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聚类随机试验（SW-CRT）。分析SW-CRT的关键在于考虑可能复杂的相关结构，这可通过指定随机效应结构实现。SW-CRT常见的随机效应结构包括随机截距、随机聚类-时段和离散时间衰减。近期，更复杂的结构如随机干预结构已被提出。实践中，恰当指定随机效应具有挑战性。稳健方差估计量（RVE）可应用于线性混合模型，在随机效应误设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中RVE的实证研究。本文首先回顾了五种适用于线性混合模型的RVE（包括标准RVE和小样本偏差校正RVE），继而通过全面的模拟研究，考察这些RVE在不同数据生成机制下对连续结局的SW-CRT的性能表现。针对每种数据生成机制，我们探究了当工作模型（随机截距模型或随机聚类-时段模型）存在误设时，使用RVE是否能提供固定效应参数的有效统计推断。结果表明，采用RVE的随机截距模型与随机聚类-时段模型性能相似。CR3型RVE估计量结合聚类数减二自由度校正始终获得最佳覆盖率，但当聚类数低于16时可能出现轻微反保守。我们总结了这些结果对实际SW-CRT线性混合模型分析的意义。