PhD Oral Exam - Maryam Jabbari Khasraghi, Mathematics and Statistics

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

Testing for Cure-Rate and Sufficient Follow-Up under Random Censoring using Extreme-Value Theory Abstract This thesis develops a unified extreme-value framework for testing the existence of a cure rate and evaluating sufficient follow-up in right-censored survival data. The central quantity of interest is the limiting survival probability p = limt→∞ S(t), which represents the long-term proportion of cured individuals. The null hypothesis H0: p = 0 corresponds to the absence of cure, while H1: p > 0 implies the existence of a cured subgroup. Further, there is said to be sufficient follow-up when the support of the non-cured lifetime distribution is contained in that of the censoring distribution, so that a non-cured individual would be uncensored in the long run.

Within this framework, we study recently proposed test statistics for (1) detecting the existence of a cure rate and (2) assessing whether follow-up is sufficient to observe all susceptible failures, assuming both the lifetime and censoring distributions are in the maximum domain of attraction of extreme-value distributions (EVD). For various types of EVD combinations, asymptotic null laws of the test-statistics and their limiting behavior under the alternative are obtained based on limiting Poisson processes of exceedance-type empirical processes, suitably normalized, of uncensored and censored observations. Simulation studies confirm the theoretical findings and demonstrate robustness across domains of attraction, offering a coherent Poisson-process-based toolkit for modern cure-rate analysis.