title: Sample size in cluster-randomized trials with time to event as the primary endpoint.
abstract: In cluster-randomized trials, groups of individuals (clusters) are randomized to the treatments or interventions to be compared. In many of those trials, the primary objective is to compare the time for an event to occur between randomized groups, and the shared frailty model well fits clustered time-to-event data. Members of the same cluster tend to be more similar than members of different clusters, causing correlations. As correlations affect the power of a trial to detect intervention effects, the clustered design has to be considered in planning the sample size. In this publication, we derive a sample size formula for clustered time-to-event data with constant marginal baseline hazards and correlation within clusters induced by a shared frailty term. The sample size formula is easy to apply and can be interpreted as an extension of the widely used Schoenfeld's formula, accounting for the clustered design of the trial. Simulations confirm the validity of the formula and its use also for non-constant marginal baseline hazards. Findings are illustrated on a cluster-randomized trial investigating methods of disseminating quality improvement to addiction treatment centers in the USA.
authors.affiliation: Institute of Medical Biostatistics, Epidemiology and Informatics, Medical Center of the Johannes Gutenberg-University, Langenbeckstr.1, 55131 Mainz, Germany. antje.jahn@unimedizin-mainz.de
authors.forename: Antje
authors.initials: A
authors.lastname: Jahn-Eimermacher
authors.forename: Katharina
authors.initials: K
authors.lastname: Ingel
authors.forename: Astrid
authors.initials: A
authors.lastname: Schneider
mesh_terms: D056808:Biostatistics / Q000379:methods*; D016000:Cluster Analysis; D023381:Endpoint Determination / Q000706:statistics & numerical data*; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D016012:Poisson Distribution; D011897:Random Allocation; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data*; D012044:Regression Analysis; D018401:Sample Size; D016320:Substance Abuse Treatment Centers / Q000706:statistics & numerical data; D019966:Substance-Related Disorders / Q000628:therapy; D013997:Time Factors; D061665:Time-to-Treatment