Bayesian strategies for posttreatment variable adjustment using principal stratification: Application to treatment noncompliance and principal surrogate endpoints

Public health and biomedical research often involves causal-inference questions that are challenging to address even with sophisticated, randomized experimental designs. Mathematical formulation of the theory of potential outcomes has shed light on many such questions allowing researchers to reach causal conclusions absent the benefits of traditional randomized experiments. Anchored by the theory of potential outcomes, the principal stratification framework (Frangakis and Rubin, 2002) has proven valuable in a variety of settings characterized by the potential for confounding by posttreatment variables, finding particular relevance in applications to HIV/AIDS treatment and prevention. Through consideration of two health-sciences research problems, this dissertation aims to broaden the applicability of principal stratification to settings with novel features that are relevant to public-health research.;The prospect of all-or-nothing treatment noncompliance in a randomized clinical trial has served as an engine for the development of potential-outcomes methods in biomedical sciences and is perhaps the simplest example in health-sciences research of potential confounding by a posttreatment variable. In a motivating oral-surgery study, we address subtleties involved in inference for causal effects when membership in the latent principal strata depends on a key pretreatment covariate. We show that the presence of a covariate predictive of treatment received can induce sensitivity in inference for the "complier average causal effect" (CAGE) (Imbens and Rubin, 1997) because estimates of the CAGE could then depend on patients from the two treatment arms who differ with regard to the key covariate. Adopting a Bayesian perspective and using Markov chain Monte Carlo for computation, we develop a strategy for drawing inference about the CAGE that reflects concerns about the comparability of units receiving different treatments. We apply the method to analyze a clinical trial comparing two treatments for jaw fractures in which the study protocol allowed surgeons to overrule the randomized treatment assignment based on their clinical judgment and the data contained a key covariate (injury severity) predictive of treatment received. The method incorporates posterior model checks reflecting the degree to which estimates of the CACE are subject to uncertainty due to the presence of a covariate predictive of treatment received.;Another setting where principal stratification has been used is the development of biomarkers and surrogate endpoints in clinical trials. Analysis of these intermediate endpoints has particular value in HIV/AIDS research when outcomes of interest may prove prohibitively difficult to measure or when the need for expedient development of therapies precludes the feasibility of studies with long follow-up time. Illustrations based on potential outcomes have shown that previously-proposed methods for estimating surrogacy based only on observed quantities can fail to capture underlying causal relationships and thus have limited utility. A principal-stratification perspective gives rise to the notion of a "principal surrogate" as a basis for estimating causal relationships among treatments, surrogates, and outcomes. Building on formulations by Frangakis and Rubin (2002) and Gilbert and Hudgens (2008), we employ a Bayesian method to estimate the "Causal Effect Predictiveness" (CEP) surface and quantify a candidate surrogate's utility for reliably predicting clinical outcomes. An important special case where the literature prominently features the notion of a principal surrogate is the setting of a vaccine trial. Recently-developed approaches making use of estimated-likelihood estimation (Pepe and Fleming, 1991) assume that the surrogate marker takes on the same constant value for all patients in one arm of the study, which might be viewed as plausible in an HIV vaccine trial where patients can be assumed to have no HIV-specific immune response under receipt of placebo (Follmann, 2006; Qin et al., 2008; Gilbert and Hudgens, 2008; Wolfson and Gilbert, 2010). We illustrate the Bayesian approach to estimation of the CEP surface in one such simulated HIV vaccine trial, highlighting improvements over previously-used methods.;Extending estimation of the CEP surface to more general settings with varying surrogate response in both trial arms has received little attention in the principal-surrogate literature, possibly due to the challenges emanating from the need to impute missing potential outcomes for all patients under study. A key motivation for a Bayesian approach is that it allows flexible imputation of missing potential outcomes, potentially avoiding the restrictive but prevailing assumption of constant surrogate response in the control group. Using Markov chain Monte Carlo for computation, we identify the joint distribution of potential outcomes that are never jointly observed through incorporation of a sensitivity parameter that is varied across a plausible range to estimate the CEP surface under various assumptions about the association between individuals' potential surrogate responses under each treatment. We extend estimation of the CEP surface to more general settings with varying surrogate response in both trial arms through simulations and an application to an AIDS clinical trial where CD4 count is a natural candidate surrogate.