On the estimation of the binomial probability in multistage clinical trials

摘要: Due to the optional sampling effect in a sequential design, maximum likelihood estimator (MLE) following tests is generally biased. In typical two-stage design employed phase II clinical trial cancer drug screening, fixed number of patients are enrolled initially. The may be terminated for lack efficacy treatment if observed responses after first stage too small. Otherwise, an additional accumulate information on as well safety. There have been numerous suggestions such studies. Here we establish that under sufficient statistic, i.e. stopping and responses, parameter binomial distribution also complete. Then, based Rao-Blackwell theorem, derive uniformly minimum variance unbiased (UMVUE) conditional expectation estimator, which this case simply only data, given complete statistic. Our results generalize multistage design. We will illustrate features UMVUE examples present numerical studies properties comparison usual MLE.