Extending the Liu estimator for the Cox proportional hazards regression model with multicollinearity

Abstract

In this article, we present the Liu estimator for the Cox proportional hazards (PH) model. The maximum partial likelihood estimator (MPLE) is commonly used for estimation of the coefficients of the Cox PH model. The MPLE performs well if the covariates are uncorrelated. However, in many situations, covariates become seriously correlated, and then the MPLE is inept to produce stable estimates for the unknown coefficients. To overcome this situation, the literature suggests using the ridge estimator as an alternative to the MPLE for the Cox PH model in the presence of multicollinearity. In the present article, we extend the Liu estimator, a popular superseder of the ridge estimator, for the Cox PH model and discuss its properties. The performance of the proposed estimator has been compared with the available estimators using the scalar mean squared error criterion through the Monte Carlo simulations. A numerical example has also been provided for the illustration.