A note on the power of Fisher's least significant difference procedure
A note on the power of Fisher's least significant difference procedure
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DOI：
10.1002/pst.210
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发表时间：
2006-10-01
影响因子：
1.5
通讯作者：
Meier, Ulrich
中科院分区：
文献类型：
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作者：
Meier, Ulrich
Fisher 的最小显着差异 (LSD) 程序是一种两步测试程序，用于对多个治疗组进行成对比较。在该过程的第一步中，对零假设进行全局检验，即所研究的所有治疗组的预期平均值相等。如果可以在预先指定的显着性水平上拒绝该全局零假设，则在该过程的第二步中，原则上允许在相同的显着性水平上执行所有成对比较（尽管在实践中，并非所有成对比较都可能是主要兴趣）。众所周知，当（且仅当）治疗组的数量为 3 时，Fisher LSD 程序可将实验 I 类错误率保持在名义显着性水平。因此，该程序可应用于在验证性意义上比较两种剂量的活性治疗与安慰剂的 III 期临床试验（而在这种情况下，无需在两个活性治疗组之间进行验证性比较）。本文研究了这种方法的功率特性。结果表明，第一步整体测试的功效——以及整个程序的功效——可能相对低于更有利的活性剂量组和安慰剂之间的成对比较的功效。为了与 Fisher 的 LSD 程序进行比较，达到一定的总体功效（无论不利剂量组的效应大小如何），可能需要比简单 Bonferroni α 调整的研究规模稍大的治疗组。因此，如果使用 Fisher 的 LSD 程序来避免 III 期临床试验的 alpha 调整，则应在计划阶段考虑由于第一步全局测试而导致的潜在功效损失。版权所有 (C) 2006 John Wiley & Sons, Ltd.
Fisher's least significant difference (LSD) procedure is a two-step testing procedure for pairwise comparisons of several treatment groups. In the first step of the procedure, a global test is performed for the null hypothesis that the expected means of all treatment groups under study are equal. If this global null hypothesis can be rejected at the pre-specified level of significance, then in the second step of the procedure, one is permitted in principle to perform all pairwise comparisons at the same level of significance (although in practice, not all of them may be of primary interest). Fishers LSD procedure is known to preserve the experimentwise type I error rate at the nominal level of significance, if (and only if) the number of treatment groups is three. The procedure may therefore be applied to phase III clinical trials comparing two doses of an active treatment against placebo in the confirmatory sense (while in this case, no confirmatory comparison has to be performed between the two active treatment groups). The power properties of this approach are examined in the present paper. It is shown that the power of the first step global test - and therefore the power of the overall procedure - may be relevantly lower than the power of the pairwise comparison between the more-favourable active dose group and placebo. Achieving a certain overall power for this comparison with Fisher's LSD procedure - irrespective of the effect size at the less-favourable dose group - may require slightly larger treatment groups than sizing the study with respect to the simple Bonferroni alpha adjustment. Therefore if Fisher's LSD procedure is used to avoid an alpha adjustment for phase III clinical trials, the potential loss of power due to the first-step global test should be considered at the planning stage. Copyright (C) 2006 John Wiley & Sons, Ltd.