P值合并法中基于有效终止概率的适应性样本量调整的优化研究

Optimization Study of Adaptive Sample-Size Re-estimation based on Efficacy Stopping Probability in Methods with Combination of P-values

目的 在P值合并法中,本文对三阶段适应性样本量调整(sample-size re-estimation, SSR)进行权重优化并基于有效终止概率(efficacy stopping probability, ESP)选择最优的设计方案。方法 以两样本均数比较的优效性检验为分析目的,在三阶段SSR下,采用基于P值之和的方法,通过设定不同的样本量分配权重、每阶段的有效终止概率、设计参数及对应低估的实际模拟参数,计算得到在不同ESP组合下的最优样本量分配权重及相应的最大功效和平均样本量(average sample number, ASN)。结果 SSR在不同的第二阶段有效终止概率(ESP_(2))下存在不同的最大功效;设定第一阶段有效终止概率(ESP1)为0.10,无论原设计及实际模拟参数为多少,ESP_(2)在0.15~0.45的范围内均能获得较好且相近的最大功效,并随着ESP_(2)的增大,相应的ASN先递减而后趋于平稳或平稳上升,其中最优设计的ESP1、ESP_(2)和ESP3分别为0.10、0.45和0.35;在ESP1设定为0.1和0.2条件下,最大功效的变化范围不同,前者最大功效的极差为1.8%,后者为5.7%。结论 三阶段适应性样本量调整在ESP1不确定的情况下,为了降低ESP_(2)的选择对试验功效的影响,建议设定较小的ESP1;当确定ESP1后,可根据实际数据模拟得到较优的ESP_(2),使设计能获得较好的功效和适宜的ASN。

Objective In the methods with combination of P-values,this paper aims to optimize the weight of sample-size allocation for the three-stage adaptive sample-size re-estimation(SSR)method and then select the optimal design based on the efficacy stopping probability(ESP).Methods Aiming at the superiority hypothesis test of two independent samples,the method with the sum of P-values was used in the three-stage adaptive sample-size re-estimation.Then the optimal weight of sample-size allocation,the corresponding power and average sample number(ASN)were calculated under the condition of different combinations of ESP by means of adjusting the weights of sample-size allocation,the ESP at each stage,the parameters of original design and its corresponding underestimated parameters in actual simulations.Results SSR had different maximum powers in the condition of different ESPs at stage 2;when the ESP 1(ESP at stage 1)was 0.1 and the ESP_(2)(ESP at stage 2)was in the range of 0.15~0.45,we could obtain similar optimal powers.Meanwhile,with the increase of the ESP_(2),the corresponding ASN started to decrease and then tended to be stable or rise steadily.Accordingly,the ESP 1,ESP_(2) and ESP 3 of the optimal design were 0.10,0.45 and 0.35 respectively.Furthermore,when ESP 1 was set at 0.1 and 0.2,maximum power fluctuated differently;the maximum power′s range of the former was 1.8%and that of the latter was 5.7%.Conclusion When the ESP 1 is uncertain in the three-stage adaptive sample-size re-estimation,it is suggested to choose the smaller ESP 1 in order to reduce the influence of ESP_(2) on the power of trial;when ESP 1 is specified,the optimal ESP_(2) can be obtained from the actual data so that the design has appropriate power and ASN.