography);− A nuclear medicine procedure plus a computer tomography scan (e.g., hybrid
imaging);− A dual energy computer tomography scan involving either two X-ray sources
or fast kV switching technique.
These examples are to be counted as one examination. It should be established
whether the code system accounts for examinations or for single steps of an
examination in order to avoid any bias.
10.
Codes often cover only a limited number of examination types and therefore
some radiological procedures are not taken into account within this framework,
although these are assumed to represent only a small fraction of the total number. The
most explicit example is that of procedures performed under fluoroscopy guidance inoperating theatres. Estimating the frequency of these procedures is very complicated.
Even the detailed categorization of examinations used in the EC DDM 1 project [E1],with 225 types of examinations in total, omitted these procedures.

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 8

11.
In the case of X-ray examinations of double-sided organs, e.g., mammograms,
coding systems do not always distinguish properly between examinations involving
one side (usually used for examinations of symptomatic persons) or both sides(usually used for screening), respectively. In this case, it might be difficult to estimate
accurate numbers.
12.
For a “multistep” examination, the corresponding dose must be thoroughly
assessed. This is especially important in the case of higher dose procedures likecomputer tomography where it can make a big difference depending on whether thenumber of examinations or the number of individual scans is counted, and whether thedose per examination or the dose per scan, respectively, is used.
13.
In a sample survey where data are received from larger healthcare providers
like hospitals, data on frequency should be available from the Radiology Information
System (RIS) and/or Hospital Information System (HIS). In RISs and HISs,
predefined code systems are used, but many different coding systems exist (even in
the same country). Uncertainties in counting can, therefore, be introduced throughinsufficient information on the coding system available. Thus, modifications in code
systems need to be taken into account and periodic reviews of the coding system
would therefore be necessary.
B.

Mistakes in the data recorded, e.g., no assessment of
duplicate examinations or typing errors

14.
Repeated examinations, e.g., due to overexposure, underexposure, and position
fault, will in some instances not be documented. Especially in the case of healthinsurance data, repeated examinations are usually not recorded and a bias can,therefore, be introduced. Similarly, in a sample survey where data are collected from a
picture archive and communications system (PACS), it might also be the case that the
PACS is set automatically to remove images from the reject folder after a short time,e.g., a few days.
15.
The repeat rate is dependent on the type of examination, type of technique(conventional/digital) and practitioner experience [N2, W1]. On the basis of a surveyof international papers on reject/retake rates published both for screen/film and digitaltechnology, Waaler et al. concluded that the use of digital imaging seems to have
reduced the percentage of image rejects/retakes from 10–15% to 3–5% mainly due toa striking reduction of images with over-/underexposure [W1]. An educated guessshould be considered to account for this kind of error.
16.
Mistakes due to typing errors are generally of a random nature and are difficult
to estimate. It can, however, be expected that they might cancel out.

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 9C.

Lack of frequency data from some important providers ofradiology services

17.
In publication RP 154 [E1], a list of healthcare providers is given that might beinvolved in providing radiology services (table A-1.1). Their inclusion in national
surveys can be used as a first step in assessing the completeness of the frequency datain each country. However, missing data from some of the health care providers given
in table A-1.1 should not be critical since their contribution to total frequency andpopulation exposure is minor (school dental services, health checks at borders,prisons, armed forces hospitals/units and medical research exposures).
Table A-1.1. Healthcare providers involved with X-ray imaging [E1]
Healthcare providers
University hospitals

Dental practices

State hospitals

Dental institutes

Private hospitals

School dental services

Private radiology institutes

Health checks at borders

General practices

Prisons

Specialist practices (e.g. cardiology,
gastroenterology, orthopaedics, pneumology,
urology, vascular surgery)

Tuberculosis screening units

Occupational medicine

Breast cancer screening units

Chiropractic clinics

Armed forces hospitals/units

18.
Key providers not covered by central statistics might be, e.g., private radiology
practices, or practices offering opportunistic screening examinations. The contributionof examinations from the latter to the total frequency is likely to vary from country tocountry, where industrialized countries are more prone to radiology services offering“off-label” imaging procedures. The potential bias due to missing these examinations
should be assessed.
19.
A major contributor to frequency data is dental radiology, accounting for about
one third or even more of all X-ray examinations in industrialized countries [E1, E2].
However, missing this component will have only a minor impact on the totalcollective dose.
D.

