ORCID

https://orcid.org/0009-0001-7784-715X

Year

2026

Season

Spring

Paper Type

Master's Thesis

College

College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)

Department

Mathematics & Statistics

NACO controlled Corporate Body

University of North Florida. Department of Mathematics and Statistics

Committee Chairperson

Dr. Elena Buzaianu

Second Advisor

Dr. Ping Sa

Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

Third Advisor

Dr. Peiyao Wang

Department Chair

Dr. Richard F. Patterson

College Dean

Kaveri Subrahmanyam

Abstract

This study explores better ways to assign patients to treatments in clinical trials with binary outcomes, such as success or failure. Adaptive methods are used to learn from early results and adjust treatment assignments during the trial, helping more patients receive better performing treatments while maintaining reliable conclusions. We focus on trials comparing multiple treatments using a two-stage design. In the first stage, several treatments are tested to identify the most promising one; in the second stage, that treatment is compared with a control. Unlike traditional equal assignment, we use adaptive allocation in the second stage to make better use of early findings. We introduce a new ridit-based approach that estimates the probability that the selected treatment is better than the control using first stage data. This method is compared with an optimal adaptive rule and the “play-the winner” strategy, which favors treatments that perform well. These approaches are evaluated based on reducing unsuccessful outcomes, limiting sample size, while maintaining control over error rates. Simulation results show that the proposed method perform well across these goals. An example involving a pancreatic cancer trial illustrates practical use. Overall, this work offers a flexible and efficient framework that improves both patient benefit and scientific rigor in modern clinical trials.

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