  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.
