title: A framework for Bayesian nonparametric inference for causal effects of mediation.
abstract: We propose a Bayesian non-parametric (BNP) framework for estimating causal effects of mediation, the natural direct, and indirect, effects. The strategy is to do this in two parts. Part 1 is a flexible model (using BNP) for the observed data distribution. Part 2 is a set of uncheckable assumptions with sensitivity parameters that in conjunction with Part 1 allows identification and estimation of the causal parameters and allows for uncertainty about these assumptions via priors on the sensitivity parameters. For Part 1, we specify a Dirichlet process mixture of multivariate normals as a prior on the joint distribution of the outcome, mediator, and covariates. This approach allows us to obtain a (simple) closed form of each marginal distribution. For Part 2, we consider two sets of assumptions: (a) the standard sequential ignorability (Imai et al., 2010) and (b) weakened set of the conditional independence type assumptions introduced in Daniels et al. (2012) and propose sensitivity analyses for both. We use this approach to assess mediation in a physical activity promotion trial.
authors.affiliation: Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts 02115, U.S.A.
authors.forename: Chanmin
authors.initials: C
authors.lastname: Kim
authors.affiliation: Department of Statistics and Data Sciences and Department of Integrative Biology, University of Texas at Austin, Austin, Texas 78712, U.S.A.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Daniels
authors.affiliation: Department of Family Medicine and Public Health, University of California, San Diego, California 92093, U.S.A.
authors.forename: Bess H
authors.initials: BH
authors.lastname: Marcus
authors.affiliation: Department of Biostatistics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A.
authors.forename: Jason A
authors.initials: JA
authors.lastname: Roy
mesh_terms: D001499:Bayes Theorem; D006801:Humans; D015233:Models, Statistical
keywords: Causal inference; Dirichlet process mixture; Sensitivity Analysis