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.
Abd ElHafeezSD’ArrigoGLeonardisD, et al.Methods to analyze time–to–event data: The Cox regression analysis. Oxid Med Cell Longev2021; 2021: 1302811.
2.
BrembillaAOllandAPuyraveauM, et al.Use of the Cox regression analysis in thoracic surgical research. J Thorac Dis2018; 10: 3891–3896.
3.
CoxDR. regression models and life-tables (with discussion). J R Stat Soc: Ser B (Stat Methodol)1972; 34: 187–220.
4.
SmithKRSlatteryMLFrenchTK. Collinear nutrients and the risk of colon cancer. J Clin Epidemiol1991; 44: 715–723.
5.
AbonazelMRAlzahraniARRSaberAA, et al.Developing ridge estimators for the extended Poisson–tweedie regression model: Method, simulation, and application. Sci African2024; 23: e02006.
6.
El-AloseyARHammadATGemeayAM. A novel zero-inflated regression model for overdispersed count data with enhancing its estimation for multicollinearity in medical data. Statistics2025; 59: 1463–1494.
7.
AbonazelMRDawoudIAwwadFA, et al.New estimators for the probit regression model with multicollinearity. Sci African2023; 19: e01565.
8.
AkramMNAminMSamiF, et al.A new conway maxwell–Poisson Liu regression estimator-method and application. J Math2022; 2022: 3323955.
9.
AlghamdiFMHammadATGolam KibriaBM, et al.On robust and non-robust modified Liu estimation in Poisson regression model with multicollinearity and outliers. Int J Uncert Fuzziness Knowled-Based Syst2025; 33: 787–823.
10.
HammadATHafezEHShahzadU, et al.New modified Liu estimators to handle the multicollinearity in the beta regression model: Simulation and applications. Mod J Stat2025; 1: 58–79.
11.
AlghamdiFMGemeayAMAbd-ElmougodGA, et al.A new class of Poisson–inverse Gaussian Liu-type regression estimator. J Nonlin Math Phys2025; 32: 48.
12.
SeifollahiSBevraniHAlbalawiO. Reducing bias in beta regression models using jackknifed Liu-type estimators: Applications to chemical data. J Math2024b; 2024: 6694880.
13.
DawoudIAbonazelMRAwwadFA. Modified Liu estimator to address the multicollinearity problem in regression models: A new biased estimation class. Sci African2022; 17: e01372.
14.
KibriaBMGLukmanAF. A new ridge–type estimator for the linear regression model: Simulations and applications. Scientifica2020; 2020: 9758378.
15.
LukmanAFKibriaBMGNzikuCK, et al. KL estimator: Dealing with multicollinearity in the logistic regression model. Mathematics2023; 11: 340.
16.
DawoudIKibriaBMG. A new biased estimator to combat the multicollinearity of the Gaussian linear regression model. Statistics2020; 3: 526–541.
17.
DawoudI. A new improved estimator for the gamma regression model. Commun Stat - Simul Comput2025; 54: 1–12.
18.
DawoudI. New two parameter inverse Gaussian regression estimators: Applications and simulation. Jordan J Math Stat2025b; 18: 1–15.
19.
AwwadFAOdeniyiKADawoudI, et al.New two-parameter estimators for the logistic regression model with multicollinearity. Sci African2022; 19: e01565.
20.
DawoudIAbonazelMR. Robust Dawoud–Kibria estimator for handling multicollinearity and outliers in the linear regression model. J Stat Comput Simul2021; 91: 3678–3692.
21.
DawoudIAwwadFATag EldinE, et al.New robust estimators for handling multicollinearity and outliers in the Poisson model: Methods, simulation and applications. Axioms2022; 11: 612.
22.
AlgamalZYAlobaidiNHammoodN, et al.Linearized ridge estimator in Cox regression modeling, 2023. DOI: 10.2139/ssrn.4609184.
23.
XueXKimMYShoreRE. Cox regression analysis in presence of collinearity: an application to assessment of health risk associated with occupational radiation exposure. Lifetime Data Anal2007; 13: 333–350.
24.
AhmadSAslamMAhmadS. Extending the Liu estimator for the Cox proportional hazards regression model with multicollinearity. Commun Stat–Simul Comput2023; 53: 5828–5841.
25.
InanDTezM. A new estimator for Cox proportional hazard regression model in presence of collinearity. Commun Stat:Theory Methods2012; 41: 2437–2444.
26.
AhmadSAslamMAhmadS, et al. development of the Aslam–Ahmad estimator for the Cox proportional and hazards regression model with multicollinearity. J Stat Comput Simul2024; 95: 426–449.
27.
SeifollahiSAlgamalZYArashiM. new insights into multicollinearity in the Cox proportional hazard models: the kibria-lukman estimator and its application. J Appl Stat2025; 52: 2672–2685.
28.
SeifollahiSBevraniH. James-Stein type estimators in beta regression model: simulation and application. Hacettepe J Math Stat2023; 52: 1046–1065.
29.
AminMAkramMNAmanullahM. On the James-Stein estimator for the Poisson regression model. Commun Stat: Simul Comput2022; 51: 5596–5608.
30.
QasimMMånssonKSjölanderP, et al.Stein-type control function maximum likelihood estimator for the probit model in the presence of endogeneity. Econometr Stat Adv online Publication2024; 28: 1–19.
31.
SeifollahiSBevraniHAlgamalZY. Improved estimators in bell regression model with application. J Stat Comput Simul2024a; 94: 2710–2726.
32.
SeifollahiSBevraniHAlgamalZY. Shrinkage estimators in zero–inflated bell regression model with application. J Stat Theory Pract2025b; 19: 1.
33.
LukmanAFDawoudIKibriaBMG, et al.A new ridge–type estimator for the gamma regression model. Scientifica2021; 2021: 5545356.
34.
AladeitanBBAdebimpeOLukmanAF, et al.Modified kibria–lukman (MKL) estimator for the Poisson regression model: application and simulation. F1000Research2021; 10: 155.
35.
SalehAKMEKibriaBMG. Improved ridge regression estimators for the logistic regression model. Comput Stat2013; 28: 2519–2558.
