Estimands in cluster-randomized trials: choosing analyses that answer the right question.

Background: Cluster-randomized trials (CRTs) involve randomizing groups of individuals (e.g. hospitals, schools or villages) to different interventions. Various approaches exist for analysing CRTs but there has been little discussion around the treatment effects (estimands) targeted by each.

Methods: We describe the different estimands that can be addressed through CRTs and demonstrate how choices between different analytic approaches can impact the interpretation of results by fundamentally changing the question being asked, or, equivalently, the target estimand.

Results: CRTs can address either the participant-average treatment effect (the average treatment effect across participants) or the cluster-average treatment effect (the average treatment effect across clusters). These two estimands can differ when participant outcomes or the treatment effect depends on the cluster size (referred to as 'informative cluster size'), which can occur for reasons such as differences in staffing levels or types of participants between small and large clusters. Furthermore, common estimators, such as mixed-effects models or generalized estimating equations with an exchangeable working correlation structure, can produce biased estimates for both the participant-average and cluster-average treatment effects when cluster size is informative. We describe alternative estimators (independence estimating equations and cluster-level analyses) that are unbiased for CRTs even when informative cluster size is present.

Conclusion: We conclude that careful specification of the estimand at the outset can ensure that the study question being addressed is clear and relevant, and, in turn, that the selected estimator provides an unbiased estimate of the desired quantity.