Novel methodologies for the analysis of complex failure time data and alternative progression-free survival estimators

This thesis comprises two main parts. Part I (Sections 1 and 2) develops novel methodologies for the analysis of complex failure time data involving masked cause, cured proportions, and latent variables. Part II (Section 3) proposes two alternative nonparametric estimators to the standard Kaplan-Meier for progression- free survival (PFS). Section 1 presents an accelerated failure time cure model for time-to-event data with masked cause of failure. We propose rank-based estimating equations for the model parameters and use a generalization of the EM algorithm for parameter estimation. An important application of the proposed method, motivated by International Breast Cancer Study Group (IBCSG) trial VIII, is the characterization of the process of treatment-induced amenorrhea (TIA) in premenopausal women with breast cancer; studies have shown that such women are particularly concerned about the impact of adjuvant therapies on their menses and fertility. Section 2 investigates another question of interest in young women with breast cancer, i.e. the association between a patient's underlying degree of ovarian function suppression (OFS) and disease-free survival (DFS) after receiving lut