Abstract

We appreciate the comment by Little et al. (2013) related to the study of Schollnberger et al. (2012) and thank our colleagues for the time they took to deal with our analysis. Little et al. (2013) state ‘‘... there are biological data suggesting [that] many inflammatory endpoints potentially relevant to circulatory disease may be differentially regulated below and above about 0.5 Gy, emphasizing the importance of assessing risks associated with exposures \0.5 Gy.’’ We agree with the statement and take it as a support of our approach to analyze the available data with a variety of models that take several possible dose dependences into account. Little et al. (2013) express a concern ‘‘... that the method of Schollnberger et al. 2012 (multi-model inference, MMI) may not adequately assess the uncertainties in model parameters’’ without elucidating reasons of their concern. However, seemingly to backup their concern, they cite Wang et al. (2012), a paper describing the development of a novel approach to ‘‘adjustment uncertainty’’ (i.e., the uncertainty about which variables should be included in the model to properly adjust for confounding), called Bayesian adjustment for confounding. We will argue below that the pre-conditions on which Wang et al. (2012) built their interesting, though not uncontested (Gutman and Rubin 2012), methodology do not apply to our analysis. When the effect of exposure on outcome is estimated, a proper adjustment for confounding variables is a general concern in epidemiology. A series of papers by Wang et al. (2012), Crainiceanu et al. (2008) and Dominici et al. (2004) addressed this problem for the correlation of air pollution and mortality. A big challenge in air pollution epidemiology is to control for possible confounding by changes in weather parameters such as temperature or humidity, which determine both the concentration of particulate matter in air and have a direct impact on mortality rates, especially among older persons and those with preexisting health conditions. Hence, such covariables are clearly correlated with exposure and outcome and can be considered as true confounders. In our study of the association between circulatory diseases and ionizing radiation, we have adjusted the risk for the main covariables of city c, sex s, age at exposure e and attained age a, for which the correlation with the radiation dose is generally small: see bottom row of the correlation matrix (Table 1), which was calculated from the raw data of LSS Report 13 with follow-up since January 1, 1968 (Preston et al. 2003), the data set that has been analyzed by Schollnberger et al. (2012). Additional adjustment for other covariables such as smoking, alcohol intake, education, type of household occupation, obesity and diabetes mellitus ‘‘had almost no impact on the associations with radiation’’ (see Table 3 and Discussion in Shimizu et al. (2010)). We have not calculated the correlation with exposure for the latter covariables but we expect again small correlations similar to those for c, s, e and a. H. Schollnberger (&) J. C. Kaiser P. Jacob Helmholtz Zentrum Munchen, Department of Radiation Sciences, Institute of Radiation Protection, 85764 Neuherberg, Germany e-mail: schoellnberger@helmholtz-muenchen.de

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