Improved survival analysis with shrinkage Kibria-Lukman estimators in the Cox model: Application to lung cancer data

The Cox proportional hazards regression model is a widely used and valuable tool for modeling survival time with predictors, however its performance can deteriorate in the presence of multicollinearity. It can lead to unreliable estimates from the maximum partial likelihood estimator. In this paper, we introduce enhanced shrinkage estimators based on the Kibria-Lukman approach to obtain more efficient coefficient estimates. Specifically, we develop linear shrinkage, Stein and its positive counterpart, pretest, and shrinkage pretest estimators that incorporate prior information about model coefficients. We derive their asymptotic bias and variance properties and evaluate their performance through extensive Monte Carlo simulations. The results demonstrate significant improvements, highlighting the practical advantages of these methods for applied researchers. We also illustrate the application of our proposed estimators using a lung cancer dataset.