Evaluating Alpha Spending Functions Applied to Observational Time-to-Event Analysis

Author

Moses Torgbenu, Stephen F Austin State UniversityFollow

Date of Award

8-2025

Degree Type

Thesis

Degree Name

Master of Science - Mathematical Sciences

Department

College of Science and Mathematics

First Advisor

Jacob Turner, Ph.D

Second Advisor

Derek Blankenship, Ph.D

Third Advisor

Robert Henderson, PhD.

Fourth Advisor

Emiliano Giudici, PhD

Abstract

This thesis explores the theoretical foundation of the alpha spending approach and extends its application beyond the conventional setting of randomized controlled trials (RCTs) to observational studies with time to event analyses. In these less structured environments, key design parameters such as the total number of events are often unknown, posing challenges for the standard implementation of sequential analysis methods.

Through simulation studies, this research delivers several important contributions. First, it presents a modified approach that uses calendar time to define the timing of interim analyses while relying on event-based information to estimate the correlation among test statistics. This adjustment is shown to restore proper control of the Type I error rate. Second, the study compares the performance of the Pocock and O’Brien-Fleming alpha spending functions, revealing that the Pocock method can become highly conservative under conditions of high censoring or small sample sizes. Third, the results provide insight into sample size requirements necessary to maintain nominal Type 1 error rates in the presence of high censoring.

The methods are applied to data from a published 2-year study assessing the effectiveness of Transitional Care Units on incident dialysis patients to illustrate their practical relevance. Although not statistically significant in the original study, the additional analysis shows a statistically significant treatment effect for all-cause mortality could have been identified as early as one year. This additional insight supports the use of adaptive interim analyses in observational program evaluations. Overall, the findings offer both theoretical and applied contributions to the use of alpha spending methods in survival analysis. They also suggest promising directions for future research, including more flexible frameworks for error control and strategies for dynamic decision-making in interim analyses.

Repository Citation

Torgbenu, Moses, "Evaluating Alpha Spending Functions Applied to Observational Time-to-Event Analysis" (2025). Electronic Theses and Dissertations. 631.
https://scholarworks.sfasu.edu/etds/631

Creative Commons License

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