Extended Cox Modelling of Survival Data with Guarantee Time

K A Adeleke, A A Abiodun, R A Ipinyomi


Proportional Hazard regression model for censored survival data often specifies that covariates have a proportional fixed effect on the hazard function of the lifetime distribution of a subject. A modification of the proportional hazards model of Cox (1972) to accommodate the non-proportional effect on hazard with a time-varying covariate and the introduction of guarantee time into the Weibull distributed baseline hazard function. Simulations were conducted to investigate properties of the models. Our approach had shown to have the best asymptotic properties in a simulation study with mean, Absolute Bias (AB) and Mean Square Error (MSE) of the parameter estimates for the models (under different levels of censoring and sample sizes) using simulated data.

Full Text:



Adeleke, K. A., Abiodun A. A.,and Ipinyomi, R.A., (2015). Semi-Parametric Non-Proportional Hazard Model With Time Varying Covariate. Journal of Modern Applied Statistical Methods: {14(2)}, 68 – 87.

Arasan, J., Lunn, M., (2009). Survival model of a parallel system with dependent failures and time varying covariates. jspi 139 944{951.

Ata, N., Sozer, T. M., (2007). Cox regression models cancer survival data. Hacettepe Journal of Mathematics and Statistics 36(2) 157{167.

Austin, P.C.,(2012). Generating survival times to simulate Cox proportional hazards models with time-varying covariates. Wiley Statist. Med. 31157{167.

Bender, R., Augustin, T., Blettner, M., (2005). Generating survival times to simulate cox proportional hazards models. Statistics in Medicine; 25(11) 1713-1723. DOI:10.1002/sim.2369.

Mood AM, Graybill FA, Boes DC. Introduction to the Theory of Statistics. McGraw-Hill: New York, 1974

Kronborg, D., Aaby, P. (1990). Piecewise Comparison of Survival Function in Stratied Proportional Hazard Models. Biometrics 46, 375-380.

Lee, E.T.,Wang, J.W., (2003). Statistical Methods for survival Data Analysis. John Wiley, New Jersey.

Leemis, L.M., Shihand, L.H., Reynertson, K., (1990). Variate generation for accelerated life and proportional hazards models with time dependent covariates. Statistics and Probability Letters; 10(6):335-339. DOI: 10.1016/0167-7152(90)90052-9.

Leemis, L.M., (1987). Variate generation for accelerated life and proportional hazards models. Operations Research; 35(6): 892-894. DOI:10.1287/opre.35.6.892.

Robert, C. P., Casella, G., (2009). Introducing Monte Carlo Methodswith R, Springer-Verlag.

Scheike, T. (2004). Time varying effect in survival analysis. Handbook of statistics Elsevier 23, 61-85. DOI 10.1016/S0169-7161(03)23004-2

Shihand, L.H., Leemis, L. M., (1993). Variate generation for a nonhomogenous Poisson process with time dependent covariates. Journal of Statistical Computation and Simulation; 44:165-186. DOI:10.1080/00949659308811457.

Sylvester, M.P., Abrahamowicz, M., (2007). Comparison of algorithms to generate event times conditional on time-dependent covariates.Statistics in Medicine; 27(14):2618-2634. DOI: 10.1002.

Wong, H., Ip, W., Zhang, R.Q., (2006). Varying-coefcient single-index model. Csda 5214581476.

Zhou, M. (2001). Understanding the cox regression models with time change covariates. The American Statistician; 55(2):153-155.


  • There are currently no refbacks.