Unrepresentative sample

20.
In a sample survey, the samples should be as representative of national
radiology practice as possible, especially if frequency data are derived from a
relatively small sample. All health care providers that might offer medical radiology
services should be considered (see table A-1.1) and the main contributors to national
radiology practice should be accounted for. Here, the aim should be to include in thesample all types of hospital and radiological practice (or the most important ones) in
similar proportions to those occurring nationally, i.e., avoid some categories ofANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 10

radiology being more likely to be included in the sample than others (and a biased, i.e.
non-random sample). Self-selection might occur if institutes volunteer to be includedin the sample and are not representative in view, for example, of their better than
average quality management system.
E.

Invalid assumptions made when scaling up data to derivefrequencies for the whole country

21.
Numbers of examinations observed in a sample or incomplete data from ahealth insurance survey must be scaled up to the whole country. However,uncertainties will be introduced wherever the assumption is made that the distributionof examinations seen in the sample is the same as that for the overall population. The
method of scaling up is dependent on the availability of specifically detailed data.
A stratification process can be performed dividing the overall radiology practice in acountry into subgroups, e.g., groups of radiology service providers, or groups ofpatients. Sampling in each stratum will usually reduce sampling error and improve therepresentativeness of the sample as a whole. The better the representativeness of thesample, the larger will be the reliability of the frequency estimate.

III. UNCERTAINTIES IN FREQUENCY ESTIMATES
A.

Uncertainty in frequency measurements by counting

22.
Although count is a common quantity, the issue of uncertainty in counting hasreceived little consideration. Thus, it is usually assumed that such measurements, theconcept of uncertainty is not applicable, or even, that a result derived by counting
actually has no uncertainty at all [B1]. The latter might be intuitively true if small
numbers are assessed by counting, e.g., the number of persons in a small room.
However, if the number of persons in a crowded marketplace is to be counted, theresult will probably be affected by an uncertainty arising from double counts, n+, or
missing counts, n-. The “true” value, M, of the counting result, N, is then:
𝑀𝑀 = 𝑁𝑁 − 𝑛𝑛+ + 𝑛𝑛−(A-1.6)

If the probability of a double count is p+, i.e., n+ = p+ ·M, and the probability of a
missing count is p-, i.e., n- = p-· M, then M would be
𝑀𝑀 =

𝑁𝑁

1+𝑝𝑝+ − 𝑝𝑝−(A-1.7)

N can be assumed to be the sum of independent counts, ni, i.e.
𝑁𝑁 = ∑𝑀𝑀
𝑖𝑖=1 𝑛𝑛𝑖𝑖(A-1.8)where each count, ni, can have the value 0 (with probability p-), 1 (with probability 1 (p+ + p-)), or 2 (with probability p+). The error probability is (p+ + p-) since p+ and pare disjoint events, and the probability of correct counting is 1 - (p+ + p-) [B1].

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 11

The variance, v, of ni is then𝑣𝑣(𝑛𝑛𝑖𝑖 ) = 𝑝𝑝+ + 𝑝𝑝− − (𝑝𝑝+ − 𝑝𝑝− )2(A-1.9)and the variance, v, of N is𝑣𝑣(𝑁𝑁) = 𝑀𝑀 · (𝑝𝑝+ + 𝑝𝑝− − (𝑝𝑝+ − 𝑝𝑝− )2 )(A-1.10)The corresponding uncertainty, u, associated with M would, thus, be [B1]𝑢𝑢 =�𝑀𝑀 · (𝑝𝑝+ + 𝑝𝑝− − (𝑝𝑝+ − 𝑝𝑝− )2 )1+ 𝑝𝑝+ − 𝑝𝑝−(A-1.11).

