Parametric causal mediation analysis with asymmetric binary regression model

Abstract The present study focuses on parametric-regression-based causal mediation analysis for binary outcomes. Existing methodologies of parametric causal mediation analysis often specify logistic and probit outcome models. However, logistic and probit models implicitly assume a symmetric shape of binary response curves and fail to capture the true relationship between explanatory variables and the outcome when the binary response curves are asymmetric. Alternatively, the present study explores parametric-regression-based causal mediation analysis using the complementary log-log model that models the outcome success probability asymmetrically. Following existing literature on causal mediation analysis, we define the controlled direct effect, natural direct effect, and natural indirect effect of the exposure on a scale suitable for the complementary log-log model. We discuss the confounding assumptions to identify these effects. We derive simple closed-form analytic expressions for these effects that are easily estimated by regression analyses. The validity of our proposed estimators is demonstrated through numerical simulations, and the methodology is illustrated with real-world data from psychological research.