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. Fei Heng

Fourth Advisor

Dr. Peiyao Wang

Department Chair

Dr. Richard F. Patterson

College Dean

Dr. Kaveri Subrahmanyam

Abstract

This study focuses on improving how clinical trials compare new treatments with a standard treatment, when the response is quantitative (normally distributed). In a common two-stage design, several new treatments are first evaluated, and the best-performing one is selected if it appears better than the standard. In the second stage, this selected treatment is compared again with the standard using additional data to confirm its effectiveness. This approach is known to be efficient in terms of accuracy and sample size savings. We extend this design by introducing an adaptive method for assigning patients to treatments in the second stage. Instead of giving patients an equal chance of receiving either the selected treatment or the standard, the proposed method adjusts the allocation in the second stage based on results observed in the first stage. As a result, more patients are assigned to the better-performing treatment. This approach is not only statistically beneficial but also ethically appealing, as it increases the likelihood that patients receive the more effective treatment while still controlling error probabilities. Overall, this work demonstrates that incorporating adaptive allocation into a two-stage clinical trial design can provide a more efficient and patient-friendly alternative.

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