Bayesian Causal Inference With Intermediates

Abstract

Causal inference from observational data can be complicated for a number of reasons, including complex functional forms for covariates, partially missing or wholly unmeasured confounders, and truncating events which obscure effects on the outcome of interest. In these instances, it can be useful to look at that intermediate variables to disentangle the causal effect of a treatment or exposure on the primary outcome of interest. Moreover, the intermediates can themselves become outcomes of interest as they become targets of public health intervention or metrics for quality of care. This dissertation explores the use of intermediate variables in two settings. In Chapter 1, we introduce a data-driven sensitivity analysis method. This Bayesian data fusion (BDF) procedure synthesizes information across multiple data sources to correct for confounding by a variable which is unmeasured in the main data set. We demonstrate this method for unmeasured exposure-induced mediator-outcome confounding in the context of Black-White racial disparities in colorectal cancer. In Chapters 2 and 3, we turn to the problem of understanding hospital readmissions among late-stage pancreatic cancer patients. Readmissions are a common proxy indicator for quality of care, but they can be truncated by death in a problem referred to as semicompeting risks. Chapter 2 lays out a general causal framework for semicompeting risks that is rooted in principal stratification. We motivate two new causal estimands: the time-varying survivor average causal effect (TV-SACE) and the restricted mean survivor average causal effect (RM-SACE). We also introduce a Bayesian estimation procedure which accommodates individual-level latent frailties, and we demonstrate its application in an evaluation of home support among newly diagnosed pancreatic cancer patients. Chapter 3 proposes a nonparametric estimation procedure for the TV-SACE and RM-SACE based on Bayesian Additive Regression Trees (BART), which allows for treatment effect heterogeneity with embedded interaction terms in the branches of the trees. With this newfound flexibility, we revisit the data analysis of Chapter 2 to understand how the changing composition of latent principal strata drives population-level effects and how heterogeneity informs individualized recommendations. Chapter 4 concludes with a discussion of unifying themes and future research directions.