Efficient estimation of indirect effects in case‐control studies using a unified likelihood framework

Mediation models are a set of statistical techniques that investigate the mechanisms that produce an observed relationship between an exposure variable and an outcome variable in order to deduce the extent to which the relationship is influenced by intermediate mediator variables. For a case‐control study, the most common mediation analysis strategy employs a counterfactual framework that permits estimation of indirect and direct effects on the odds ratio scale for dichotomous outcomes, assuming either binary or continuous mediators. While this framework has become an important tool for mediation analysis, we demonstrate that we can embed this approach in a unified likelihood framework for mediation analysis in case‐control studies that leverages more features of the data (in particular, the relationship between exposure and mediator) to improve efficiency of indirect effect estimates. One important feature of our likelihood approach is that it naturally incorporates cases within the exposure‐mediator model to improve efficiency. Our approach does not require knowledge of disease prevalence and can model confounders and exposure‐mediator interactions, and is straightforward to implement in standard statistical software. We illustrate our approach using both simulated data and real data from a case‐control genetic study of lung cancer.