Date of Graduation

12-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics (PhD)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor/Mentor

Zhang, Qingyang

Committee Member

Chakraborty, Avishek

Second Committee Member

Petris, Giovanni

Keywords

clinical trials; loss to follow-up; non-proportional hazards; restricted distance covariance (rdcov); right censoring; survival analysis

Abstract

When treatment effects change over time, standard statistical methods, such as the log-rank test and the Cox proportional hazards model, may give misleading results. This dissertation presents the restricted distance covariance (rdcov) test, a nonparametric method that compares survival curves between groups within a chosen study period [0, τ] using right censored data. The statistic measures the dependence between pre-specified group labels and survival times using pairwise distances from Kaplan-Meier estimates. Our method does not rely on the proportional hazards assumption, and it equals zero only when survival functions are identical across groups. Thus, this test can be applied to trials with multiple arms. Due to the difficulty of analytically calculating p-values, we recommend a general permutation test procedure. Our simulation studies demon- strate that under non-proportional hazard settings such as delayed effects, crossing hazards, and diminished effects, rdcov shows higher power than the Cox PH model, and remains competitive. Applications to an immunotherapy trial with late treatment effects and to breast cancer survival data confirm that rdcov can identify clinically meaningful differences between survival curves. Our method can be a competitive alternative to the standard methods for testing survival functions. A second topic of this dissertation is to propose a novel method for handling loss-to-follow-up time distribution in real-world trials with staggered enrollment. By linking survival time, dropout time, and administrative follow-up, we propose an analytical calculation for the distribution of loss-to- follow-up time, and a numerical approach to reconstruct the follow-up time distribution from the specified loss-to-follow-up time distribution, providing more accurate estimation and prediction for these distributions, which are essential for clinical trial simulations.

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