Gray's extension of Cox's proportional hazards (PH) model for right-censored survival data allows for a departure from the PH assumption via introduction of time-varying regression coefficients (TVC) using penalized splines. Gray's work focused on estimation, inference and residual analyses, but...

Survival analysis has been used to estimate underlying survival or failure probabilities and to estimate the effects of covariates on survival times. The Cox proportional hazards regression model is the most commonly used approach. However, in practical situations, the assumption of proportional...