  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.
