Department of Medicine, School of Medicine, University of Alabama, Birmingham, AL, USA.
Clin Trials. 2011 Feb;8(1):27-36. doi: 10.1177/1740774510391492. Epub 2010 Dec 16.
The statistical power of cluster randomized trials depends on two sample size components, the number of clusters per group and the numbers of individuals within clusters (cluster size). Variable cluster sizes are common and this variation alone may have significant impact on study power. Previous approaches have taken this into account by either adjusting total sample size using a designated design effect or adjusting the number of clusters according to an assessment of the relative efficiency of unequal versus equal cluster sizes.
This article defines a relative efficiency of unequal versus equal cluster sizes using noncentrality parameters, investigates properties of this measure, and proposes an approach for adjusting the required sample size accordingly.
We focus on comparing two groups with normally distributed outcomes using t-test, and use the noncentrality parameter to define the relative efficiency of unequal versus equal cluster sizes and show that statistical power depends only on this parameter for a given number of clusters. We calculate the sample size required for an unequal cluster sizes trial to have the same power as one with equal cluster sizes.
Relative efficiency based on the noncentrality parameter is straightforward to calculate and easy to interpret. It connects the required mean cluster size directly to the required sample size with equal cluster sizes. Consequently, our approach first determines the sample size requirements with equal cluster sizes for a pre-specified study power and then calculates the required mean cluster size while keeping the number of clusters unchanged. Our approach allows adjustment in mean cluster size alone or simultaneous adjustment in mean cluster size and number of clusters, and is a flexible alternative to and a useful complement to existing methods. Comparison indicated that we have defined a relative efficiency that is greater than the relative efficiency in the literature under some conditions.
Our measure of relative efficiency might be less than the measure in the literature under some conditions, underestimating the relative efficiency.
The relative efficiency of unequal versus equal cluster sizes defined using the noncentrality parameter suggests a sample size approach that is a flexible alternative and a useful complement to existing methods.
群组随机试验的统计功效取决于两个样本量组成部分，即每组的群组数量和群组内的个体数量（群组大小）。可变群组大小很常见，仅这种变化就可能对研究功效产生重大影响。以前的方法通过使用指定的设计效应调整总样本量，或者根据对不等效与等效群组大小的相对效率的评估来调整群组数量，从而考虑到这一点。
本文使用非中心参数定义不等效与等效群组大小的相对效率，研究该度量的性质，并提出相应的方法来调整所需的样本量。
我们专注于使用 t 检验比较两组正态分布的结果，并使用非中心参数定义不等效与等效群组大小的相对效率，并表明对于给定数量的群组，统计功效仅取决于该参数。我们计算了具有不等群组大小的试验所需的样本量，以使等效群组大小的试验具有相同的功效。
基于非中心参数的相对效率计算简单，易于解释。它将所需的平均群组大小直接与等效群组大小的所需样本量联系起来。因此，我们的方法首先确定了具有指定研究功效的等效群组大小的样本量要求，然后在保持群组数量不变的情况下计算所需的平均群组大小。我们的方法允许单独调整平均群组大小或同时调整平均群组大小和群组数量，是现有方法的灵活替代方法，也是有用的补充。比较表明，在某些条件下，我们定义的相对效率大于文献中的相对效率。
在某些条件下，我们的相对效率衡量标准可能小于文献中的衡量标准，从而低估了相对效率。
使用非中心参数定义的不等效与等效群组大小的相对效率表明，样本量方法是现有方法的灵活替代方法，也是有用的补充。
