RERF Report No. 6-17

A research paper published in the Journal of Radiological Protection§“A semiparametric approach to evaluate the potential for harm from low-dose radiation
exposure”
Kyoji Furukawa, Munechika Misumi
J Radiol Prot; 38(1):286-98, 2018/3(doi: 10.1088/1361-6498/aaa57c)

Study Findings
While high levels of radiation exposure are widely recognized to cause adverse healtheffects, the lowest potentially harmful radiation dose has yet to be identified. Using asimulation approach, *1 this study showed that a conventional approach based on a simple
parametric dose-response model*2 (e.g., a linear no-threshold model*3) can be unexpectedly
inefficient, biased, and/or inaccurate in uncertainty evaluations at a low-dose range.
Furthermore, we demonstrated that a semiparametric model*4 assuming no specific form withrespect to dose-response can be flexibly fitted to various plausible dose-response curves while
appropriately handling risk-estimation uncertainty.
*1 Simulation approach: by repeating computer-based experiment simulations, this method
is used to verify risk values estimated by a given statistical model.
2* Parametric model: like the linear no-threshold model (βx), describes how risk increases
with dose (x) using a set of parameters (β).
3* Linear no-threshold model: assumes that risk increases in proportion to increasing doseswith no threshold.
*4 Semiparametric model: falls between a parametric model and a nonparametric model,
which assumes no specific form with respect to dose response.
Explanation
While high levels of radiation exposure are widely recognized to cause adverse healtheffects, defining the lowest potentially harmful dose remains a controversial issue. Given thatepidemiological studies of a practical size are unlikely to provide sufficient statistical power*
to detect small risks associated with low doses of radiation, it is necessary to accurately
evaluate how uncertain these risk estimation results are. Using simulations that assume
various dose-response relationships with a threshold dose (the lowest exposure at which risk
is generated), we showed that a conventional approach based on simple parametric models(e.g., linear models with or without a threshold) can be unexpectedly inefficient, biased,and/or inaccurate in uncertainty evaluations in a low-dose range. In contrast, with noassumption of a specific function form, a semiparametric model can be flexibly fitted tovarious plausible dose-response curves while appropriately handling risk uncertainty. In
particular, this approach can evaluate with relative accuracy the dose range in which athreshold might exist in dose-response relationships, while retaining sufficient statisticalpower to indicate a small increase in risk beyond the threshold. As a result, this approach issuitable for use in analyzing the risk of low-dose radiation exposure.
* Statistical power: probability that the existence of an effect or influence to be estimatedcan be correctly declared by a statistical test when such an effect or influence does exist;
the probability increases when the amount of data or the effect to be estimated is large.
1. Study Purpose
The purpose of this study was to use simulations to compare the estimation performance1

RERF Report No. 6-17of conventional approaches based on a parametric model and that of a semiparametricdose-response model, when a threshold is assumed to actually exist in dose-risk relationships.
2. Study Methods
This study considered a semiparametric model that conducts smoothing of adose-response function connecting piecewise-linear functions defined over closely spaced
dose categories, by handling the coefficients of piecewise functions as random slopes andallowing for autocorrelations between adjacent line sections. Both parametric andsemiparametric approaches were used to estimate data simulated under dose-response
relationships with various thresholds. Further, by repeating estimations using data simulatedon the basis of various dose responses with threshold, we evaluated the performance of theproposed approach compared with that of the conventional parametric approach in terms ofbias, efficiency, and precision of uncertainty estimation. Also, both approaches were applied
to analysis of solid-cancer incidence in the Life Span Study (LSS) cohort of atomic bomb
survivors (1958–2009), and the estimated dose-response curves with interval estimates werecompared.
3. Study Results
In the conventional approach utilizing a parametric model, if non-linearity or thresholds
existed in dose-response relationships in a low-dose range, bias and uncertainty wereunderestimated. In contrast, the semiparametric approach, with or without non-linearity orthresholds, produced estimation results with generally little bias, thus showing an ability toaccurately evaluate uncertainty. Further, in the LSS data analysis, in comparison with results
estimated by the conventional parametric model, the results by the proposed approach showedthat the interval estimation in a low-dose range was wider, despite similar maximum
likelihood estimation values, suggesting that no obvious risk increase was caused by exposurein a low-dose range.
Study SignificanceThe semiparametric model used in this study mostly obviates the analyst’s need for theassumption and option settings usually required to estimate radiation risk. In both high-doseand low-dose ranges, this model can reliably infer uncertainty in risk estimation while flexibly
adapting to data from dose-response curves of various shapes. We therefore consider thisapproach effective in accurately estimating tolerable levels of radiation exposure as well as
the characteristics of risk involved in low-dose exposure.

§Journal of Radiological Protection is a U.K. based peer-reviewed academic journal published by the Society
for Radiological Protection that carries a wide range of original papers and commentaries on radiation
epidemiology and biology related to radiation protection. (Impact factor in 2017/2018: 1.274)

2