Department of Clinical Sciences, UT Southwestern Medical Center, Dallas, TX 75390, USA.
Contemp Clin Trials. 2011 May;32(3):412-7. doi: 10.1016/j.cct.2011.01.002. Epub 2011 Jan 15.
In many studies, investigators have perceived the number of repeated measurements as a fixed design characteristic. However, the number of repeated measurements is a design choice that can be informed by statistical considerations. In this paper, we investigate how the number of repeated measurements affects the required sample size in longitudinal studies with scheduled assessment times and a fixed total duration. It is shown that the required sample size always decreases as the number of measurements per subject increases under the compound symmetry (CS) correlation. The magnitude of sample size reduction, however, quickly shrinks to less than 5% when the number of measurements per subject increases beyond 4. We then reveal a counterintuitive property of the AR(1) correlation structure, under which making additional measurements from each subject might increase the sample size requirement. This observation suggests that practitioners should be cautious about assuming the AR(1) model in repeated measurements studies, whether in experimental design or in data analysis. Finally, we show that by introducing measurement error into the AR(1) model, the counterintuitive behavior disappears. That is, additional measurements per subject result in reduced sample sizes.
在许多研究中，研究人员将重复测量的次数视为固定的设计特征。然而，重复测量的次数是一个设计选择，可以根据统计考虑来确定。在本文中，我们研究了在具有预定评估时间和固定总持续时间的纵向研究中，重复测量的次数如何影响所需的样本量。结果表明，在复合对称（CS）相关下，随着每个受试者的测量次数增加，所需的样本量总是减少。然而，当每个受试者的测量次数增加到 4 次以上时，样本量减少的幅度迅速缩小到 5%以下。然后，我们揭示了 AR(1)相关结构的一个反直觉性质，即在每个受试者中进行额外的测量可能会增加样本量需求。这一观察结果表明，无论在实验设计还是数据分析中，从业者在重复测量研究中都应谨慎假设 AR(1)模型。最后，我们表明，通过在 AR(1)模型中引入测量误差，反直觉行为消失。也就是说，每个受试者的额外测量会减少样本量。
