Choosing covariates in the analysis of cluster randomised trials.

Abstract

Covariate adjustment is common in the analysis of randomised trials, and can increase statistical power without increasing sample size. Published research on covariate adjustment, and guidance for choosing covariates, focusses on trials where individuals are randomised to treatments. In cluster randomised trials (CRTs) clusters of individuals are randomised. Valid analyses of CRTs account for the structure imposed by cluster randomisation. There is limited published research on the e ects of covariate adjustment, or guidance for choosing covariates, in analyses of CRTs. I summarise existing guidance for choosing covariates in individually randomised trials and CRTs, and review the methods used to investigate the e ects of covariate adjustment. I review the use of adjusted analyses in published CRTs. I use simulation, analytic methods, and analyses of trial data to investigate the e ects of covariate adjustment in mixed models. I use these results to form guidance for choosing covariates in analyses of CRTs. Guidance to choose covariates a priori and adjust for covariates used to stratify randomisation is also applicable to CRTs. I provide guidance speci c to CRTs using linear and logistic mixed models. Cluster size, the intra-cluster correlations (ICCs) of the outcome and covariate, and the strength of the relationship between the outcome and covariate in uence the power of adjusted analyses and the precision of treatment e ect estimates. An a priori estimate of the product of cluster size and the ICC of the outcome can be used to assist choosing covariates. When this product is close to one, adjusting for a cluster level covariate or a covariate with a negligible ICC provide similar increases in power. For smaller values of this product, adjusting for a cluster level covariate gives minimal increases in power. The use of separate withincluster and contextual covariate e ect parameters may increase power further in some circumstances.