On the estimation of the binomial probability in multistage clinical trials.
Due to the optional sampling effect in a sequential design, the maximum likelihood estimator (MLE) following sequential tests is generally biased. In a typical two-stage design employed in a phase II clinical trial in cancer drug screening, a fixed number of patients are enrolled initially. The trial may be terminated for lack of clinical efficacy of treatment if the observed number of treatment responses after the first stage is too small. Otherwise, an additional fixed number of patients are enrolled to accumulate additional information on efficacy as well as on safety. There have been numerous suggestions for design of such two-stage studies. Here we establish that under the two-stage design the sufficient statistic, i.e. stopping stage and the number of treatment responses, for the parameter of the binomial distribution is also complete. Then, based on the Rao-Blackwell theorem, we derive the uniformly minimum variance unbiased estimator (UMVUE) as the conditional expectation of an unbiased estimator, which in this case is simply the maximum likelihood estimator based only on the first stage data, given the complete sufficient statistic. Our results generalize to a multistage design. We will illustrate features of the UMVUE based on two-stage phase II clinical trial design examples and present results of numerical studies on the properties of the UMVUE in comparison to the usual MLE.
Jung
Sin-Ho
SH
Department of Biostatistics and Bioinformatics, Duke University, Durham, North Carolina 27710, USA. jung0005@surgerytrials.duke.edu
Kim
Kyung Mann
KM
D017322:Clinical Trials, Phase II as Topic / Q000379:methods*; D016001:Confidence Intervals; D004341:Drug Evaluation / Q000379:methods; D006801:Humans; D016013:Likelihood Functions; D009369:Neoplasms / Q000188:drug therapy; D009716:Numerical Analysis, Computer-Assisted; D012107:Research Design; D013223:Statistics as Topic / Q000379:methods*; D013269:Stochastic Processes