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

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.

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

Data arising from longitudinal studies are commonly analyzed with generalized estimating equations. Previous literature has shown that liberal inference may result from the use of the empirical sandwich covariance matrix estimator when the number of subjects is small. Therefore, two different approaches have been used to improve the validity of inference. First, many different small-sample corrections to the empirical estimator have been offered in order to reduce bias in resulting standard error estimates. Second, critical values can be obtained from a t-distribution or an F-distribution with approximated degrees of freedom. Although limited studies on the comparison of these small-sample corrections and degrees of freedom have been published, there is a need for a comprehensive study of currently existing methods in a wider range of scenarios. Therefore, in this manuscript, we conduct such a simulation study, finding two methods to attain nominal type I error rates more consistently than other methods in a variety of settings: First, a recently proposed method by Westgate and Burchett (2016, Statistics in Medicine 35, 3733-3744) that specifies both a covariance estimator and degrees of freedom, and second, an average of two popular corrections developed by Mancl and DeRouen (2001, Biometrics 57, 126-134) and Kauermann and Carroll (2001, Journal of the American Statistical Association 96, 1387-1396) with degrees of freedom equaling the number of subjects minus the number of parameters in the marginal model.

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

Cluster randomized trials (CRTs) are studies in which clusters of subjects are randomized to different trial arms. Due to the nature of outcomes within the same cluster to be correlated, generalized estimating equations (GEE) are growing as a popular choice for the analysis of data arising from CRTs. In the past, research has shown that analyses using GEE could result in liberal inference due to the use of the empirical sandwich covariance matrix estimator, which can yield negatively biased standard error estimates when the number of clusters is not large. Many techniques have been presented to correct this negative bias; however, use of these corrections can still result in biased standard error estimates and thus test sizes that are not consistently at their nominal level. Therefore, there is a need for an improved correction such that nominal type I error rates will consistently result. In this manuscript, we study the use of recently developed corrections for empirical standard error estimation and the use of a combination of two popular corrections. In an extensive simulation study, we found that nominal type I error rates can be consistently attained when using an average of two popular corrections developed by Mancl and DeRouen (, Biometrics 57, 126-134) and Kauermann and Carroll (, Journal of the American Statistical Association 96, 1387-1396). Therefore, use of this new correction was found to notably outperform the use of previously recommended corrections.