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A mediator acts as a third variable in the causal pathway between a risk factor and an outcome. In this paper, we consider the estimation of the mediation effect when the mediator is a binary variable. We give a precise definition of the mediation effect and examine asymptotic properties of five different estimators of the mediation effect. Our theoretical developments, which are supported by a Monte Carlo study, show that the estimators that account for the binary nature of the mediator are consistent for the mediation effect defined in this paper while other estimators are inconsistent. We use these estimators to study the mediation effect of chronic cerebral infarction in the causal relationship between the apolipoprotein E epsilon4 allele and cognitive function among 233 deceased participants from the Religious Orders Study, a longitudinal, clinical-pathologic study of aging and Alzheimer's disease.
Yan et al. (Wed,) studied this question.