Maintaining the validity of inference in small‐sample stepped wedge cluster randomized trials with binary outcomes when using generalized estimating equations

Abstract

Stepped wedge cluster trials are an increasingly popular alternative to traditional parallel cluster randomized trials. Such trials often utilize a small number of clusters and numerous time intervals, and these components must be considered when choosing an analysis method. A generalized linear mixed model containing a random intercept and fixed time and intervention covariates is the most common analysis approach. However, the sole use of a random intercept applies a constant intraclass correlation coefficient structure, which is an assumption that is likely to be violated given stepped wedge trials (SWTs) have multiple time intervals. Alternatively, generalized estimating equations (GEE) are robust to the misspecification of the working correlation structure, although it has been shown that small‐sample adjustments to standard error estimates and the use of appropriate degrees of freedom are required to maintain the validity of inference when the number of clusters is small. In this article, we show, using an extensive simulation study based on a motivating example and a more general design, the use of GEE can maintain the validity of inference in small‐sample SWTs with binary outcomes. Furthermore, we show which combinations of bias corrections to standard error estimates and degrees of freedom work best in terms of attaining nominal type I error rates.

Sample size and power considerations for cluster randomized trials with count outcomes subject to right truncation

“…Ford and Westgate (2017) further considered a hybrid bias‐correction that averages the MD and KC standard errors and found the ‐test with this new standard error maintains valid type I error rate under variable cluster sizes with both continuous and binary outcomes. The adequate performance on type I error of this hybrid bias‐correction has also been observed in simulations with more complex stepped wedge designs (Ford & Westgate, 2020). We will also examine whether the average MD/KC standard error (abbreviated as AVG) has adequate performance in our simulation scenario with clustered counts.…”

Randomization‐based inference for a marginal treatment effect in stepped wedge cluster randomized trials

“…For example, GEEs may be advantageous in settings where the underlying correlation structure is impacted by treatment assignment, since our randomization‐based method relies on such features being unaffected by the intervention, whereas GEEs do not. However, valid GEE‐based inference requires either a large number of clusters or an appropriate small‐sample adjustment, the latter of which is complicated by the fact that the performance of different adjustment methods can vary depending on attributes of the trial, such as cluster size variability 14‐17 . As we presented in Section 2.3, randomization‐based inference may have the advantage over GEE in terms of it naturally accounting for design features in the analysis without requiring additional covariates being introduced into the regression model, thus, maintaining a nonstratified marginal target of inference.…”

Methods for dealing with unequal cluster sizes in cluster randomized trials: A scoping review

“…In terms of applying GEE to binary outcomes, Li et al [87] proposed an efficient estimating equations approach to analyze cluster-period means which requires less computation time and showed that when the number of clusters is limited and cluster sizes are unequal, the proposed matrix-adjusted estimating equations can still substantially improve the coverage of the correlations parameters. Both Thompson et al [88] and Ford and Westgate [89] conducted large simulation studies to compare small-sample standard-error corrections such as Fay and Graubard (FG); Mancl and DeRouen (MD); Kauermann and Carroll (KC) etc. for GEE when cluster sizes vary and the number of clusters is small.…”