Demystifying estimands in cluster-randomised trials

Abstract

Estimands can help clarify the interpretation of treatment effects and ensure that estimators are aligned with 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, describe their assumptions, and show consistency (i.e. asymptotically unbiased estimation) for a series of analyses based on cluster-level summaries. Then, through a re-analysis 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 the conclusions by leading to smaller treatment effect estimates. We conclude that careful specification of the estimand, along with an appropriate choice of estimator, is essential to ensuring that cluster-randomised trials address the right question.

Keywords: Estimand; analysis of cluster-level summaries; cluster-average; cluster-randomised trial; cluster-specific; independence estimating equations; marginal; participant-average.

Figure 1.

Difference between marginal participant- versus cluster-average odds ratio for ‘post-extubation stridor’ in the randomised evaluation of sedation titration for respiratory failure (RESTORE) trial. Each bubble denotes the proportion of events in that cluster. The size of the bubbles represents the weight given to each cluster, with hollow bubbles representing the participant-average weighting, and solid bubbles denoting the cluster-average weighting. The overall treatment group means are closer together under the cluster-average weighting than the participant-average weighting, owing to the cluster-average weighting giving more weight to smaller clusters with smaller between-group differences.