Causal Modeling with Principal Stratification to Assess Effects of Treatment with Partial Compliance, Noncompliance, and Principal Surrogacy in Longitudinal and Time-to-Event Settings.

Abstract

Much research in the social and health sciences aims to understand the causal relationship between an intervention and an outcome, and a variety of statistical methods have been developed to answer these questions. However, in many situations, such causal relationships are not readily obtained even in well-conducted randomized clinical trials due to problems with noncompliance or partial compliance. More generally, conditioning on variables such as compliance that are observed post-randomization destroys the causal interpretation of treatment effects in statistical models. Therefore it is desirable to develop statistical methods to accommodate post-randomization variables in regression while retaining the causal interpretation of the effect of treatment. Recent research in causal inference under the potential outcome framework aims to solve the problem, in which a potential outcome is defined as the value an outcome would take after assignment to a different treatment arm than the one actual observed. Under the potential outcome framework, Frangakis and Rubin (2002) defined principal strata as the joint distribution of adjustment variables under different treatment arms, and proposed to estimate the causal effect of treatment within these principal strata. I develop two methods to account for noncompliance or partial compliance behavior in clinical studies using the potential outcome framework with the principal stratification approach. The first focuses on time varying noncompliance behavior in randomized longitudinal clinical studies, jointly estimating how causal effects of treatment impact compliance behavior and vice-versa. The second methods considers the problem of partial compliance, identifying subjects' principal strata membership based on the potential values of subjects' adverse events and dosing behavior over time. I also consider the problem of developing surrogate markers for main clinical outcomes of interest. I propose a causal model using the joint distribution of the surrogate markers under the different treatment arms and assess this ``principal surrogacy'' when time-to-event primary outcomes are of interest. Bayesian estimation methods with Markov chain Monte Carlo algorithms are adopted to accommodate complex missing data structures. The randomized clinical trials motivating the methods are used to illustrate the proposed causal models, and simulation studies are conducted to investigate their repeated sampling properties.