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Abstract:
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In biomedical and epidemiological studies, it is often of interest to estimate both the direct and indirect effects of exposures on some outcomes. For example, in reproductive epidemiology, researchers are interested in the effect of exposures to environmental pollutants on infertility, both directly and through some mediators such as semen parameters. When the number of exposures and mediators are both large, it is desirable to conduct variable selections simultaneously with estimations. With this motivation, in this paper, we propose a Bayesian regularized joint modeling approach. By delineating the causal pathways, the proposed approach can provide a complete picture of the exposure effects either from the exposures or through the mediators. Besides the L1 penalty on each individual effect, we consider shrinkage on the pathway effects, which makes the mediator effects dependent on the effects of exposures on the mediators. This enables us to filter out the weak pathways and achieve great model parsimony. In addition to simulation studies in a variety of scenarios, we apply this data-driven approach to data from the Longitudinal Investigation of Fertility and the Environment.
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