title: The number of primary events per variable affects estimation of the subdistribution hazard competing risks model.
abstract: OBJECTIVE
  To examine the effect of the number of events per variable (EPV) on the accuracy of estimated regression coefficients, standard errors, empirical coverage rates of estimated confidence intervals, and empirical estimates of statistical power when using the Fine-Gray subdistribution hazard regression model to assess the effect of covariates on the incidence of events that occur over time in the presence of competing risks.
  
  
  METHODS
  Monte Carlo simulations were used. We considered two different definitions of the number of EPV. One included events of any type that occurred (both primary events and competing events), whereas the other included only the number of primary events that occurred.
  
  
  RESULTS
  The definition of EPV that included only the number of primary events was preferable to the alternative definition, as the number of competing events had minimal impact on estimation. In general, 40-50 EPV were necessary to ensure accurate estimation of regression coefficients and associated quantities. However, if all of the covariates are continuous or are binary with moderate prevalence, then 10 EPV are sufficient to ensure accurate estimation.
  
  
  CONCLUSIONS
  Analysts must base the number of EPV on the number of primary events that occurred.
authors.affiliation: Institute for Clinical Evaluative Sciences, G106, 2075 Bayview Avenue, Toronto, Ontario M4N 3M5, Canada; Institute of Health Management, Policy and Evaluation, University of Toronto, 155 College Street, Toronto, Ontario M5T 3M6, Canada; Schulich Heart Research Program, Sunnybrook Research Institute, 2075 Bayview Avenue, Toronto, Ontario M4N 3M5, Canada. Electronic address: peter.austin@ices.on.ca.
authors.forename: Peter C
authors.initials: PC
authors.lastname: Austin
authors.affiliation: Institute of Statistics, Ulm University, Helmholtzstr. 20, Ulm 89081, Germany.
authors.forename: Arthur
authors.initials: A
authors.lastname: Allignol
authors.affiliation: Department of Biostatistics, University of North Carolina, 135 Dauer Drive, 3101 McGavran-Greenberg Hall, CB #7420 Chapel Hill, NC 27599-7420, USA; Department of Statistics & Operations Research, University of North Carolina, 318 Hanes Hall, CB# 3260, Chapel Hill, NC 27599-3260, USA.
authors.forename: Jason P
authors.initials: JP
authors.lastname: Fine
mesh_terms: D002318:Cardiovascular Diseases / Q000209:etiology / Q000401:mortality; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D009010:Monte Carlo Method; D016016:Proportional Hazards Models; D012044:Regression Analysis; D018570:Risk Assessment; D012307:Risk Factors
keywords: Competing risks; Events per variable; Fine–Gray regression model; Sample size; Subdistribution hazard model; Survival analysis