On the estimation of the binomial probability in multistage clinical trials
On the estimation of the binomial probability in multistage clinical trials
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DOI：
10.1002/sim.1653
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发表时间：
2004-03-30
影响因子：
2
通讯作者：
Kim, KM
中科院分区：
文献类型：
--
作者：
Jung, SH;Kim, KM
由于序贯设计中的抽样效应是可选择的，序贯检验的极大似然估计量（MLE）通常是有偏的。在癌症药物筛选的II期临床试验中采用的典型两阶段设计中，最初招募固定数量的患者。如果在第一阶段后观察到的治疗反应数量太少，则试验可能因缺乏治疗的临床疗效而终止。否则，将招募额外的固定数量的患者，以积累关于疗效和安全性的额外信息。对于这种两阶段研究的设计有许多建议。在这里，我们确定了在两阶段设计下，二项分布参数的充分统计量（即停止阶段和治疗应答数量）也是完整的。然后，基于Rao-Blackwell定理，我们推导出一致最小方差无偏估计（UMVUE）作为无偏估计的条件期望，在这种情况下，它只是基于第一阶段数据的最大似然估计，给定完全充分统计量。我们的结果推广到多阶段设计。我们将说明的UMVUE的两个阶段的II期临床试验设计的例子的基础上的功能和目前的数值研究结果的UMVUE的属性相比，通常的MLE。版权所有（C）2004约翰威利父子有限公司。
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. Copyright (C) 2004 John Wiley Sons, Ltd.