Methodological improvements to meta-analysis of low dose rate studies and derivation of dose and dose-rate effectiveness factors

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%.