Date of Award

6-26-2026

Date Published

August 2026

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

Pinyuen Chen

Keywords

Binary Endpoint;Multiple Endpoints;Ranking and Selection;Subset Selection

Abstract

This dissertation studies clinical trial designs for comparing multiple experimental treatments with a control when each treatment is evaluated using two possibly dependent binary endpoints, typically efficacy and safety. Motivated by the growing importance of multi-endpoint decision making in clinical research, the dissertation develops exact ranking-and-selection procedures that avoid large-sample normal approximations and instead rely on exact probability calculations. Throughout, dependence between the two endpoints within a treatment arm is accommodated through an odds-ratio-based framework, and the underlying computations are carried out using bivariate binomial and quadrinomial distributions. After an introductory chapter that reviews the methodological background and motivates treatment selection with two binary endpoints in comparison with a control, the dissertation presents three related design frameworks. The first develops a fixed-sample-size subset-selection procedure for identifying all experimental treatments that are superior to the control on both endpoints. Exact design parameters are derived under three settings: independent endpoints, dependent endpoints with known association, and dependent endpoints with unknown association. The second extends this framework to a curtailed sequential procedure with explicit sampling, stopping, and decision rules, and shows that the sequential design preserves the same probability-of-correct-selection guarantee as the fixed-sample procedure while often reducing the expected sample size. The third addresses a more stringent selection objective: among the treatments that exceed the control on both efficacy and safety, select the one with the highest efficacy rate; if no treatment satisfies both criteria, the control treatment is selected instead. Taken together, these results provide a unified exact-design framework for treatment selection with two dependent binary endpoints in the presence of a control arm. The final chapter summarizes the main contributions of the dissertation and discusses directions for future research, including broader dependence structures, more flexible decision criteria, and extensions to more complex clinical trial settings.

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Open Access

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