Radiation dose response estimation with emphasis on low dose range using restricted cubic splines: application to all solid cancer mortality data, 1950-2003, in atomic bomb survivors.

Using the all solid cancer mortality data set of the Life Span Study (LSS) cohort from 1950 to 2003 (LSS Report 14) data among atomic bomb survivors, excess relative risk (ERR) statistical analyses were performed using the second degree polynomial and the threshold and restricted cubic spline (RCS) dose response models. For the RCS models with 3 to 7 knots of equally spaced percentiles with margins in the dose range greater than 50 mGy, the dose response was assumed to be linear at less than 70 to 90 mGy. Due to the skewed dose distribution of atomic bomb survivors, the current knot system for the RCS analysis results in a detailed depiction of the dose response as less than approximately 0.5 Gy. The 6 knot RCS models for the all-solid cancer mortality dose response of the whole dose or less than 2 Gy were selected with the AIC model selection criterion and fit significantly better (p < 0.05) than the linear (L) model. The usual RCS includes the L-global model but not the quadratic (Q) nor linear-quadratic (LQ) global models. The authors extended the RCS to include L or LQ global models by putting L or LQ constraints on the cubic spline in the lower and upper tails, and the best RCS model selected with AIC criterion was the usual RCS with L-constraints in both the lower and upper tails. The selected RCS had a linear dose-response model in the lower dose range (i.e., < 0.2-0.3 Gy) and was compatible with the linear no-threshold (LNT) model in this dose range. The proposed method is also useful in describing the dose response of a specific cancer or non-cancer disease incidence/mortality.