title: Many multicenter trials had few events per center, requiring analysis via random-effects models or GEEs.
abstract: OBJECTIVE
  Adjustment for center in multicenter trials is recommended when there are between-center differences or when randomization has been stratified by center. However, common methods of analysis (such as fixed-effects, Mantel-Haenszel, or stratified Cox models) often require a large number of patients or events per center to perform well.
  
  
  METHODS
  We reviewed 206 multicenter randomized trials published in four general medical journals to assess the average number of patients and events per center and determine whether appropriate methods of analysis were used in trials with few patients or events per center.
  
  
  RESULTS
  The median number of events per center/treatment arm combination for trials using a binary or survival outcome was 3 (interquartile range, 1-10). Sixteen percent of trials had less than 1 event per center/treatment combination, 50% fewer than 3, and 63% fewer than 5. Of the trials which adjusted for center using a method of analysis which requires a large number of events per center, 6% had less than 1 event per center-treatment combination, 25% fewer than 3, and 50% fewer than 5. Methods of analysis that allow for few events per center, such as random-effects models or generalized estimating equations (GEEs), were rarely used.
  
  
  CONCLUSIONS
  Many multicenter trials contain few events per center. Adjustment for center using random-effects models or GEE with model-based (non-robust) standard errors may be beneficial in these scenarios.
authors.affiliation: Pragmatic Clinical Trials Unit, Centre for Primary Care and Public Health, Queen Mary University of London, 58 Turner Street, London E1 2AB, UK. Electronic address: b.kahan@qmul.ac.uk.
authors.forename: Brennan C
authors.initials: BC
authors.lastname: Kahan
authors.affiliation: Division of Epidemiology, Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, 708 Blockley Hall, 423 Guardian Drive, Philadelphia, PA 19146, USA.
authors.forename: Michael O
authors.initials: MO
authors.lastname: Harhay
mesh_terms: D015982:Bias; D003625:Data Collection; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D015337:Multicenter Studies as Topic / Q000706:statistics & numerical data*; D063868:Patient Outcome Assessment; D010506:Periodicals as Topic; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data*; D018401:Sample Size; D013223:Statistics as Topic
keywords: Center effects; Covariate adjustment; Generalized estimating equations; Multicenter trial; Random-effects models; Randomized controlled trial