If it can be assumed that the probabilities of double counts and missed counts are thesame, p+ = p-, the measurement by counting, N, is equal to the true value, M, and theuncertainty is small for large N (e.g., u = 0.3% for N = 10,000 and p+ = p- = 5%).
23.
If there is no reason to believe that p+ and p- are high and/or differ widely, theuncertainty in frequency measurement by counting is, therefore, minor; in particular,
for larger N, as is usually the case for frequencies of radiological examinations, it canbe assumed to be negligible.
B.

Uncertainty in frequency estimate for “sample survey”

24.
As an example, consider the methodology of the United Kingdom survey by
the National Radiation Protection Board [T1]. This survey was based on data fromtwo National Health Service (NHS) regions in 1997/98. A sample of 38 NHS hospitaltrusts in these regions provided data from their RIS with detailed information on
annual numbers of different types of X-ray examination. Feedback was received from
58% of all trusts covering 68% of all X-ray examinations in the two regions, andabout 16% of all X-ray examinations in England. The survey data were extrapolated to
the whole of the NHS by means of annual total numbers of all types of X-ray
examination conducted in each trust that were collected by the Department of Health.
The same approach was chosen to estimate X-ray examination frequencies in NHS
hospitals in Wales and Northern Ireland. Since identical levels of radiology provisionwere found in England, Wales and Northern Ireland, the same level was assumed toapply to Scotland where no total numbers were available.
25.
For each type of X-ray examination, the standard deviation in the percentage
frequency at each trust was calculated. The standard deviation, s, was then converted
to the standard error of the mean, u, to account for the variations between the minstitutions in the sample for each type of X-ray exam:
𝑢𝑢 =

𝑠𝑠

√𝑚𝑚

(A-1.12)the SEM, u, decreases with increasing number of institutions, m.
C.

Uncertainty in frequency estimate for “insurance data survey”

26.
If the survey is based on health insurance data (or otherwise data from central
statistics), data are usually available at regular (e.g., annual) intervals. In this case,

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 12

time series of frequency data can be derived. The assessment of time series offrequencies enables one to detect and analyse discontinuities or outliers by comparing
figures from different years. If discontinuities can be explained, e.g., through a change
in the code system, the data can be revised, and the overall uncertainty in the
population dose estimate can therefore be decreased. In the case of an inexplicablediscontinuity, typing errors or similar might be present, and the outlier can beconsidered for exclusion.
27.
Even if health insurance data can be assumed to be complete, random errors
should nevertheless be taken into account. Having time series of frequencies, thestandard deviation, s, can be calculated. If m is the number of points of time where
frequency data were evaluated, and Ny are the frequency estimates, s is defined as thesquare root of the variance or the square root of the mean square deviations of thevalues Ny, from their arithmetic mean, 𝑁𝑁¯ :�∑𝑚𝑚
𝑦𝑦=1�𝑁𝑁𝑦𝑦 −𝑁𝑁�

𝑠𝑠 = �

𝑚𝑚−1

2

�=𝑤𝑤𝑤𝑤𝑤𝑤ℎ 𝑁𝑁∑𝑚𝑚
𝑦𝑦=1 𝑁𝑁𝑦𝑦𝑚𝑚(A-1.13).

28.
The standard deviation may serve as a measure of uncertainty. Therefore,
assuming that variations in the X-ray examination frequencies over a certain period oftime are interpreted as random uncertainties, the uncertainties in Ny can beapproximated by the standard deviation of the corresponding m frequencies, Ny. This
would be a conservative approach. If the time series shows clear evidence of a trend,
this can be accounted for via a regression analysis by using the “residual standard
deviation”, sr, which can be written as�𝑦𝑦 �∑𝑚𝑚 �𝑁𝑁𝑦𝑦 −𝑁𝑁

𝑦𝑦=1
𝑠𝑠𝑟𝑟 = �𝑚𝑚−𝑝𝑝

2(A-1.14)

�𝑦𝑦 is the value on the regression curve and p is the number of parameters in thewhere 𝑁𝑁
regression function (e.g. p = 2 in case of a linear regression). The uncertainty at a 95%
confidence level is about twice the (residual) standard deviation (figure A-1.I).

