Rezaei-Darzi Ehsan, Grantham Kelsey L, Forbes Andrew B, Kasza Jessica
School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia.
BMC Med Res Methodol. 2025 May 10;25(1):127. doi: 10.1186/s12874-025-02567-5.
Staircase designs are incomplete stepped wedge designs that, unlike standard stepped wedge designs, require clusters to contribute data for only a limited number of trial periods. Previous work has provided formulae based on asymptotic results for the calculation of the power of staircase designs to detect treatment effects of interest.
We conduct a simulation study to assess the finite sample performance of these formulae, and the impact of misspecifying the correlation structure when analysing data from staircase designs on inference for the treatment effect, under a range of realistic trial settings. This study focuses on basic staircase designs with one control period followed by one intervention period in each sequence. We simulate staircase trial datasets with continuous outcomes and a repeated cross-sectional measurement scheme under exchangeable and block-exchangeable intracluster correlation structures, and then fit linear mixed models with linear and categorical time period effects. For settings with a small number of clusters, Kenward-Roger and Satterthwaite small-sample corrections are applied. Comparisons are made between nominal and observed Type I error rates, and theoretically-derived study power and empirical power. The impact on inference for the treatment effect when misspecifying the intracluster correlation structure is assessed through considering performance metrics including bias and 95% confidence interval coverage.
Data analysis assuming an exchangeable correlation structure and application of the Satterthwaite correction controls Type I error well when the correlation structure is correctly specified, and there are a sufficient number of clusters. For the true block-exchangeable model, when fitting the correct model with the Satterthwaite correction, the observed Type I error (empirical power) can be higher (lower) than the nominal (i.e., theoretical) value when there is only 1 cluster per sequence, but otherwise, it aligns well with the nominal (theoretical) value. Misspecification of the correlation structure (fitting an exchangeable model when the true structure is block-exchangeable) can lead to inflated Type I error and poor confidence interval coverage.
Staircase designs with one cluster per sequence should be used with caution. Additionally, using a correlation structure that allows for decay is preferable for making valid inferences for the estimation of the treatment effect.
阶梯设计是不完整的阶梯楔形设计，与标准阶梯楔形设计不同，它要求群组仅在有限数量的试验期内提供数据。先前的工作已经给出了基于渐近结果的公式，用于计算阶梯设计检测感兴趣治疗效果的功效。
我们进行了一项模拟研究，以评估这些公式在有限样本情况下的性能，以及在一系列实际试验设置下，分析阶梯设计数据时错误指定相关结构对治疗效果推断的影响。本研究聚焦于每个序列有一个对照期后接一个干预期的基本阶梯设计。我们在可交换和块可交换的组内相关结构下，模拟具有连续结局和重复横断面测量方案的阶梯试验数据集，然后拟合具有线性和分类时间段效应的线性混合模型。对于群组数量较少的设置，应用肯沃德 - 罗杰和萨特思韦特小样本校正。比较名义和观察到的I型错误率，以及理论推导的研究功效和实证功效。通过考虑包括偏差和95%置信区间覆盖率在内的性能指标，评估错误指定组内相关结构时对治疗效果推断的影响。
当相关结构正确指定且有足够数量的群组时，假设可交换相关结构并应用萨特思韦特校正进行数据分析能很好地控制I型错误。对于真正的块可交换模型，当使用萨特思韦特校正拟合正确模型时，每个序列只有1个群组时，观察到的I型错误（实证功效）可能高于（低于）名义（即理论）值，但在其他情况下，它与名义（理论）值吻合良好。相关结构的错误指定（当真实结构是块可交换时拟合可交换模型）可能导致I型错误膨胀和置信区间覆盖率不佳。
每个序列有1个群组的阶梯设计应谨慎使用。此外，使用允许衰减的相关结构对于对治疗效果估计进行有效推断更可取。
