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