The residual standard deviation is 145,000. The uncertainty in the 2015 frequency value at the 95% confidence level is about twice the residual standard deviationor 10% of the 2015 frequency value

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 13

Figure A-1.I. Example of time series of examination frequencies with decreasing trend

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 14

IV. UNCERTAINTIES IN DOSE ESTIMATES
29.
In order to estimate the population dose from medical exposure, estimates ofrepresentative mean effective doses for each type of X-ray or nuclear medicine
examination (or of those that make a significant contribution to the collective dose)are needed. Typically, patient dose surveys are performed at a limited number ofimaging sites. In the case of X-rays, such surveys are based on measurements or
calculations of practical dose quantities (e.g., entrance surface dose (ESD); dose-area
product (DAP)). However, doses delivered in a specific institution for a standard
clinical indication can be fraught with a high variability in data collected within andbetween patient samples. As an example of the application of statistical considerationsin the selection of an appropriate sample size in local surveys, see, for example,
Taylor et al. who determined the variability of computed tomography dose index(CTDI) and dose-length product (DLP) data, and proposed a minimum sample size toachieve an expected precision [T3]. For nuclear medicine procedures, doses perprocedure are derived by multiplying the mean administered activity with a dosecoefficient which relates the activity to the effective dose to the patient, as publishedby the International Commission on Radiological Protection (ICRP) [I1, I2, I3, I4].
Administered activities can vary considerably between imaging sites.
30.
To derive a typical national value for a particular type of examination, meandoses from a sample of representative imaging sites are usually collected. For eachsite, mean dose values (or mean administered activities for nuclear medicine
procedures) for every type of examination (category) are calculated, and mean valuesof the “site means” are assessed. Uncertainties in effective dose estimates can arise
from a range of different sources [E1].
A.

Uncertainties in basic dose measurements

31.
Generally, uncertainties in dose measurement are small compared with thevariation in dose seen in a sample of patients undergoing the same X-ray examinationin the same hospital and compared with the variation in mean doses for the same Xray examination between all hospitals in a national survey.
32.
In accordance with Report 74 [I5] of the International Commission on
Radiation Units and Measurements (ICRU), an uncertainty of no more than 7% at the
95% confidence level is, in general, achievable for patient dose measurements indiagnostic radiology if the calibration procedures and measurement methods are taken
into account as described in the ICRU report [I5]. Since this cannot be assumed for all
patient dose surveys, the uncertainties might be higher. The uncertainties in individual
basic dose measurements are, nevertheless, small compared with the uncertainties dueto the variation in dose seen in a sample of patients undergoing the same X-ray
examination in the same institution, and small compared with the variation in meandoses for the same X-ray examination between all institutions in a national survey.
Consequently, they will not have a significant impact on the overall accuracy of themean effective dose estimate associated with each type of X-ray examination.

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 15

33.
There are numerous sources of uncertainty in estimates of collective effective
dose in nuclear medicine in relation to both the number of procedures and theeffective dose from those procedures. A significant number of common nuclear
medicine examinations can be performed using different protocols which may involve
several different radiopharmaceuticals (e.g., myocardial perfusion scans can be
performed using a 1-day protocol, 2-day protocol, 201Tl-Cl, 99mTc-sestamibi or 99mTctetrofosmin). The effective dose from each of these protocols may vary significantly
and national statistics may not clearly distinguish between the different protocols.
34.
Internal dose estimations are based on mathematical phantoms derived fromcomputer tomography data of the human anatomy and biokinetic parameters related tothe behaviour of the particular radiopharmaceutical, namely the fractional uptake andeffective half-time in organs of the body. Stabin [S1] has shown that the combined
uncertainties in any given radiopharmaceutical dose estimate are typically, at aminimum, a factor of two and may be considerably greater, in general because of
normal human variability, and particularly in disease states.
B.

