Demystifying estimands in cluster-randomised trials

Estimands can help clarify the interpretation of treatment effects and ensure that estimators are aligned to the study's objectives. Cluster randomised trials require additional attributes to be defined within the estimand compared to individually randomised trials, including whether treatment effects are marginal or cluster specific, and whether they are participant or cluster average. In this paper, we provide formal definitions of estimands encompassing both these attributes using potential outcomes notation and describe differences between them. We then provide an overview of estimators for each estimand and describe their assumptions. Then, through a reanalysis of a published cluster randomised trial, we demonstrate that the choice of both estimand and estimator can affect interpretation. For instance, the estimated odds ratio ranged from 1.38 (p=0.17) to 1.83 (p=0.03) depending on the target estimand, and for some estimands, the choice of estimator affected conclusions by leading to smaller treatment effect estimates. We conclude that careful specification of the estimand, along with appropriate choice of estimator, are essential to ensuring that cluster randomised trials are addressing the right question.