Title: Novel methodologies for the analysis of complex failure time data and alternative progression-free survival estimators
Description: 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 luteinizing-hormone-releasing hormone (LHRH) agonists as adjuvant therapy. LHRH agonists have the potential to preserve fertility after treatment, thus, reducing the negative effects on the patient's reproductive health. A latent class joint model (LCJM), which accommodates masked cause and cured proportions in the surrogates, is proposed to explore this association of interest using the same IBCSG dataset as in Section 1. The last section proposes two alternative nonparametric estimators of PFS. Simulations confirm that the standard Kaplan-Meier (KM) estimator can result in significantly biased estimates of PFS. Currently, to ameliorate this bias, several sensitivity analyses based on different definitions of PFS censoring are usually conducted. However, these definitions of censoring, although convenient, are not based on statistical theory. Our proposed estimators statistically incorporate survival data often available for those patients who are censored with respect to progression to obtain less biased estimates. Through simulations, we show that these estimators greatly reduce the bias of the standard KM estimator and can be utilized as alternative PFS sensitivity analysis tools. An example is given using an advanced breast cancer study.