Analysis of Departures from Linearity in the Dose Response for Japanese Atomic Bomb Survivor Solid Cancer Mortality and Cancer Incidence Data and Assessment of Low-Dose Extrapolation Factors.

Although leukemia in the Japanese atomic bomb survivor data has long exhibited upward curvature, until recently this appeared not to be the case for solid cancer. It has been suggested that the recently observed upward curvature in the dose response for the Japanese atomic bomb survivor solid cancer mortality data may be accounted for by flattening of the dose response in the moderate dose range (0.3-0.7 Gy). To investigate this, the latest version available of the solid cancer mortality and incidence datasets (with follow-up over the years 1950-2003 and 1958-2009 respectively) for the Life Span Study cohort of atomic bomb survivors were used to assess possible departures from linearity in the moderate dose range. Linear-spline models were fitted, also up to 6th order polynomial models in dose (higher order polynomials tended not to converge). The organ dose used for all solid cancers was weighted dose to the colon. There are modest indications of departures from linearity for the mortality data, whether using polynomial or linear-spline models. Use of the Akaike information criterion (AIC) suggests that the optimal model for the mortality data is given by a 5th order polynomial in dose. There is borderline significant (P = 0.071) indication of improvement provided by a linear-spline model in the mortality data. The low-dose extrapolation factor (LDEF), which measures the degree of overestimation of low-dose linear slope by the linear slope fitted over some specified dose range, is generally between 1.1-2.0 depending on the dose range, with upper confidence limits that sometimes exceed 10; although LDEF < 1 for the lowest dose range (<0.5 Gy), there are substantial uncertainties, with an upper confidence limit that exceeds 1.6. There are generally only modest indications of departures from linearity for the solid cancer incidence data, whether using polynomial or linear-spline models. In contrast to the mortality data, there are much weaker indications of improvement in fit provided by higher order polynomials, and only weak indications (P > 0.2) of improvement provided by linear-spline models. Nevertheless, use of AIC suggests that the optimal model for the incidence data is given by a 3rd order polynomial. LDEF evaluated over various dose ranges is generally between 1.2-1.4 with upper confidence limits that generally exceed 1.6; although LDEF < 1 for the lowest dose range (<0.5 Gy), there are substantial uncertainties, with an upper confidence limit that substantially exceeds 2.0. In summary, the evidence we have presented for higher order powers than the second in the dose response is not overwhelmingly strong, and is to some extent dependent on dose range. A feature of the dose response, which is reflected in the higher-order polynomials fitted to the data, is a leveling off or even a downturn in the response at doses >2 Gy. The linear-quadratic model is very widely used for modeling of dose response, and has been widely used in radiotherapy oncology applications as part of treatment planning. There is a theoretical basis for this model, based on the two-target model, although the data used to validate this has been mainly in vitro; there may be more complicated interactions than are implied by a two-target model, but the contributions made by these, which would contribute to higher order (than quadratic) powers of dose, may not be very pronounced over moderate ranges of dose.