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.

翻译：关于基于主要利益二进制变量的分层案件控制程序,我们从抽样设计中得出对二进制变量后勤模型参数的扭曲的表述,这在进行调解分析(在因果框架内)时特别相关,在结果和调解人都是二进制的环境下,进行分层案件控制数据分析。我们的识别结果为估算和最大相似性估计开辟了道路。然后,我们进行模拟研究,显示结果和调解人模型参数的估测者在基于加权的现有方法方面的效率提高。作为示例,我们重新分析德国的案件控制数据集,以便调查降低免疫能力对排虫性发作的影响是否通过吸收气态酸抑制剂来调解。