Heo Moonseong, Kim Namhee, Rinke Michael L, Wylie-Rosett Judith
1 Department of Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, NY, USA.
2 Department of Radiology, Albert Einstein College of Medicine, Bronx, NY, USA.
Stat Methods Med Res. 2018 Feb;27(2):480-489. doi: 10.1177/0962280216632564. Epub 2016 Mar 17.
Stepped-wedge (SW) designs have been steadily implemented in a variety of trials. A SW design typically assumes a three-level hierarchical data structure where participants are nested within times or periods which are in turn nested within clusters. Therefore, statistical models for analysis of SW trial data need to consider two correlations, the first and second level correlations. Existing power functions and sample size determination formulas had been derived based on statistical models for two-level data structures. Consequently, the second-level correlation has not been incorporated in conventional power analyses. In this paper, we derived a closed-form explicit power function based on a statistical model for three-level continuous outcome data. The power function is based on a pooled overall estimate of stratified cluster-specific estimates of an intervention effect. The sampling distribution of the pooled estimate is derived by applying a fixed-effect meta-analytic approach. Simulation studies verified that the derived power function is unbiased and can be applicable to varying number of participants per period per cluster. In addition, when data structures are assumed to have two levels, we compare three types of power functions by conducting additional simulation studies under a two-level statistical model. In this case, the power function based on a sampling distribution of a marginal, as opposed to pooled, estimate of the intervention effect performed the best. Extensions of power functions to binary outcomes are also suggested.
阶梯楔形（SW）设计已在各种试验中稳步实施。SW设计通常假定为三级分层数据结构，其中参与者嵌套在时间或时期内，而时间或时期又嵌套在群组中。因此，用于分析SW试验数据的统计模型需要考虑两种相关性，即一级相关性和二级相关性。现有的功效函数和样本量确定公式是基于二级数据结构的统计模型推导出来的。因此，二级相关性未纳入传统的功效分析中。在本文中，我们基于三级连续结局数据的统计模型推导了一个封闭形式的显式功效函数。该功效函数基于干预效应的分层群组特定估计的合并总体估计。合并估计的抽样分布是通过应用固定效应荟萃分析方法推导出来的。模拟研究验证了所推导的功效函数是无偏的，并且可适用于每个群组每个时期不同数量的参与者。此外，当假设数据结构为两级时，我们在两级统计模型下通过进行额外的模拟研究来比较三种类型的功效函数。在这种情况下，基于干预效应的边际估计（而非合并估计）的抽样分布的功效函数表现最佳。还提出了将功效函数扩展到二元结局的方法。
