Department of Mathematics & Statistics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India.
J Biopharm Stat. 2024 Mar;34(2):164-189. doi: 10.1080/10543406.2023.2183962. Epub 2023 Mar 5.
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 available treatments. The most effective treatment is adjudged based on numerical values of some statistic corresponding to the 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 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 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.
在临床研究中，一个常见的问题是估计可用治疗方法中最有效的治疗方法（例如，均值最大的治疗方法）的效果。最有效的治疗方法是根据与治疗方法相对应的某些统计量的数值来判断。对于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，将两种治疗方法独立地施用于每个 个受试者，然后选择样本均值较大的治疗方法。为了研究被判定为更有效的治疗方法的效果（即估计其均值），我们考虑两阶段 DLD，在设计的第二阶段，进一步对 个受试者施用被判定为更有效的治疗方法。我们获得了一些用于估计被判定为更有效的治疗方法的平均效果的可接受性和最小最大结果。最大似然估计量被证明是最小最大和可接受的。我们表明，所选治疗方法均值的一致最小方差条件无偏估计量（UMVCUE）是不可接受的，并获得了改进的估计量。在此过程中，我们还为任意位置和置换不变估计量的不可接受性推导了一个充分条件，并在满足此充分条件的情况下提供了支配估计量。通过模拟研究比较了各种竞争估计量的均方误差和偏差性能。还提供了一个真实数据示例来说明。
