A Bayesian Nonparametric Approach for Causal Inference with Multiple Mediators
PresenterFlash Talk Presenter
Samrat is currently a Postdoctoral Researcher at the University of Pennsylvania, Department of Statistics (Wharton School). Prior to this position, he completed his M.STAT. from Indian Statistical Institute and received his Ph.D. in Statistics from the University of Florida. Before starting his graduate life at the UF, he also worked at Ernst & Young and Credit Suisse as a Credit Risk Model developer. Throughout his academic and professional career, Samrat has traversed different paradigms of Data Science and Machine Learning with 7 years of experience and training in cutting-edge technicalities. Some of his key areas of expertise are: High Dimensional Data, Statistical Machine Learning, Causal Inference and High Dimensional VAR.
Mediation analysis with contemporaneously observed multiple mediators is a significant area of causal inference. Recent methodologies dealing with multiple mediators are based on parametric models and thus may suffer from parametric misspecification. Also, the existing literature estimates the joint mediation effect as the sum of individual mediators effect, which, on many occasions, is not a reasonable assumption. In this paper, we propose a methodology that overcomes the two aforementioned drawbacks in the existing literature. Our method is based on a novel Bayesian nonparametric (BNP) approach, wherein, the joint distribution of the observed data (outcome, mediators, treatment, and confounders) is modeled flexibly using an enriched Dirichlet process with three levels: the first level characterizing the conditional distribution of the outcome given the mediators, treatment and the confounders, the second level corresponding to the conditional distribution of each of the mediators given the treatment and the confounders, and the third level corresponding to the distribution of the treatment and the confounders. Using the joint distribution in the EDP, we use standardization (g-computation) to compute causal mediation effects. The efficacy of our proposed method is demonstrated with simulations. Also, we apply our proposed method to analyze data from a study of Ventilator-associated Pneumonia (VAP) co-infected patients, where the effect of the abundance of Pseudomonas on VAP infection is suspected to be mediated through various antibiotic exposures.
KeywordsBayesian nonparametric, Enriched Dirichlet Process, Multiple mediators
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