Confounding of indirect effects in the "real world": Exploring the range of bias due to a common cause of the mediator and outcome

Several investigators have demonstrated that assessment of indirect effects is biased in the presence of a common cause of the intermediate variable and the outcome. However, little work has been done to determine the degree of bias that will be caused by this type of confounding, and whether this bias will materially affect the identification of indirect effects. To address this crucial question, we have developed simulations based on a sufficient-component cause model for mediation. Confounding of the mediator can be introduced into such a model by specifying a common component cause of the intermediate variable and the outcome. By testing a range of prevalence proportions for each independent component cause, we vary both mediational effects and the strength of confounding. These simulations are designed to yield both (1) the true indirect effect of interest (pure and/or total indirect effect) and (2) the observed indirect effect. A comparison of these values indicates the range of bias due to uncontrolled confounding of the intermediate variable. Simulation techniques will be applied to a motivating example from the Health Effects of Arsenic Longitudinal Study. In this example, arsenic exposure is associated with mortality, and the investigators hypothesize that this association is at least partially mediated through skin lesions. Based on known prevalences and strengths of association, simulations will be developed to assess the degree to which inference regarding this hypothesis might be biased.