B-Spline in the Cox Regression with Application to Cervical Cancer

Recently, Cox proportional hazard (PH) models have played an important role and become increasingly famous in survival analysis. A crucial assumption of the Cox model is the proportional hazards assumption, that is the covariates do not vary over time. One way to check this assumption is to utilize martingale residuals. Martingale residual is an estimate of the overage of events seen in the data but not covered by the model. These residuals are used to examine the best functional form for a given covariate using an assumed Cox model for the remaining covariates. However, one problem that could be occurred when applying martingale residuals is that they tend to be asymmetric and the line does not fall around zero. Hence, in this paper, the main discussion will focus on the use of smoothing martingale residuals, another type of martingale residuals that give a higher rate of flexibility, by using B-spline and the relation to another smoothing technique, locally weighted scatterplot smoothing (LOWESS). An analysis of variables that probably affect the survival rate of patients with cervical cancer is used for illustration.