title: Adequate sample size for developing prediction models is not simply related to events per variable.
abstract: The choice of an adequate sample size for a Cox regression analysis is generally based on the rule of thumb derived from simulation studies of a minimum of 10 events per variable (EPV). One simulation study suggested scenarios in which the 10 EPV rule can be relaxed. The effect of a range of binary predictors with varying prevalence, reflecting clinical practice, has not yet been fully investigated.
  
  
  
  We conducted an extended resampling study using a large general-practice data set, comprising over 2 million anonymized patient records, to examine the EPV requirements for prediction models with low-prevalence binary predictors developed using Cox regression. The performance of the models was then evaluated using an independent external validation data set. We investigated both fully specified models and models derived using variable selection.
  
  
  
  Our results indicated that an EPV rule of thumb should be data driven and that EPV ≥ 20 ​ generally eliminates bias in regression coefficients when many low-prevalence predictors are included in a Cox model.
  
  
  
  Higher EPV is needed when low-prevalence predictors are present in a model to eliminate bias in regression coefficients and improve predictive accuracy.
authors.affiliation: Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology & Musculoskeletal Diseases, Botnar Research Centre, University of Oxford, Windmill Road, Oxford OX3 7LD, UK. Electronic address: emmanuel.ogundimu@csm.ox.ac.uk.
authors.forename: Emmanuel O
authors.initials: EO
authors.lastname: Ogundimu
authors.affiliation: Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology & Musculoskeletal Diseases, Botnar Research Centre, University of Oxford, Windmill Road, Oxford OX3 7LD, UK.
authors.forename: Douglas G
authors.initials: DG
authors.lastname: Altman
authors.affiliation: Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology & Musculoskeletal Diseases, Botnar Research Centre, University of Oxford, Windmill Road, Oxford OX3 7LD, UK.
authors.forename: Gary S
authors.initials: GS
authors.lastname: Collins
mesh_terms: D000328:Adult; D001499:Bayes Theorem; D035843:Biomedical Research / Q000379:methods* / Q000706:statistics & numerical data*; D005260:Female; D005544:Forecasting / Q000379:methods*; D006801:Humans; D016015:Logistic Models; D008297:Male; D008875:Middle Aged; D018579:Patient Selection; D016016:Proportional Hazards Models; D012044:Regression Analysis; D012107:Research Design; D018401:Sample Size
keywords: Cox model; Events per variable; External validation; Predictive modeling; Resampling study; Sample size