  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.
