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.
","abstract_html":"<p>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.</p> <p> 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.</p> <p> 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.</p>","abstract_has_math":false,"creators":["Torgbenu, Moses"],"institution":null,"degree_name":"Master of Science - Mathematical Sciences","degree_level":"Thesis","degree_discipline":"College of Science and Mathematics","degree_department":null,"school":null,"contributors":["Jacob Turner, Ph.D","Derek Blankenship, Ph.D","Robert Henderson, PhD."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-08-01T07:00:00Z","date_published":"2025-08-01T07:00:00Z","updated_at":"2026-07-24T04:30:49Z","subjects":["Time-to-Event","Survival Analysis","Alpha Spending Functions","O'Brien-Fleming","Pocock","Adaptive Design","Applied Statistics","Bioinformatics","Biostatistics","Clinical Trials","Longitudinal Data Analysis and Time Series","Statistical Methodology"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.sfasu.edu/etds/631","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jacob Turner, Ph.D","Derek Blankenship, Ph.D","Robert Henderson, PhD."]},{"key":"dc:creator","label":"Author","values":["Torgbenu, Moses"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2025-08-06T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["College of Science and Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science - Mathematical Sciences"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Time-to-Event","Survival Analysis","Alpha Spending Functions","O'Brien-Fleming","Pocock","Adaptive Design","Applied Statistics","Bioinformatics","Biostatistics","Clinical Trials","Longitudinal Data Analysis and Time Series","Statistical Methodology"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.sfasu.edu/etds/631"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Evaluating Alpha Spending Functions Applied to Observational Time-to-Event Analysis"]}]}],"canonical_facts":{"dc:contributor":["Jacob Turner, Ph.D","Derek Blankenship, Ph.D","Robert Henderson, PhD."],"dc:creator":["Torgbenu, Moses"],"dc:date.available":["2025-08-06T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://scholarworks.sfasu.edu/etds/631"],"dc:subject":["Time-to-Event","Survival Analysis","Alpha Spending Functions","O'Brien-Fleming","Pocock","Adaptive Design","Applied Statistics","Bioinformatics","Biostatistics","Clinical Trials","Longitudinal Data Analysis and Time Series","Statistical Methodology"],"dc:title":["Evaluating Alpha Spending Functions Applied to Observational Time-to-Event Analysis"],"thesis:degree_discipline":["College of Science and Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science - Mathematical Sciences"]},"updated_at":"2026-07-24T04:30:49Z"}