Bioinformatics; Biostatistics; Bootstrap methods; Design of clinical trials; Statistical methods in financial econometrics; Stochastic process; Weighted likelihood
CAREER: Use of Covariate Information in Adaptive Designs
An adaptive design is a sequential design where the design points are chosen based on both previous design points and the outcomes at those design points. Covariate information is often available and usually very important in statistical inference. Very few adaptive designs described in the literature attempt to incorporate covariate information. This proposal is concerned with using covariate information in adaptive designs. The investigator proposes a new class of adaptive designs under some optimal criteria. The new designs (i) can incorporate covariate information; and (ii) exhibit certain desired properties when there is no covariate information. The investigator then studies the properties of the proposed designs when incorporating covariates. Further he investigates the relationship between efficiency of estimation and the total number of failures in experiments. Based on these results , the investigator develops a procedure to select a suitable adaptive design for a particular problem. In clinical trials, prognostic factors are often available and usually very important. How to incorporate prognostic factors (covariates) into trial design is a critical, and conceptually difficult, problem. Adaptive designs use data sequentially as it is collected, making use of it in deciding, for example, how to allocate future subjects between treatment groups or even whether or not future subjects are needed to achieve some accuracy objective. In this proposal, the investigator will thoroughly investigate using covariate information in adaptive designs. Upon completion of this project, a class of adaptive designs, which incorporates covariate information, will be available for clinical trials and other experiments. Applications exist in a wide variety of fields: industrial experiments, bioassay, and clinical trials. The full impact of these designs will be realized through dissemination in the literature, presentations, group working sessions, and interdisciplinary collaborations. The project will stimulate researchers and students to work in the area of adaptive designs, and should lead to numerous graduate and undergraduate level projects and these.
Power, Variability, & Optimality in Adaptive Designs
Adaptive designs are sequentially accruing data in allocation decisions to reach some objective. In this proposal, the objective is based on an optimization of criterion, such as minimizing cost of an experiment. We propose to use the power of a hypothesis test as a benchmark for comparisons of adaptive designs. We explicitly derive the relationship between power and the design in terms of bias of the target allocation from the actual allocation and overdispersion induced by the design. For four classes of adaptive designs, urn models, sequential maximum likelihood procedures, doubly adaptive biased coin designs and treatment effect mappings, we plan to uniquely unify the theory for easy comparison based on power, optimality and variability. We describe potential research topics and an integrated plan to involve students across two campuses.