Epidemiological studies of cancer rates associated with external and internal exposure to ionizing radiation have been subject to extensive reviews by various scientific bodies. It has long been assumed that radiation-induced cancer risks at low doses or low-dose rates are lower (per unit dose) than those at higher doses and dose rates. Based on a mixture of experimental and epidemiologic evidence the International Commission on Radiological Protection recommended the use of a dose and dose-rate effectiveness factor for purposes of radiological protection to reduce solid cancer risks obtained from moderate-to-high acute dose studies (e.g. those derived from the Japanese atomic bomb survivors) when applied to low dose or low-dose rate exposures. In the last few years there have been a number of attempts at assessing the effect of extrapolation of dose rate via direct comparison of observed risks in low-dose rate occupational studies and appropriately age/sex-adjusted analyses of the Japanese atomic bomb survivors. The usual approach is to consider the ratio of the excess relative risks in the two studies, a measure of the inverse of the dose rate effectiveness factor. This can be estimated using standard meta-analysis with inverse weighting of ratios of relative risks using variances derived via the delta method. In this paper certain potential statistical problems in the ratio of estimated excess relative risks for low-dose rate studies to the excess relative risk in the Japanese atomic bomb survivors are discussed, specifically the absence of a well-defined mean and the theoretically unbounded variance of this ratio. A slightly different method of meta-analysis for estimating uncertainties of these ratios is proposed, motivated by Fieller’s theorem, which leads to slightly different central estimates and confidence intervals for the dose rate effectiveness factor. However, given the uncertainties in the data, the differences in mean values and uncertainties from the dose rate effectiveness factor estimated using delta-method-based meta-analysis are not substantial, generally less than 70%.

与外部和内部电离辐射暴露相关的癌症发病率的流行病学研究已受到各个科学机构的广泛审查。长期以来，人们一直认为低剂量或低剂量率下的辐射诱发癌症风险（每单位剂量）低于高剂量和剂量率下的辐射诱发癌症风险。基于实验和流行病学证据，国际放射防护委员会建议使用剂量和剂量率有效性因子进行放射防护，以降低中高急性剂量研究（例如那些源自日本原子弹幸存者）应用于低剂量或低剂量率暴露时。在过去的几年中，人们尝试通过直接比较低剂量率职业研究中观察到的风险以及对日本原子弹幸存者进行适当的年龄/性别调整分析来评估剂量率外推的效果。通常的方法是考虑两项研究中超额相对风险的比率，这是剂量率有效性因子倒数的度量。这可以使用标准荟萃分析来估计，并使用通过德尔塔方法得出的方差对相对风险比率进行反向加权。本文讨论了低剂量率研究的估计超额相对风险与日本原子弹幸存者的超额相对风险之比的某些潜在统计问题，特别是缺乏明确定义的均值和理论上无界方差这个比例。受菲勒定理的启发，提出了一种稍微不同的荟萃分析方法来估计这些比率的不确定性，这导致剂量率有效性因子的中心估计值和置信区间略有不同。然而，考虑到数据的不确定性，使用基于delta方法的荟萃分析估计的剂量率有效性因子的平均值和不确定性差异并不大，一般小于70%。