基于内部预试验的样本量重估计在成组序贯设计中的应用研究

Application Study of Sample Size Re-estimation based on Internal Pilot Study in Group Sequential Design

目的使用内部预试验解决成组序贯设计中方差未知时样本量估计的问题,同时得出内部预试验适宜的样本量。方法以两样本均数比较的优效性检验为分析目的,利用损耗函数法在拒绝型成组序贯设计下,通过设定不同的内部预试验样本量、方差真实值和方差估计值,计算方差重估法的Ι类错误、功效Power和平均样本量。结果方差估计正确时,方差重估法能控制Ι类错误,功效和平均样本量随着内部预试验样本量n 0的增加而增加,当n 0≥20时能获得较好的功效和适宜的平均样本量;方差估计错误时,方差重估法同样能控制Ι类错误且不会出现传统成组序贯设计中功效过高或过低的情况,当标准差估计值s为10,标准差真实值σ分别为6、8、12和14时,该方法的功效分别为0.895、0.886、0.887和0.887。结论方差重估法能有效解决成组序贯设计中方差未知的问题,避免了方差错误估计时导致的功效异常。

Objective Using internal pilot study(IPS)to solve the problem of sample size estimation in group sequential design with unknown variance and to obtain the appropriate sample size of IPS(n 0).Methods Aiming at the statistical superiority hypothesis test of two independent samples,under the condition of group sequential design of error spending approach with early stopping to reject the null hypothesis,the type I error,power and average sample number(ASN)of variance re-estimation method were calculated by means of adjusting n 0,the true variance(σ)and the estimate of variance(s).Results When the estimation of variance was unbiased,the type I errors of variance re-estimation method were controlled at around 0.05,and the power and ASN were up slightly with the increase of sample size of IPS.Under the condition of n 0≥20,appropriate power and ASN can be obtained.When the estimation of variance was biased,the type I errors of variance re-estimation method were controlled,and the desired power would be maintained at around 0.9.Under the condition that s was 10 and the true standard deviation was set at 6,8,12 and 14,the powers of this method were 0.895,0.886,0.887 and 0.887 respectively.Conclusion The variance re-estimation method can solve the problem of unknown variance in group sequential designs,and avoid the abnormality in power resulting from biased estimation of variance.