Bayesian Causal Mediation Analysis for Group Randomized Designs with Homogeneous and Heterogeneous Effects: Simulation and Case Study

Abstract

A fully Bayesian approach to causal mediation analysis for group-randomized designs is presented. A unique contribution of this article is the combination of Bayesian inferential methods with G-computation to address the problem of heterogeneous treatment or mediator effects. A detailed simulation study shows that this approach has excellent frequentist properties, particularly in the case of small sample sizes with accurate informative priors. The simulation study also demonstrates that the proposed approach can take into account heterogeneous treatment or mediator effects without bias. A case study using data from a school-based randomized intervention designed to increase parent social capital leading to improved behavioral and academic outcomes in children is offered to illustrate the Bayesian approach to causal mediation in group-randomized designs.

A Tutorial in Bayesian Potential Outcomes Mediation Analysis

“…This tutorial focused on the single mediator model, however, potential outcomes estimators for two mediator models have begun to appear in the literature (Albert & Nelson, 2011; Avin, Shpitser, & Pearl, 2005; Daniel, De Stavola, Cousens, & Vansteelandt., 2015; Imai & Yamamoto, 2013; Lange, Rasmussen, & Thygesen, 2013; Nguyen, Webb-Vargas, Koning, & Stuart, 2016; Taguri, Featherstone, & Cheng, 2015; VanderWeele & Vansteelandt, 2013; Wang, Nelson, & Albert, 2013; Yu, Fan, & Wu, 2014; Zheng & Zhou, 2015) and analogous methods as those described in this paper could be applied to do Bayesian potential outcomes mediation analysis with more than one mediator. There is a growing literature examining potential outcomes estimation in the Bayesian framework for more complex models (Daniels, Roy, Kim, Hogan, & Perri, 2012; Elliott, Raghunathan, & Li, 2010; Forastiere, Mealli, & VanderWeele, 2015; Park & Kaplan, 2015). The goal of this paper was to provide a step-by-step introduction with code in several software packages that illustrates how to do causal Bayesian mediation analysis for the single mediator model.…”

“…The causal effects based on the potential outcomes framework are traditionally computed using a frequentist framework and several Bayesian approaches for causal inference in more complex models have been developed (Daniels, Roy, Kim, Hogan, & Perri, 2012; Elliott, Raghunathan, & Li, 2010; Forastiere, Mealli, & VanderWeele, 2015; Park & Kaplan, 2015), however, a Bayesian approach for the single mediator causal model has yet to be described. Next, we introduce Bayesian methods and steps to obtain posterior distributions of the causal effects.…”

“…Current applications of Bayesian methods for causal inference exist for principal stratification (Elliott, Raghunathan, & Li, 2010), nonparametric Bayesian methods for models with a continuous mediator and a binary response (Daniels, Roy, Kim, Hogan, & Perri, 2012), encouragement designs (Forastiere, Mealli, & VanderWeele, 2015), and G-computation in multilevel models (Park & Kaplan, 2015). Computing causal effects for the single mediator model in the Bayesian framework requires fitting the model represented by Equations 2 and 4, and using the values of the coefficients at each MCMC draw to compute the causal effects in Equations 5–9.…”

Causal inference with large-scale assessments in education from a Bayesian perspective: a review and synthesis

“… Press (2003) notes that there are advantages and disadvantages to adopting subjective Bayesian practice which I summarize here. Of relevance to the the use of Bayesian methods for causal inference, the major advantage in using subjective priors is that it is the only way to encode prior research findings into an analysis.…”

“…In the absence of prior data and perhaps the inability to obtain expert opinion, then so-called “objective” priors can be implemented. The advantages of objective priors, as pointed out by Press (2003) is that (a) objective priors can be used as benchmarks against which choices of other priors can be compared, (b) objective priors reflect the view that little information is available about the process that generated the data, (c) there are cases in which the results of a Bayesian analysis with an objective prior provides results equivalent to those based on a frequentist analysis, and (d) objective priors are sensible public policy priors insofar as they allow for policy analysis without incorporating the prior knowledge of the analyst.…”