估计的和理论的保证以及启动Ⅲ期试验的概率  

The Estimated and Theoretical Assurances and the Probabilities of Launching a PhaseⅢTrial

作　　者：张应应 荣腾中[1,2] 李曼曼 ZHANG Yingying;RONG Tengzhong;LI Manman(Department of Statistics and Actuarial Science,Chongqing University,Chongqing,401331,China;Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing University,Chongqing,401331,China)

机构地区：[1]重庆大学统计与精算学系,重庆401331 [2]重庆大学分析数学与应用重庆市重点实验室,重庆401331

出　　处：《应用概率统计》2022年第1期53-70,共18页Chinese Journal of Applied Probability and Statistics

基　　金：The research was supported by the Ministry of Education(MOE)project of Humanities and Social Sciences on the west and the border area(Grant Nos.20XJC910001,14XJC910001);the National Social Science Fund of China(Grant No.21XTJ001);the National Natural Science Foundation of China(Grant Nos.12001068,11671060).

摘　　要：预期的Ⅱ期试验通常会导致Ⅲ期试验失败.对于随机分为两个治疗组的随机对照的Ⅱ期和Ⅲ期试验,在假设正态分布响应的方差已知的情况下,我们解析性地获得了这三种情况下的估计的和理论的保证(无、加性和乘性偏差调整).在一些较小的假设下,我们证明了对这三种情况下的估计保证分别是Ⅱ期试验的每组患者数和Ⅱ期试验观察到的治疗效果的增加函数;对于情况三,估计的保证是保留因子的增加函数.当Ⅲ期试验的实际处理效果假定为已知常数时,我们证明,这三种情况的理论保证是常数,等于设计功率或1减去Ⅱ型误差.此外,我们还表明,估计的保证总是小于理论的保证.我们还得到了三种情况下启动Ⅲ期研究的概率的解析公式.此外,对于情况三,我们表明启动Ⅲ期研究的概率是保留因子的一个增加函数.根据我们的理论研究,我们发现Ⅲ期的真实处理效果在模拟中没有影响.最后,通过仿真对理论研究进行了说明.Prospective phaseⅡtrials usually result in failures in phaseⅢtrials.For randomized controlled phaseⅡand phaseⅢtrials which are conducted with patients randomized to one of two treatments where the variances of the normally distributed responses are assumed to be known,we analytically obtain the estimated and theoretical assurances for the three cases(no,additive,and multiplicative bias adjustments).Under some minor assumptions,we show that the estimated assurances for the three cases are increasing functions of the per group number of patients and the observed treatment effect of the phaseⅡtrial,respectively;and for Case 3,the estimated assurance is an increasing function of the retention factor.When the true treatment effect of phaseⅢis assumed to be a known constant,we show that the theoretical assurances for the three cases are constants which are equal to the designed power or one minus the typeⅡerror.Moreover,we show that the estimated assurances are always less than the theoretical assurance.We also obtain the analytical formulas of the probabilities of launching a phaseⅢstudy for the three cases.Moreover,for Case 3,we show that the probability of launching a phaseⅢstudy is an increasing function of the retention factor.According to our theoretical investigations,we find that the true treatment effect of phaseⅢhas no effect in the simulations.Finally,the simulations are conducted to illustrate the theoretical investigations.

关 键 词：第Ⅱ/Ⅲ期临床试验 成功概率 保证 启动标准 通过/不通过的决定 

分 类 号：O212[理学—概率论与数理统计]