Abstract:
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Mediation analysis assesses the effect of study exposures on an outcome both through and around specific mediators. While mediation analysis with multiple mediators has been addressed in recent literature, the case involved multiple exposures has received little attention. To fill this gap, we consider regularizations that allow simultaneous effect selection and estimation, while stabilizing model fit and accounting for model selection uncertainty. We analytically show that a two-stage approach regularizing regression coefficients does not guarantee a unimodal posterior distribution and that a product-of-coefficient approach regularizing direct and indirect effects tends to penalize excessively. We propose a regularized difference-of-coefficient approach bypassing these limitations. Using the connection between regularizations and Bayesian hierarchical models with Laplace prior, we develop an efficient Markov chain Monte Carlo algorithm for posterior estimation and inference. Through simulations, we show that the proposed approach has better empirical performances compared to some alternatives. The methodology is illustrated using two epidemiological studies in human reproduction.
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