Table 2.

Estimands and estimators for cluster-randomized trials

Estimand	Description	Method of estimation
Participant-average treatment effecta	Average treatment effect across participants (i.e. ‘How effective is the intervention for the average participant?’). Here, each participant is given equal weight	Cluster-level analysis Calculate cluster-level summaries (e.g. mean outcome in each cluster) Analyse cluster-level summaries using a weighted regression model (with weights equal to $n_i$, and robust standard errors) to give each participant equal weight. Participant-level analysis Independence estimating equations on participant-level data (which give equal weight to each participant) using robust standard errors that account for correlation between participants in the same cluster (e.g. GEE with a working independence correlation structure and robust standard errors or maximum-likelihood/least squares estimators with cluster-robust standard errors)
Cluster-average treatment effecta	Average treatment effect across clusters (i.e. ‘How effective is the intervention for the average cluster?’). Here, each cluster is given equal weight	Cluster-level analysis Calculate cluster-level summaries (e.g. mean outcome in each cluster) Analyse cluster-level summaries using regression model (unweighted, so that each cluster is given equal weight) Participant-level analysis Weighted independence estimating equations on participant-level data using robust standard errors, with inverse cluster-size weights equal to $\frac{1}{n_i}$ to give equal weight to each cluster

^aFor collapsible effect measures (e.g. the difference in means, risk difference or risk ratio), the participant-average and cluster-average estimands will coincide unless the treatment effect varies according to cluster size. For non-collapsible effect measures (e.g. odds ratio, hazard ratio), the participant-average and cluster-average estimands will only coincide if there is no difference in either outcomes or treatment effects between small and large clusters. GEE, generalized estimating equation.