Sample size determination for comparing several survival curves with unequal allocations
Sample size determination for comparing several survival curves with unequal allocations
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DOI：
10.1002/sim.1771
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发表时间：
2004-06-15
影响因子：
2
通讯作者：
Singh, B
中科院分区：
文献类型：
--
作者：
Halabi, S;Singh, B
Ahnn和安德森推导了未分层和分层设计的样本量公式，假设受试者平等分配至3个或更多治疗组。我们推广的样本量公式，允许不平等的分配。此外，我们将死亡的总体概率定义为1减去分层设计的删失比例。这个定义也导致了与Ahnn和安德森的分层情况下的非中心性参数的定义略有不同。假设比例风险，根据预先规定的把握度、显著性水平、风险比、受试者分配至多个治疗组和已知删失比例确定样本量。在比例风险设置中，考虑了三种情况：（1）指数失效-指数截尾，（2）指数失效-均匀截尾，和（3）威布尔失效（假设所有组的形状参数相同）-均匀截尾。在未分层病例的所有三种情况下，假设所有治疗组的删失分布相同。对于分层对数秩检验，假设治疗组和分层之间的删失分布相同。此外，公式已经开发，以提供近似的权力的测试，根据前两个或前四个时刻的渐近分布。我们观察到以下两个主要发现的基础上模拟。首先，对数秩检验的模拟功效不依赖于删失机制。其次，对于0.05的显著性水平和0.80的功效，所需的样本量n与删失模式无关。此外，当一系列替代品接近零假设时，精确（渐近）和模拟功效之间存在非常接近的一致性。二阶矩和四阶矩幂级数近似也产生与精确（渐近）幂密切一致的幂。在不平等分配的情况下，我们的模拟表明，当50%的患者被分配到风险最小的治疗组时，经验功效始终高于预先设定的功效0.80的目标值。版权所有（C）2004约翰威利父子有限公司。
Ahnn and Anderson derived sample size formulae for unstratified and stratified designs assuming equal allocation of subjects to three or more treatment groups. We generalize the sample size formulae to allow for unequal allocation. In addition, we define the overall probability of death to be equal to one minus the censored proportion for the stratified design. This definition also leads to a slightly different definition of the non-centrality parameter than that of Ahnn and Anderson for the stratified case. Assuming proportional hazards, sample sizes are determined for a prespecified power, significance level, hazard ratios, allocation of subjects to several treatment groups, and known censored proportion. In the proportional hazards setting, three cases are considered: (1) exponential failures-exponential censoring, (2) exponential failures-uniform censoring, and (3) Weibull failures (assuming same shape parameter for all groups)-uniform censoring. In all three cases of the unstratified case, it is assumed that the censoring distribution is the same for all of the treatment groups. For the stratified log-rank test, it is assumed the same censoring distribution across the treatment groups and the strata. Further, formulae have been developed to provide approximate powers for the test, based upon the first two or first four-moments of the asymptotic distribution.We observe the following two major findings based on the simulations. First, the simulated power of the log-rank test does not depend on the censoring mechanism. Second, for a significance level of 0.05 and power of 0.80, the required sample size n is independent of the censoring pattern. Moreover, there is very close agreement between the exact (asymptotic) and simulated powers when a sequence of alternatives is close to the null hypothesis. Two-moment and four-moment power series approximations also yield powers in close agreement with the exact (asymptotic) power. With unequal allocations, our simulations show that the empirical powers are consistently above the target value of prespecified power of 0.80 when 50 per cent of the patients are allocated to the treatment group with the smallest hazard. Copyright (C) 2004 John Wiley Sons, Ltd.