Uncertainties due to variations in patient dose between
imaging sites and limited sample size of sites

35.
As a source for estimating random uncertainties, the dose distributions
observed in the UK National Patient Dose Database—one of the most extensive
databases of this type in Europe—can be utilised. Uncertainties were derived from theobserved variation of the mean dose values at each imaging site.
36.
The standard deviation, s, was converted to the standard error of the mean, u,
to account for the variations between the m institutions in the sample for each type of
X-ray exam,
𝑢𝑢 =

𝑠𝑠

(A-1.15)√𝑚𝑚with s being the standard deviation of the site mean doses for each type of X-ray
examination. Since the SEM, u, is decreasing with increasing number of institutions,m, values of uncertainty in the estimated mean dose value at the 95% confidence level(2 * SEM) can be approximated as a function of sample size, as shown in table A-1.2(based on table 17 in RP 154 [E1]).
Table A-1.2. Uncertainties in mean effective dose estimates as a function of sample
size, based on UK National Patient Dose Database (from [E1])Sample size (number of imaging sites)

Uncertainties at 95% confidence level
(%)

>100

±10

20–100

±25

5–19

±50

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 16

37.
These estimates refer merely to random uncertainties, i.e. any systematic errors
due to bias in a sample of imaging sites are not accounted for. If no dose
measurements have been performed for a particular examination, an estimate of meaneffective dose from another country can be assumed. Optimally, a country is selected
where the radiology practice is expected to be similar to that in the home country andthe estimate is based on measurements at least 20 imaging sites. If this is not the case,the uncertainties will be larger. In RP 154 [E1], a factor of 2 is suggested for theuncertainty at a 95% confidence level (+100%, −50%).
C.

Uncertainties due to the conversion coefficients used toassess effective doses

38.
Uncertainties due to conversion coefficients depend on how closely the
exposure conditions and the phantom for which the conversion coefficients were
calculated match the average exposure conditions and the average patient for a
specific X-ray examination. These systematic uncertainties are difficult to quantify but
should be small for common examinations (with a 95% confidence limit of probably
no more than about ±10%). For less common examinations, the uncertainty estimates
could rise to about ±25%.
39.
Another consideration is the common practice of applying a single value oftypical effective dose in relation to both adult and paediatric patients. Whereas there
are significant differences in the typical levels of practical dose metrics between
patients of different (age-related) standard size, this is offset by corresponding
differences in the effective dose coefficient such that the variations in effective dose
between adults and children undergoing similar types of examination are reduced[E1]. For most types of examination, adults also account for the majority of patientnumbers. However, use of a single value of E does represent a potential source of
uncertainty in estimates of population dose.
D.

Overall uncertainties in mean effective dose estimates40.
On the basis of the considerations in subsections IV.A to IV.C, the following
estimates, shown in table A-1.3, for uncertainties in dose estimates were proposed by
EC DDM 1 project as a rough guide [E1].

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 17

Table A-1.3. Overall uncertainties in mean effective dose estimates as a function ofsample size and matching of exposure conditions for conversion coefficients [E1]Sample size (number of imaging sites) andmatching of conversion coefficients

Uncertainties at 95% confidence level (%)
Sample size

Conversion
coefficient

Overall>100
Good conversion coefficients match

±10

±10

±14

20–100Good conversion coefficients match

±25

±10

±27

5–19
Good conversion coefficients match

±50

±10

±51

>100
Poor conversion coefficients match

±10

±25

±27

20–100
Poor CC match

±25

±25

±35

5–19
Poor conversion coefficients match

±50

±25

±56

Foreign data onlya
a

+100
−50

Unless the radiology practice in the foreign country is similar to that in the country making the estimation.

