Year

2025

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. Yisu Jia

Third Advisor

Dr. Fei Heng

Department Chair

Dr. Richard Patterson

College Dean

Dr. Kaveri Subrahmanyam

Abstract

A two-stage design is developed for comparing the means of multiple normally distributed treatment groups under a known common variance, with the aim of identifying the treatment with the highest mean while minimizing the expected sample size, a crucial consideration in clinical trials. The proposed methodology integrates elements of both hypothesis testing and selection procedures to achieve greater efficiency and decision-making power. In the initial stage, if no treatment exhibits a mean surpassing a predefined efficacy threshold, the trial is terminated early, conserving resources. If one or more treatments exceed the threshold, the procedure advances to a second stage, where additional data is collected for the treatment group with the highest observed mean, followed by a formal hypothesis test against a control to determine its effectiveness. The design is optimized through the principle of the least favorable configuration (LFC), which focuses on minimizing expected sample size under the most challenging conditions for detection. As this approach blends selection and testing, conventional definitions of type I error and power are modified to suit the hybrid framework. For any given significance level and target power, the procedure outlines how to derive suitable design parameters, ultimately selecting the design with the lowest expected sample size from among feasible candidates.

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