| Group sequential clinical trials have become the accepted method for monitoring the results of an ongoing trial. These methods allows early termination of a trial based on the results of "interim analyses" that are conducted after each of the groups of subjects are entered on the study. Existing methods for designing these types of trials are currently comprised of several different constructions, each of which addresses a different clinical setting. The purpose of this dissertation is to unify these constructions into a single framework. This is accomplished by first proposing a general algebraic family of stopping rules for group sequential designs, and then constructing a statistical interpretation of the family. Both Bayesian and frequentist approaches are included in this unification. The properties of the unified family of designs is examined, which lends insight into the similarities and differences between existing approaches to group sequential designs. This work is motivated by several clinical examples, and the clinical application of these designs is given detailed consideration. A particular example is used to illustrate the application of these methods, and to describe how they would be implemented in an ongoing monitoring program for a clinical trial. |