V. OVERALL UNCERTAINTIES – PROPAGATION OF
UNCERTAINTY
41.
The result of a survey on medical population exposures cannot be assessed
directly but is composed of several numbers and measures from different sources thatare combined following a predefined algorithm.
42.
Since most of these quantities are associated with random or systematic errors,
the final result of a survey will also deviate from the true value, i.e. each error will betransferred by the algorithm that is to be performed. This is called propagation of
uncertainty and there exist established procedures to estimate the total deviation of the
final result from the true value (e.g. [T2]).
43.
Assuming the sources of error to be independent (not correlated), the overall
standard uncertainty u, of the quantity N which is a function of other quantities N1,
N2….Nx, is given by
𝑢𝑢 = 𝑢𝑢(𝑁𝑁1 , … , 𝑁𝑁𝑥𝑥 , 𝑢𝑢1 , … , 𝑢𝑢𝑥𝑥 ) = �∑𝑥𝑥𝑖𝑖=1 �where uj is the absolute uncertainty of Nj andrespect to Ni.
44.

𝜕𝜕𝜕𝜕

𝜕𝜕𝑁𝑁𝑖𝑖

𝜕𝜕𝜕𝜕𝜕𝜕𝑁𝑁𝑖𝑖𝑢𝑢𝑖𝑖 �

2(A-1.16)is the partial derivative of N with

If the quantity of interest, N, is made up of a sum,
𝑁𝑁 = ∑𝑥𝑥𝑖𝑖=1 𝑁𝑁𝑖𝑖

(A-1.17)

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 18

the above formula is reduced to𝑢𝑢 = �∑𝑥𝑥𝑖𝑖=1 𝑢𝑢𝑖𝑖 2(A-1.18)

𝑁𝑁 = ∏𝑥𝑥𝑖𝑖=1 𝑁𝑁𝑖𝑖

(A-1.19)

i.e. u is the root mean square sum of the absolute uncertainties ui.
If N is made up of a product,

the above given formula is reduced to𝑢𝑢2𝑢𝑢 = 𝑁𝑁 �∑𝑥𝑥𝑖𝑖=1 � 𝑖𝑖 �
𝑁𝑁𝑖𝑖

(A-1.20)

i.e. the relative uncertainty, u/N, is the root mean square sum of the relative
uncertainties of Ni. See figure A-1.II for an example of a product with two factors.
45.
Commonly, there are errors affecting the result in one direction as well as
errors affecting the results in the other direction. Therefore, there is a certain chancethat these errors cancel out. This is especially true for random errors. Therefore, evensome large individual uncertainties might have only a small impact on the overall
uncertainty. However, systematic errors can, at worst, also add up.
46.
To exclude in this case a serious under- or over-estimation of the overall
uncertainty, uncertainties with a clear sign ± should be considered separately. For
example, in the case of repeat examinations, the error will have a plus-sign. To avoid
an underestimation of the overall frequency and also an overestimation of the overall
uncertainty, the repeat rate, r, should already be included in the frequency estimate, M,
M=N+rN(A-1.21)with N being the frequency value observed and r being the repeat rate not accounted
for in N. The associated uncertainties, ur, and uN, can then be allowed for separately toestimate the uncertainty uM of M:
𝑢𝑢

47.

2

𝑢𝑢 𝑁𝑁 2𝑢𝑢𝑀𝑀 = 𝑀𝑀 �� 𝑁𝑁� + � 𝑟𝑟 �𝑁𝑁

𝑀𝑀(A-1.22)

To illustrate the propagation of uncertainties, two examples are given:(a) Example 1: Table A-1.4 illustrates the propagation of uncertainty in relation to
the sum of five examination counts, na to ne, each associated with a specificlevel of uncertainty, ua to ue. The total absolute uncertainty is given by:
𝑢𝑢 = �∑𝐸𝐸𝑖𝑖=𝐴𝐴 𝑢𝑢𝑖𝑖 2(A-1.23)

The uncertainties for examinations C–E are relatively high, but their individual
contributions to the overall uncertainty are minor since these examinations
collectively account for only 15% of the total number of examinations.

