Linear mixed models are commonly used in analyzing stepped-wedge cluster randomized trials (SW-CRTs). A key consideration for analyzing a SW-CRT is accounting for the potentially complex correlation structure, which can be achieved by specifying a random effects structure. Common random effects structures for a SW-CRT include random intercept, random cluster-by-period, and discrete-time decay. Recently, more complex structures, such as the random intervention structure, have been proposed. In practice, specifying appropriate random effects can be challenging. Robust variance estimators (RVE) may be applied to linear mixed models to provide consistent estimators of standard errors of fixed effect parameters in the presence of random-effects misspecification. However, there has been no empirical investigation of RVE for SW-CRT. In this paper, we first review five RVEs (both standard and small-sample bias-corrected RVEs) that are available for linear mixed models. We then describe a comprehensive simulation study to examine the performance of these RVEs for SW-CRTs with a continuous outcome under different data generators. For each data generator, we investigate whether the use of a RVE with either the random intercept model or the random cluster-by-period model is sufficient to provide valid statistical inference for fixed effect parameters, when these working models are subject to misspecification. Our results indicate that the random intercept and random cluster-by-period models with RVEs performed similarly. The CR3 RVE estimator, coupled with the number of clusters minus two degrees of freedom correction, consistently gave the best coverage results, but could be slightly anti-conservative when the number of clusters was below 16. We summarize the implications of our results for linear mixed model analysis of SW-CRTs in practice.

翻译：线性混合模型常用于分析阶梯楔形集群随机试验（SW-CRTs）。分析SW-CRT的一个关键考虑因素是处理潜在复杂的相关结构，这可以通过指定随机效应结构来实现。SW-CRT常见的随机效应结构包括随机截距、随机集群-时间交互以及离散时间衰减。最近，更复杂的结构（如随机干预结构）已被提出。在实践中，指定合适的随机效应可能具有挑战性。稳健方差估计（RVE）可应用于线性混合模型，以在随机效应误指定情况下提供固定效应参数标准误的一致估计。然而，目前尚无针对SW-CRT的RVE实证研究。本文首先回顾了线性混合模型可用的五种RVE（包括标准RVE和小样本偏差校正RVE）。随后，我们描述了一项全面的模拟研究，以检验这些RVE在不同数据生成机制下对连续结局SW-CRT的性能表现。针对每种数据生成机制，我们探讨了在随机截距模型或随机集群-时间交互模型存在误指定时，使用RVE是否足以对固定效应参数提供有效的统计推断。结果表明，结合RVE的随机截距模型和随机集群-时间交互模型表现相似。CR3型RVE估计量配合集群数减二自由度校正后，始终给出最佳的覆盖率结果，但当集群数低于16时可能略微偏保守。我们总结了这些结果对实践中SW-CRT线性混合模型分析的启示意义。