Abstract：
A common problem faced in clinical studies is that of estimating the effect of the most effective (e.g. the one having the largest mean) treatment among k(≥2) available treatments. The most effective treatment is adjudged based on numerical values of some statistic corresponding to the k treatments. A proper design for such problems is the so-called \"Drop-the-Losers Design (DLD)\". We consider two treatments whose effects are described by independent Gaussian distributions having different unknown means and a common known variance. To select the more effective treatment, the two treatments are independently administered to n1 subjects each and the treatment corresponding to the larger sample mean is selected. To study the effect of the adjudged more effective treatment (i.e. estimating its mean), we consider the two-stage DLD in which n2 subjects are further administered the adjudged more effective treatment in the second stage of the design. We obtain some admissibility and minimaxity results for estimating the mean effect of the adjudged more effective treatment. The maximum likelihood estimator is shown to be minimax and admissible. We show that the uniformly minimum variance conditionally unbiased estimator (UMVCUE) of the selected treatment mean is inadmissible and obtain an improved estimator. In this process, we also derive a sufficient condition for inadmissibility of an arbitrary location and permutation equivariant estimator and provide dominating estimators in cases, where this sufficient condition is satisfied. The mean squared error and the bias performances of various competing estimators are compared via a simulation study. A real data example is also provided for illustration purpose.
摘要：
临床研究中面临的一个常见问题是估计k(≥2)种可用治疗中最有效(例如具有最大平均)治疗的效果。根据与k种处理相对应的一些统计量的数值来判断最有效的处理。针对此类问题的适当设计是所谓的“丢弃失败者设计(DLD)”。我们考虑两种治疗方法，其效果由具有不同未知均值和共同已知方差的独立高斯分布描述。为了选择更有效的治疗方法，将两种治疗各自独立地给予n1个受试者,并且选择对应于较大样本平均值的治疗。为了研究判定的更有效治疗的效果(即估计其平均值)，我们考虑两阶段DLD,其中n2受试者在设计的第二阶段被认为是更有效的治疗.我们获得了一些可容许性和最小性结果，以估计所判定的更有效治疗的平均效果。最大似然估计器显示为minimax且可允许。我们证明了所选治疗均值的均匀最小方差条件无偏估计器（UMVCUE）是不可接受的，并获得了改进的估计器。在这个过程中,我们还得出了任意位置和置换等变估计器不可接受性的充分条件，并在某些情况下提供了主导估计器，在满足这个充分条件的情况下。通过仿真研究比较了各种竞争估计器的均方误差和偏差性能。为了说明的目的,还提供了真实的数据示例。
