Demystifying estimands in cluster-randomised trials

TL;DR

This paper clarifies the concept of estimands in cluster-randomised trials, formalizes their definitions, and demonstrates how their choice influences interpretation and conclusions of such studies.

Contribution

It provides formal definitions of estimands in cluster trials, compares estimators, and highlights the impact of estimand choice on trial interpretation.

Findings

Different estimands lead to varying effect estimates.

Estimator choice can alter the statistical significance of results.

Careful specification of estimands improves trial interpretation.

Abstract

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, describe their assumptions, and show consistency (i.e. asymptotically unbiased estimation) for a series of analyses based on cluster level summaries. 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 the conclusions by leading to smaller treatment effect estimates. We conclude that careful specification of the estimand, along with an appropriate choice of estimator, are essential to ensuring that cluster randomised trials address the right question.