Because of the ethical and economic considerations in the design of clinical trials to test the efficacy and possible toxic effects of a newly developed drug or therapy, and because of the inherent sequential nature of the information flow during the course of the trial, there has been increasing interest from the biopharmaceutical industry in group sequential methods that can adapt to information acquired during the course of the trial and reduce the cost and study duration of conventional trials which assume a fixed sample size/study duration. An important objective of this research is to develop a comprehensive methodology for the design and analysis of group sequential trials. Certain long-standing problems in the field will be resolved in this connection, including valid confidence intervals following group sequential tests, calendar time versus information time in the case of failure-time endpoints, and sample size re-estimation during the course of a trial. A closely related objective is the development of nonlinear and nonparametric methods for the analysis of clinical trials with multiple endpoints, particularly those with combined efficacy-toxicity outcomes in cancer, arthritis and rheumatism treatments. Understanding the toxic-therapeutic relationships of these treatments will also help physicians to individualize and adapt the dose for different patients. Another objective of this research is to develop efficient statistical methods for nonlinear mixed effects models in population pharmacokinetics and for other problems in clinical pharmacology.
