The overarching goal of this project is to develop Bayesian non-parametric (BNP) methods for estimating causal effects from complex data. We focus on two broad areas: survival analysis with time-varying treatments and mediation. For survival outcomes, we develop BNP methods for estimating causal parameters from structural nested failure time models, both for discrete and continuous-time problems. Likelihood-based methods have generally not been implemented for these models, because it would require many parametric modeling assumptions. Our BNP approach should provide greater flexibility than parametric models, while maintaining computational advantages. We will develop these methods for a wide array of scenarios (e.g., multinomial or continuous-valued treatment, known or unknown censoring times) and develop sensitivity analysis methods and informative priors related to untestable assumptions. For causal mediation analysis, we will extend our previous work in a variety of ways. Most importantly, we will weaken identifying assumptions with the inclusion of covariates in the models. In addition, we will generalize to a wider variety of outcomes and types of mediation (e.g. longitudinal or multiple mediators). We will also develop methods for handling non-ignorable dropout in settings with mediation. Our methods have broad applications, and we will utilize them to draw novel clinical inference from several behavioral intervention trials, and from a study on the hepatic safety of classes of antiretroviral medications.
In clinical research studies involving treatment comparisons, there is often interest in the comparative effectiveness of various treatment strategies, or on the effect of mediating variables. It is therefore of great importance to have statistical methods that can handle the complexities of these data, without relying on strong modeling assumptions. This project develops new, robust Bayesian methods for inferring causal effects from complex studies of this nature.