Complementary Log Regression for Sufficient-Cause Modeling of Epidemiologic Data

The logistic regression model is the workhorse of epidemiological data analysis. The model helps to clarify the relationship between multiple exposures and a binary outcome. Logistic regression analysis is readily implemented using existing statistical software, and this has contributed to it becoming a routine procedure for epidemiologists. In this paper, the authors focus on a causal model which has recently received much attention from the epidemiologic community, namely, the sufficient-component cause model (causal-pie model). The authors show that the sufficient-component cause model is associated with a particular ‘link’ function: the complementary log link. In a complementary log regression, the exponentiated coefficient of a main-effect term corresponds to an adjusted ‘peril ratio’, and the coefficient of a cross-product term can be used directly to test for causal mechanistic interaction (sufficient-cause interaction). The authors provide detailed instructions on how to perform a complementary log regression using existing statistical software and use three datasets to illustrate the methodology. Complementary log regression is the model of choice for sufficient-cause analysis of binary outcomes. Its implementation is as easy as conventional logistic regression.