VARIABLE SELECTION AND ESTIMATION IN BAYESIAN CAUSAL MEDIATION ANALYSIS

Causal mediation analysis has emerged as a valuable tool in various fields, allowing for decomposing total effects into direct and indirect effects. However, identifying the mediation effects relies on assumptions of no unmeasured confounding in the exposure-mediator, exposure-outcome, and mediator-outcome relationships. Moreover, there is often an interest in examining the effects of a mixture of exposures on the outcome, which poses challenges in determining the appropriate set of confounding variables. Therefore, we proposed a Bayesian mediation analysis that simultaneously selects common confounding variables associated with the two exposures, mediator, and outcome, by employing spike and slab group lasso using MCMC algorithms. The inclusion and exclusion of confounding variables were determined by posterior inclusion probability. We estimated the total effect of treatments on the outcome, natural direct effect of treatments directly on the outcome or through unknown/unmeasured mediators, and natural indirect effects of treatments on the outcome that operate through prespecified mediators using posterior samples. Furthermore, we estimated the mediated effects attributable to each exposure alone and their interaction. To handle potential multicollinearity resulting from two-way interactions among two binary exposures and a binary mediator, we explored two priors: stochastic search variable selection and the elastic net. We conducted simulation studies under various scenarios and evaluated the estimation properties and posterior inclusion probabilities. Finally, we applied the proposed methods to data from the Medical Information Mart for Intensive Care III database containing de-identified clinic data of patients admitted to intensive care units (ICUs). We revisited the relationship between transthoracic echocardiography, dobutamine use, and survival time within 28 days since admission to ICUs mediated through norepinephrine use, to further investigate the potential pathways linking these associations.