Firth's penalized method in Cox proportional hazard framework for developing predictive models for sparse or heavily censored survival data

Abstract

This paper explored the use of Firth's penalized method in the Cox PH framework, which was originally proposed for solving the problem of separation, for developing prediction model for sparse or heavily censored survival data. An extensive simulation study, based on both breast cancer data and simulated data, were conducted to evaluate the predictive performance of the Firth's penalized model over the standard Cox model. The predictive performance of the models developed in training data were assessed in test data by estimating some well-known performance measures such as calibration slope and concordance statistics for both models and compared their results. The results revealed that Firth's penalized model showed substantial improvement over the MLE-based standard Cox model by providing accurate estimate of the true predictive (discriminative) performance and removing overfitting to some extent. The methods were further illustrated using birth-interval data with high percentage of censoring and the results support the simulation findings.