The investigator will explore theoretical properties of randomization procedures with applications to sequential randomized clinical trials. The first problem the investigator will address is sequential monitoring of randomization tests following restricted randomization, which will require extensive use of techniques in sequential analysis and nonparametric statistical inference. The second problem the investigator will address is the development and properties of response-adaptive randomization procedures, including procedures designed for continuous responses, and survival responses with censoring. The third problem the investigator will address is certain theoretical properties of covariate-adaptive randomization procedures, particularly randomization-based inference procedures following covariate-adaptive randomization. The ultimate goal of the investigator is to complete a systmeatic study of randomization, its properties, and its relevance in clinical trials.
The investigator will explore properties of randomization, the hallmark of a well-designed clinical trial. The first problem the investigator will address is sequential monitoring of randomized clinical trials, which refers to making early decisions about the effectiveness of new therapies when compelling evidence is accrued at an interim point in a clinical trial. There are currently no sequential monitoring techniques available that allow the randomization itself to be incorporate into these decisions, and hence current methodology completely ignores the design of the trial in the analysis. The second problem the investigator will address is response-adaptive randomization, and he will develop new procedures for clinical trials where the outcome is time-to-event or some continous measure, e.g. cholesterol level. These response-adaptive procedures are attractive from an ethical point of view, because they seek to maximize power to detect a relevant clinical outcome, while simultaneously minimizing the expected number of treatment failures patients will experience while participating in the clinical trial. The third problem the investigator will address is proporties of covariate-adaptive randomization procedures, which is designed to minimize tial imbalances in important confounding variables that might bias results of the clinical trial. Each of these topics is relevant to today's clinical trials in the drug development phase of new pharmaceuticals.
