Efficiency of a hybrid Kibria–Lukman estimator in the Cox regression model with survival data application

This paper develops and evaluates a new hybrid Kibria–Lukman estimator for the Cox regression model to more effectively handle severe multicollinearity in survival data. The Cox model is widely used for time data analysis, but strong linear dependencies among covariates make the maximum likelihood estimator unstable, inflating variance and mean squared error and potentially yielding insignificant coefficient estimates even when groups of predictors are jointly important. Building on the existing Kibria–Lukman and Lukmantype biased estimators, the proposed hybrid Kibria–Lukman estimator for the Cox regression model introduces an additional biasing structure designed to further shrink estimates along ill-conditioned directions of the information matrix while preserving relevant signal in well-identified directions. Analytical expressions for the bias, variance, and mean squared error are derived under the Cox regression framework, and optimal biasing parameters are obtained through a data-driven strategy. A comprehensive Monte Carlo simulation study, spanning multiple sample sizes, degrees of multicollinearity, and censoring rates, shows that the hybrid estimator consistently achieves the smallest average mean squared error compared with the maximum likelihood, ridge, Liu, Liu-type, and Kibria–Lukman estimators. The practical utility of the new estimator is further demonstrated using two real survival datasets from the lung cancer study and the National Wilm’s Tumor Study, where it provides more stable coefficient estimates and improved model fit in the presence of pronounced multicollinearity. These findings indicate that the proposed hybrid Kibria–Lukman estimator offers a robust and efficient alternative for Cox regression analysis when covariates are highly correlated, with clear gains in estimation accuracy over existing biased estimators