Jason Roy

Arman Oganisian, Jason A. Roy

Substantial advances in Bayesian methods for causal inference have been developed in recent years. We provide an introduction to Bayesian inference for causal effects for practicing statisticians who have some familiarity with Bayesian models and would like an overview of what it can add to causal estimation in practical settings. In the paper, we demonstrate how priors can induce shrinkage and sparsity on parametric models and be used to perform probabilistic sensitivity analyses around causal assumptions. We provide an overview of nonparametric Bayesian estimation and survey their applications in the causal inference literature. Inference in the point-treatment and time-varying treatment settings are considered. For the latter, we explore both static and dynamic treatment regimes. Throughout, we illustrate implementation using off-the-shelf open source software. We hope the reader will walk away with implementation-level knowledge of Bayesian causal inference using both parametric and nonparametric models. All synthetic examples and code used in the paper are publicly available on a companion GitHub repository.

Arman Oganisian, Nandita Mitra, Jason Roy

Cost-effectiveness analyses (CEAs) are at the center of health economic decision making. While these analyses help policy analysts and economists determine coverage, inform policy, and guide resource allocation, they are statistically challenging for several reasons. Cost and effectiveness are correlated and follow complex joint distributions which are difficult to capture parametrically. Effectiveness (often measured as increased survival time) and accumulated cost tends to be right-censored in many applications. Moreover, CEAs are often conducted using observational data with non-random treatment assignment. Policy-relevant causal estimation therefore requires robust confounding control. Finally, current CEA methods do not address cost-effectiveness heterogeneity in a principled way - often presenting population-averaged estimates even though significant effect heterogeneity may exist. Motivated by these challenges, we develop a nonparametric Bayesian model for joint cost-survival distributions in the presence of censoring. Our approach utilizes a joint Enriched Dirichlet Process prior on the covariate effects of cost and survival time, while using a Gamma Process prior on the baseline survival time hazard. Causal CEA estimands, with policy-relevant interpretations, are identified and estimated via a Bayesian nonparametric g-computation procedure. Finally, we outline how the induced clustering of the Enriched Dirichlet Process can be used to adaptively detect presence of subgroups with different cost-effectiveness profiles. We outline an MCMC procedure for full posterior inference and evaluate frequentist properties via simulations. We use our model to assess the cost-efficacy of chemotherapy versus radiation adjuvant therapy for treating endometrial cancer in the SEER-Medicare database.