1. This article suggests solution to check the log-linear relationship assumption of covariates with hazards in Cox Proportional Hazard analysis.

Cox Proportional Hazard regression analysis have assumption about proportional hazards and the second one is that there is a log-linear relationship between the independent variables (covariates) and the underlying hazard function.

The Cox PH module includes many graphical displays of different types of residuals that can be useful in performing many types of model diagnostics.

According to Hosmer and Lemeshow (2008), the martingale residuals can be created for the model WITHOUT the covariate of interest, and then plotted against the covariate of interest along with a smoothed scatterplot fit (e.g. lowess). The smooth provides an estimate of the functional form of the covariate in the log hazard.

To create these plots, the user would need to create a Cox model without the variable of interest, save the martingale residuals and create the 2D scatterplot for the variable of interest and the martingale residuals with the corresponding lowess fit.