Shrinkage methods enhanced the accuracy of parameter estimation using Cox models with small number of events

I. Feng Lin, Wushou Peter Chang, Yi Nan Liao

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


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. Study Design and Setting: 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.

Original languageEnglish
Pages (from-to)743-751
Number of pages9
JournalJournal of Clinical Epidemiology
Issue number7
Publication statusPublished - Jul 2013


  • Bayesian methods
  • Cancer risk assessment
  • Cox proportional hazard model
  • Firth's penalized likelihood
  • Partial likelihood
  • Small number of events

ASJC Scopus subject areas

  • Epidemiology


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