Comments on “Studies of the mortality of atomic bomb survivors, report 14, 1950–2003: an overview of cancer and noncancer diseases” (Radiat. Res., 177, 229–243, 2012)

This letter is regarding the recent article “Studies of the mortality of atomic bomb survivors, report 14, 1950–2003: an overview of cancer and noncancer diseases” (Radiat. Res., 177, 229–243, 2012) (1). In the article, the cancer mortality data of the atomic bomb survivors was fitted to an excess relative risk (ERR) model using linear and linear-quadratic dose-dependences for the ERR. Their conclusion after a formal dose threshold analysis was that there was no threshold for excess cancer risk.

We are generally concerned that the functional forms the authors chose for dose dependence were not flexible enough and might have led them to the conclusion of a zero dose threshold. For example, the linear-quadratic model was very restrictive, and the restrictions may have caused the linear quadratic curve to pass through the ERR=zero point at zero dose in Figure 4. While there is strong theoretical evidence why the ERR should be zero at zero dose in a controlled environment, there is less convincing evidence that this should be the case in an observational study. It is well known that there are many confounding factors that could influence the cancer mortality patterns observed in such studies. While the authors did control for potential confounders, a more flexible model that does not necessarily result in the line of best fit to cross the y-axis at zero cannot be ruled out.

We have re-analyzed the atomic bomb survivor data using a more flexible model that would allow the line of best fit to cross the y-axis at any location, and also would allow for negative predicted ERRs. For this analysis, we obtained the point estimates and 95% confidence intervals (CIs) for the ERRs from the authors. Using the 95% CIs, we were able to approximate the variance of the estimator at each point (variance = [upper 95% CI -ERR]²/1.96²). We regressed ERR on colon dose where colon dose was entered into the model via a restricted cubic spline with four knots at empirical quantiles (2). We allowed for an intercept term in the model. In fitting the model, we used regression weights equal to the inverse of the variance of the point estimates, as is appropriate when analyzing summarized data (3). In this analysis, the data strongly determine the shape of the fit.

Our results are presented in Figure 1. The flexible model does not show a monotone increase in ERR from zero dose, but becomes monotone increasing only after the dose reaches approximately 0.27 Gy. Also, the pointwise 95% CIs are below zero for most doses below 0.49 Gy. This does not prove that there is a threshold effect at 0.27 Gy or 0.49 Gy, but does demonstrate that there is too much variability in the data to suggest that the threshold for the harmful effect of radiation is zero. This could result from natural variability in the data, or from the effects of unmeasured and uncorrected confounding. Again, while the authors did adjust for some confounders, forcing the intercept of this line to pass through zero, as the authors did, assumes that all possible confounders of the effect of radiation dose on mortality were measured and corrected for. Our results suggest that this assumption of no-residual confounding might have been too strong.

Figure 1.

Excess relative risk (ERR) for all solid cancer in atomic bomb survivors in relation to radiation exposure. The black circles and error bars represent ERR and 95% CI for the dose categories. Data from Ozasa et al. (2012). Solid Line - fit to the ERR data using a multiple linear regression in which weighted colon dose was entered into the model using a restricted cubic spline transformation with four knots. Regression weights were equal to the inverse of the variance of the point estimates. Dashed lines are 95% CI of the fit.

In summary, our analysis that allowed for a more flexible model in fitting of the atomic bomb survivor data demonstrates that there is too much variability in the data to conclude that the dose threshold for excess cancers is zero dose.