A Bayesian Semiparametric Approach to Intermediate Variables in Causal Inference

• Published in: Journal of the American Statistical Association Vol. 106; no. 496; pp. 1331 - 1344
• Main Authors: Schwartz, Scott L., Li, Fan, Mealli, Fabrizia
• Format: Journal Article
• Language: English
• Published: Alexandria, VA American Statistical Association 01.12.2011; Taylor & Francis Ltd
• Subjects: Applications; Applications and Case Studies; Bayesian analysis; Bayesian method; Body mass index; Cardiovascular disease; Cardiovascular diseases; Causal inference; Clinical outcomes; Clinical research; Clinical trials; Clustering; Cohort analysis; Comparative analysis; Distribution; Estimation methods; Exact sciences and technology; Framing; General topics; Inference; Intermediate variables; Manifolds and cell complexes; Mathematics; Medical sciences; Medical statistics; Medical treatment; Medication adherence; Modeling; Multivariate analysis; Nonparametric models; Parametric models; Patient compliance; Physical activity; Placebos; Probability and statistics; Sampling; Sciences and techniques of general use; Statistics; Stratification; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Treatment needs; Variables; Sweden; Biometrics; Compliance; Cluster analysis (statistics); Mixture model; Principal stratification; Non parametric estimation; Cardiovascular disease; Parametric model; Multivariate analysis; Information loss; Parametric method; Medical science; Cohort study; Clinical trial; Posterior distribution; Bayes estimation; Mixed distribution; Bayesian nonparametrics; Discriminant analysis; Dirichlet process; Statistical estimation; Gibbs sampling; Joint distribution; Semiparametric method; Statistical method; Randomized design
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/jasa.2011.ap10425

In causal inference studies, treatment comparisons often need to be adjusted for confounded post-treatment variables. Principal stratification (PS) is a framework to deal with such variables within the potential outcome approach to causal inference. Continuous intermediate variables introduce inferential challenges to PS analysis. Existing methods either dichotomize the intermediate variable, or assume a fully parametric model for the joint distribution of the potential intermediate variables. However, the former is subject to information loss and arbitrary choice of the cutoff point and the latter is often inadequate to represent complex distributional and clustering features. We propose a Bayesian semiparametric approach that consists of a flexible parametric model for the potential outcomes and a Bayesian nonparametric model for the potential intermediate outcomes using a Dirichlet process mixture (DPM) model. The DPM approach provides flexibility in modeling the possibly complex joint distribution of the potential intermediate outcomes and offers better interpretability of results through its clustering feature. Gibbs sampling based posterior inference is developed. We illustrate the method by two applications: one concerning partial compliance in a randomized clinical trial, and one concerning the causal mechanism between physical activity, body mass index, and cardiovascular disease in the observational Swedish National March Cohort study.