Bias in Low Dose Risk Estimation due to the Constant RBE Assumption in RERF Studies

Radiation exposure from the atomic bombs in Hiroshima and Nagasaki consisted of both gamma and neutron radiation. Because the main goal of analyzing Radiation Effects Research Foundation (RERF) data is to estimate the increased risk from gamma radiation alone, the analysis approach has been to weight the typically more potent neutron dose with a constant relative biological effectiveness (RBE) factor and add it to the gamma dose to form a weighted total dose, which is considered equivalent to a pure gamma dose. However, in many experimental systems, it has been shown that the RBE of neutron radiation relative to gamma radiation is not constant. The possibly incorrect assumption of constant RBE can lead to bias in estimating the excess risk due to gamma radiation exposure. We investigated analytically the potential bias resulting from the constant RBE assumption over a range of organ doses, assuming constant RBE and true limiting maximum RBE values and gamma and neutron dose response curvatures, with particular attention to risk estimation in the low dose range. The results of the analytic investigation are confirmed in a simulation study. We show that in the low dose range, the relationship between excess relative risk (ERR) and weighted total dose depends on the assumed constant RBE, the true limiting maximum RBE, the curvatures of the gamma and neutron dose responses, and the moments of the distribution of gamma radiation dose conditional on the weighted total dose. Assuming a constant RBE in analysis that equals the true limiting maximum RBE does not guarantee negligible bias unless there is no curvature in the dose response. The existence of positive curvature in this case induces negative bias. However, at very low doses, which may be of interest, e.g., 0.1 Gy, the bias will be small. At higher doses, assuming a constant RBE can still lead to significant bias, even if its value matches the true limiting maximum RBE. When interpreting the estimated excess risk from analyses of RERF data, it is important to recognize the bias that may come from assuming a constant RBE-weighted neutron dose.