Robust analysis of stepped wedge trials using composite likelihood models

Stepped wedge trials (SWTs) are a type of cluster randomized trial that involve repeated measures on clusters and design-induced confounding between time and treatment. Although mixed models are commonly used to analyze SWTs, they are susceptible to misspecification particularly for cluster-longitudinal designs such as SWTs. Mixed model estimation leverages both "horizontal" or within-cluster information and "vertical" or between-cluster information. To use horizontal information in a mixed model, both the mean model and correlation structure must be correctly specified or accounted for, since time is confounded with treatment and measurements are likely correlated within clusters. Alternative non-parametric methods have been proposed that use only vertical information; these are more robust because between-cluster comparisons in a SWT preserve randomization, but these non-parametric methods are not very efficient. We propose a composite likelihood method that focuses on vertical information, but has the flexibility to recover efficiency by using additional horizontal information. We compare the properties and performance of various methods, using simulations based on COVID-19 data and a demonstration of application to the LIRE trial. We found that a vertical composite likelihood model that leverages baseline data is more robust than traditional methods, and more efficient than methods that use only vertical information. We hope that these results demonstrate the potential value of model-based vertical methods for SWTs with a large number of clusters, and that these new tools are useful to researchers who are concerned about misspecification of traditional models.