Across a wide range of academic disciplines, government agencies, and business sectors, drawing inferences about causal effects of treatments, intervention, and actions is central to decision making. In both randomized experiments and observational studies, it is increasingly common that treatment comparisons need to be adjusted for confounded intermediate variables; i.e., post-treatment variables potentially affected by the treatment and also affecting the response. Multivariate information is routinely collected in real-world applications involving intermediate variables, but it is infrequently and ineffectively used in causal inference. This research project will develop general purpose statistical methods and software for such multivariate analysis under the principal stratification framework within the Rubin Causal Model. A core methodological focus will be to develop cutting-edge Bayesian models, methods, and computation for flexible multivariate analysis, latent structure, nonparametric analysis, model selection, and factor analysis for drawing valid causal inferences in the presence of intermediate variables. In particular, this project will develop Bayesian parametric, semi-parametric, and non-parametric bivariate models that exploit multiple outcomes of different types to improve the estimation of weakly identified causal estimands in studies with binary or continuous intermediate variables. A Bayesian factor model also will be developed for causal studies with multiple intermediate variables.
This project will improve statistical analyses for causal inference with intermediate variables, hence enabling more accurate conclusions from experimental and observational intervention studies across many disciplines. The research will blend theory and methodological developments with motivating applications in areas including health policy, epidemiology, social sciences, and economics. The open source R/Matlab software developed from the research will provide valuable data analysis and educational tools for the scientific community.
