Finite-sample corrected generalized estimating equation of population average treatment effects in stepped wedge cluster randomized trials

Abstract

Stepped wedge designs are increasingly commonplace and advantageous for cluster randomized trials (CRTs) when it is both unethical to assign placebo and it is logistically difficult to allocate an intervention simultaneously to many clusters. We study marginal mean models fit with generalized estimating equations (GEE) for assessing treatment effectiveness in stepped wedge CRTs. This approach has advantages over the more commonly used mixed models that (1) the population-average parameters have an important interpretation for public health applications and (2) they avoid untestable assumptions on latent variable distributions and avoid parametric assumptions about error distributions, therefore providing more robust evidence on treatment effects. However, CRTs typically have a small number of clusters, rendering the standard GEE sandwich variance estimator biased and highly variable and hence yielding incorrect inferences. We study the usual asymptotic GEE inferences (i.e., using sandwich variance estimators and asymptotic normality) and four small-sample corrections to GEE for stepped wedge CRTs and for parallel CRTs as a comparison. We show by simulation that the small-sample corrections provide improvement, with one correction appearing to provide at least nominal coverage even with only 10 clusters per group. These results demonstrate the viability of the marginal mean approach for both stepped wedge and parallel CRTs. We also study the comparative performance of the corrected methods for stepped wedge and parallel designs, and describe how the methods can accommodate interval censoring of individual failure times and incorporate semiparametric efficient estimators.

A comparison of bias‐corrected empirical covariance estimators with generalized estimating equations in small‐sample longitudinal study settings

“…Additionally, with use of MBN, we observe overly conservative type I error rates in some settings and liberal type I error rates in other settings. In many settings, we observe similar inference with KC and FG, as is consistent with previous literature . We note in our results that we find FG SEs and type I error rates to be slightly more liberal in certain settings for Scenarios 2 and 3 and use of KC to more often result in empirical type I error rates within the desired range.…”

Improved standard error estimator for maintaining the validity of inference in cluster randomized trials with a small number of clusters

“…While test sizes are very similar for the degrees of freedom approach for the KC and FG estimators, test sizes differ with the PW degrees of freedom approach. We note that although the two estimators are similar analytically, computation of the KC and FG estimators involve inversions of different matrices, and as matrices for the FG estimator typically have lower dimensions, results can be more stable (Scott et al., ). We note our findings deviate from previous literature, as Li and Redden () found the FG correction to work well and be preferable relative to the KC correction for larger levels of cluster variation ( 0.6).…”

“…Furthermore, the Fay and Graubard () bias‐corrected SE estimator has previously been found to perform similarly to the bias‐corrected SE estimator proposed by Kauermann and Carroll () (Morel and Neerchal, ) and identically in some balanced situations (SAS Institute Inc., ). A modified version of the Fay and Graubard () estimator (Ziegler, ) has been shown to be analytically equivalent to the Kauermann and Carroll () estimator (Scott et al., ). Li and Redden () conducted a simulation study in CRT settings in which a marginal logistic regression model with a trial arm indicator as the only covariate was utilized and found that the correction of Kauermann and Carroll () for empirical SE estimation is preferable for small to moderate variations in cluster size, that is a coefficient of variation () of 0.5 or less, but suggested that the Fay and Graubard () correction is preferable for higher cluster size values.…”

Current issues in the design and analysis of stepped wedge trials

“…Model based approaches include generalized linear mixed models (glmm) (Hussey & Hughes, 2007) or generalized estimating equations (gee) (Scott et al, 2015). …”

“…This can be accomplished by extending model (1) to $$Y_{ijk}=\mu +{\alpha }_i+{\beta }_j+L_{ij\ell }{\theta }_{\ell }+e_{ijk}$$ where ℓ is the number of time steps since the intervention was introduced (ℓ = 0 for control intervals, ℓ = 1 in the time step in which the intervention is introduced, ℓ ≤ T − 1) (Scott et al, 2015). Setting L ij ℓ = 1 if the j th time interval in the i th cluster is ℓ (≥ 1) intervals since the introduction of the intervention and 0 otherwise provides an estimate of the time-on-treatment effects, θ ℓ .…”