RERF Report No. 4-15

Paper published in Risk Analysis§“A Bayesian semiparametric model for radiation dose-response estimation”
Kyoji Furukawa, Munechika Misumi, John B. Cologne, Harry M. Cullings
Risk Analysis :1-13, 2015 [ONLINE AHEAD OF PRINT](doi: 10.1111/risa.12513)
Study Findings
This study proposed a new statistical approach using a semiparametric model* to estimate thedose-response relationship under a framework of Bayesian statistics* —one of the primary objectivesof radiation risk analysis—with increased accuracy. Without assuming a specific parametric model,*such as the linear non-threshold model,* this approach can estimate various dose-response curves withuncertainty more accurately and therefore is expected to be particularly useful in evaluating the risk
associated with low-dose exposure.
*Semiparametric model: falls between a parametric model and a nonparametric model, whichassumes no specific form with respect to dose response*Bayesian statistics: generalizes the conventional statistics by introducing a “prior probability”
based on common senses or experiences and enables us to conduct data analysis more flexibly.
The term “Bayesian semiparametric model” in the title indicates a semiparametric model under
this framework of Bayesian statistics.
*Parametric model: describes how risk increases with dose (x) with a set of parameters (β), such as
the linear non-threshold dose model (βx)*Linear non-threshold model: assumes risk to be monotonically increasing in proportion to theincreasing doseExplanation
Characterizing the dose-response relationship and estimating acceptable exposure levels are theprimary goals of risk assessment. In analyses of health risks associated with exposure to radiation,
while there is clear agreement that moderate to high radiation doses cause harmful effects in humans,
information is limited for understanding the possible biological effects at low doses, e.g., less than 100mGy, which is the dose range relevant to most radiation exposures today. While a simple parametricmodel, such as the linear non-threshold model, is interpretable and supported by some biologicalconsiderations, risk analysis based on a simple parametric structure can be misleading in evaluating
the risk and its uncertainty associated with low-dose exposure. In particular, a linear model with afixed value at the lowest dose (e.g., zero response at zero dose) can only accommodate linear
confidence bounds that narrow to a point at the low-dose end. This study proposed a new approach
using a semiparametric model that is flexible in regard to the shape of both the mean response and theconfidence bounds and evaluated its performance in comparison with the conventional approach ofparametric models.
1. Study purpose
The main purpose of this study was to show that a semiparametric dose-response model thatassumes no specific parametric function form can be an alternative approach that is appropriate for
evaluation of risk associated with radiation exposure, especially at low doses.
2. Study methods
This study considered a semiparametric dose-response model that has a connected
piecewise-linear, dose-response function with a correlation structure among the random slope
coefficients defined over closely spaced dose categories, which was applied to radiation-dose-response
estimation. Using simulations under several plausible dose-response relationships, we evaluated the1RERF Report No. 4-15

performance of the proposed approach compared to those of the conventional parametric approach interms of bias, efficiency, and precision of uncertainty estimation. Also, the proposed approach wasapplied to analysis of solid cancer incidence in the Life Span Study (LSS) cohort of atomic-bomb
survivors (1958–1998), and the estimated dose-response curves with interval estimates were comparedto those obtained by other approaches.

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3. Study results
Our simulation study demonstrated that the conventional approach using parametric models could
be problematic in bias and underestimation of uncertainty when a non-linearity was assumed in thedose response at a low dose range. In contrast, the proposed approach produced results that wereoverall less biased and more accurate in uncertainty estimation. In analysis of the LSS data, comparedto the conventional linear non-threshold model, the proposed approach estimated smaller risks withwider interval estimates at low doses, which indicated no clear evidence of an increased risk up to 100
mGy of exposure (Figure).

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Figure: Excess relative risk (ERR) for all solid cancer in the Life Span Study cohort (1958–1998) in relation to radiation exposure, estimated by the linear non-threshold model (black) andthe semiparametric model (red) over the entire dose range (left) and at 0–0.4 Gy (right). Dashedcurves are 95% confidence (or credible) intervals. All estimates are gender-averaged ERRs atage 70 after exposure at age 30.

Study SignificanceWith relatively few assumptions and modeling options to be made by the analyst, thesemiparametric model proposed in this study can be flexibly fitted to data generated by various shapesof dose-response curves with uncertainty appropriately handled at any dose range and therefore isexpected to be particularly useful in characterizing risk at a low dose range and accurately estimating
acceptable exposure levels.
The Radiation Effects Research Foundation has studied A-bomb survivors and their offspring in Hiroshima
and Nagasaki for more than 60 years. RERF’s research achievements are considered the principal scientific basis
for radiation risk assessment by the United Nations Scientific Committee on the Effects of Atomic Radiation(UNSCEAR) and for recommendations regarding radiation protection standards by the International2

RERF Report No. 4-15

Commission on Radiological Protection (ICRP). RERF expresses its profound gratitude to the A-bomb survivors
and survivors’ offspring for their cooperation in our studies.
§Risk Analysis is a U.S.-based peer-reviewed academic journal published by the Society for Risk Analysis thatcarries original papers and commentaries on a wide range of subjects related to risk analysis. (Impact factor in2014: 2.502)

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