| In this dissertation, we develop and evaluate methods for adjusting for treatment non-compliance in a randomized clinical trial with time-to-event outcome within the proportional hazards framework. Adopting the terminology in Cuzick et al. [2007], we assume the patient population consists of three (possibly) latent groups: the ambivalent group, the insisters and the refusers, and we are interested in analyzing the treatment effect, or the covariate by treatment interaction effect, within the ambivalent group. In Chapter 1, we propose a weighted per-protocol (Wtd PP) approach, and motivated by the pseudo likelihood (PL) considered in Cuzick et al. [2007], we also consider a full likelihood (FL) approach and for both likelihood methods, we propose an EM algorithm for estimation. In Chapter 2, we consider a biomarker study conducted within a clinical trial with non-compliance, where the interest is to estimate the interaction effect between the biomarker and the treatment but it is only feasible to collect the biomarker information from a selected sample of the patients enrolled on the trial. We propose a weighted likelihood (WL) method, a weighted pseudo likelihood (WPL) method and a doubly weighted per-protocol (DWtd PP) method by weighting the corresponding estimating equations in Chapter 1. In Chapter 3, we explore the impact of various assumptions of non-compliance on the performance of the methods considered in Chapter 1 and the commonly used intention-to-treat (ITT), as-treated (AT) and the per-protocol (PP) methods. Results from the first two chapters show that the likelihood methods and the weighted likelihood methods are unbiased, when the underlying model is correctly specified in the likelihood specification, and they are more efficient than the Wtd PP method and the DWtd PP method when the number of risk parameters is moderate. The Wtd PP method and the DWtd PP method are potentially more robust to outcome model misspecifications among the insisters and the refusers. Results from Chapter 3 suggest that when treatment non-compliance is present, careful considerations need to be given to the design and analysis of a clinical trial, and various methods could be considered given the specific setting of the trial. |
