Mediation analysis with case-control sampling: Identification and estimation in the presence of a binary mediator

TL;DR

This paper develops methods to accurately estimate mediation effects in stratified case-control studies with binary mediators and outcomes, addressing sampling distortions and improving estimation efficiency.

Contribution

It derives the expression of sampling distortion on logistic model parameters and introduces new estimation techniques for mediation analysis in case-control data.

Findings

New identification formulas for logistic models under stratified sampling

Simulation shows improved estimator efficiency over existing weighting methods

Reanalysis of German dataset illustrates practical application of the methods

Abstract

With reference to a stratified case-control procedure based on a binary variable of primary interest, we derive the expression of the distortion induced by the sampling design on the parameters of the logistic model of a secondary variable. This is particularly relevant when performing mediation analysis (possibly in a causal framework) with stratified case-control data in settings where both the outcome and the mediator are binary. Our identification result opens the way to M-estimation and Maximum Likelihood estimation. We then conduct a simulation study showing the gain in efficiency of the estimators of both the outcome and mediator model parameters w.r. to existing methods, based on weighting. As an illustrative example, we reanalyze a German case-control dataset in order to investigate whether the effect of reduced immunocompetency on listeriosis onset is mediated by the intake of gastric acid suppressors.