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

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.

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.

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.

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.