Estimation of total mediation effect for a binary trait in a case-control study for high-dimensional omics mediators

Mediation analysis helps uncover how exposures impact outcomes through intermediate variables. Traditional mean-based total mediation effect measures can suffer from the cancellation of opposite component-wise effects and existing methods often lack the power to capture weak effects in high-dimensional mediators. Additionally, most existing work has focused on continuous outcomes, with limited attention to binary outcomes, particularly in case-control studies. To fill in this gap, we propose an R ² total mediation effect measure under the liability framework, providing a causal interpretation and applicable to various high-dimensional mediation models. We develop a cross-fitted, modified Haseman-Elston regression-based estimation procedure tailored for case-control studies, which can also be applied to cohort studies with reduced efficiency. Our estimator remains consistent with non-mediators and weak effect sizes in extensive simulations. Theoretical justification on consistency is provided under mild conditions. In the Women’s Health Initiative of 2150 individuals, we found that 89% (CI: 73% 91%) of the variation in the underlying liability for coronary heart disease associated with BMI can be explained by metabolomics.