title: Shrinkage methods enhanced the accuracy of parameter estimation using Cox models with small number of events.
abstract: OBJECTIVE
  When the number of events is small during Cox regression analysis, it is unclear what alternative analytical strategies can be used and when this type of alternative approach is needed. This study explores several analytical strategies in this situation.
  
  
  METHODS
  Simulations and sensitivity analyses were performed on data with numbers of events per predictive variable (EPVs) below 10 using a Cox model with a partial likelihood (PL), Firth's penalized likelihood, or the Bayesian approach.
  
  
  RESULTS
  For scenarios involving binary predictors with an EPV of six or less, the simulations showed that the Firth and Bayesian approaches were more accurate than was PL. The performances of various approaches were similar when the EPV was greater than six in the binary predictor. Furthermore, the performances involving continuous predictors were similar, regardless of the EPV. The bias and precision of the parameter estimates using Bayesian analysis depended on the selection of priors.
  
  
  CONCLUSIONS
  When the EPV is six or less, the results for categorical predictors tend to be too conservative. Firth's estimator may be a good alternative in this situation. Appropriate choices of priors when using Bayesian analysis should increase the accuracy of the parameter estimates, although this requires expertise.
authors.affiliation: Institute of Public Health, School of Medicine, National Yang-Ming University, 155 Section 2, Li-Nong Street, Taipei 11221, Taiwan. iflin@ym.edu.tw
authors.forename: I-Feng
authors.initials: IF
authors.lastname: Lin
authors.forename: Wushou Peter
authors.initials: WP
authors.lastname: Chang
authors.forename: Yi-Nan
authors.initials: YN
authors.lastname: Liao
mesh_terms: D001499:Bayes Theorem; D016010:Binomial Distribution; D015331:Cohort Studies; D003198:Computer Simulation; D004781:Environmental Exposure / Q000032:analysis*; D006801:Humans; D008432:Mathematical Computing; D016016:Proportional Hazards Models; D011834:Radiation Monitoring / Q000379:methods*; D012107:Research Design; D013624:Taiwan