Sequential Analysis with Applications to Clinical Trials

Abstract

The topic of the thesis is an overview of some sequential and change-point detection methods with applications to clinical trials. Performing sequential monitoring is important for ethical, economical and other reasons. It is important to terminate a study as soon as possible when potentially harmful treatments are used or when financial resources are limited. The modern theory of sequential testing of hypotheses started with works of Wald and Barnard on quality control of military supplies during World War II. Since then sequential methods received a lot of attention. In this thesis we consider application of truncated sequential methods to four different models. First, we consider sequential testing of composite hypotheses in the presence of nuisance parameters. Second, we describe sequential procedures for binary data with risk-adjustment. Then, we consider non-parametric methods for sequential monitoring of longitudinal data. We finish the thesis with an example of monitoring proportions in the context of waiting time at emergency departments in hospitals.