Julious Steven A, McIntyre Nikki E
University of Sheffield-Medical Statistics Group, Health Services Research, ScHARR University of Sheffield, Regent Court, 30 Regent Steet, Sheffield, Yorkshire S14DA, United Kingdom.
Pharm Stat. 2012 Mar-Apr;11(2):177-85. doi: 10.1002/pst.515. Epub 2012 Mar 1.
In Clinical trials involving multiple comparisons of interest, the importance of controlling the trial Type I error is well-understood and well-documented. Moreover, when these comparisons are themselves correlated, methodologies exist for accounting for the correlation in the trial design, when calculating the trial significance levels. However, less well-documented is the fact that there are some circumstances where multiple comparisons affect the Type II error rather than the Type I error, and failure to account for this, can result in a reduction in the overall trial power. In this paper, we describe sample size calculations for clinical trials involving multiple correlated comparisons, where all the comparisons must be statistically significant for the trial to provide evidence of effect, and show how such calculations have to account for multiplicity in the Type II error. For the situation of two comparisons, we provide a result which assumes a bivariate Normal distribution. For the general case of two or more comparisons we provide a solution using inflation factors to increase the sample size relative to the case of a single outcome. We begin with a simple case of two comparisons assuming a bivariate Normal distribution, show how to factor in correlation between comparisons and then generalise our findings to situations with two or more comparisons. These methods are easy to apply, and we demonstrate how accounting for the multiplicity in the Type II error leads, at most, to modest increases in the sample size.
在涉及多个感兴趣比较的临床试验中，控制试验I型错误的重要性已得到充分理解和记录。此外，当这些比较本身存在相关性时，在计算试验显著性水平时，存在一些方法可用于在试验设计中考虑相关性。然而，记录较少的一个事实是，在某些情况下，多重比较会影响II型错误而非I型错误，若未考虑这一点，可能会导致整体试验效能降低。在本文中，我们描述了涉及多个相关比较的临床试验的样本量计算方法，其中所有比较都必须具有统计学显著性，试验才能提供效应证据，并展示了此类计算如何考虑II型错误中的多重性。对于两个比较的情况，我们给出了一个假设二元正态分布的结果。对于两个或更多比较的一般情况，我们提供了一种使用膨胀因子的解决方案，以相对于单个结果的情况增加样本量。我们从假设二元正态分布的两个比较的简单情况开始，展示如何考虑比较之间的相关性，然后将我们的发现推广到两个或更多比较的情况。这些方法易于应用，并且我们展示了考虑II型错误中的多重性最多只会导致样本量适度增加。