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 19

Table A-1.4. Example of estimating uncertainties from the number of examinations(frequencies)
Examinationsb

95% confidence level
Absolute uncertainty on
frequency

Relative uncertainty on
frequency (%) due tovariance

A

7 000 000

420 000

6B

4 500 000

360 000

8C

1 400 000

210 000

15

D

350 000

35 00010E260 000

Totala

Absolute
number of
examinations

13 510 000

65 000a

25

596 280b4.4

Sum of absolute numbers of frequencies.
Root mean square sum of absolute uncertainties on frequency.

(b) Example 2: Table A-1.5 presents the combination of frequencies, NA to NE,
and estimates of effective dose per examination type, EA to EE, to assess thetotal collective dose, S.
𝑆𝑆 = ∑𝐸𝐸𝑖𝑖=𝐴𝐴 𝑁𝑁𝑖𝑖 𝐸𝐸𝑖𝑖

(A-1.24)For each examination A-E, the relative uncertainty vi in the collective dose Ni ∙Ei is estimated by the root mean square sum of the relative uncertainty in thefrequency estimate, ui/Ni, and the relative uncertainty in the estimate of meaneffective dose per examination, uEi/ Ei (i=A to E).
𝑢𝑢

2

𝑢𝑢𝐸𝐸𝑖𝑖 2

𝑣𝑣𝑖𝑖 = �� 𝑖𝑖 � + �
𝑁𝑁𝑖𝑖

𝐸𝐸𝑖𝑖

�

(A-1.25)

Since the relative uncertainty vi, in example 2, is considerably larger than therelative uncertainty ui/Ni for the frequency, the effective dose uncertainty per
examination is the determining factor for the value of the collective dose
uncertainty (figure A-1.II).

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 20

Figure A-1.II. Propagation of Uncertainty - Uncertainty of a ProductUncertainty of N·M (z-axis) where N and M are associated with relative uncertainties<100% (x- and y-axes)
The maximum of the N·M uncertainty is √2 (141%)

Table A-1.5. Examples of estimating uncertainties for total collective effective dose
Relative uncertainty
on frequencya(%)

Effective dose per
examination(mSv)

Collective
effective dose(man Sv)

Absolute
uncertainty oncollective effective
dose (man Sv)

Relative
uncertainty oncollective doseb(%)

7 000 000

6

0.3

15

2 100

339

16

B

4 500 000

8

0.1

35

450

161

36

C

1 400 000

15

0.4

50

560

292

52

D

350 000

10

2.2

20

770

172

22

E

260 000

25

0.6

80

156

130

84

d

13

13 510 000

4.4

95% confidence level.
Root mean square sum of relative uncertainty on frequency and relative uncertainty on dose estimate.
c
Sum of collective doses.
dRoot mean square sum of absolute uncertainties on collective dose.
b

Relative
uncertainty on
effective dose per
examination (%)a

A

Total
a

Absolute number of
examinations

4 036

c

522

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 21

Examinations

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 22

48.
The impact of examination A’s uncertainty in association with the collective
dose for examination A is decisive since A contributes most to total collective
effective dose. The impact of examination E, on the other hand, is, in spite of the large
uncertainty, minor since E contributes least to total collective effective dose. Zontar etal. [Z1] provides an example of the assessment of the overall uncertainty for a national
estimate of collective effective dose.
49.
It can be assumed that the combined standard uncertainty takes the form of anormal distribution and there is a 68% confidence that the estimated value lies within
the stated limits. If uncertainties are expressed in terms of the 95% confidence limits,
this corresponds approximately to twice the standard uncertainties.

ANNEX A, ATTACHMENT A-1: SOURCES AND MANAGEMENT OF UNCERTAINTIES IN MEDICAL EXPOSURE ASSESSMENT 23

REFERENCES
B1
D1
E1

E2

I1

I2

I3

I4

I5
N1

N2
S1
T1

T2
T3
W1
Z1

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