Six graphical procedures to check the assumption of proportional hazards for the Cox model are described and compared. A new way of comparing the graphical procedures using a Kolmogorov-Smirnov like maximum deviation criterion for rejection is derived for each procedure. The procedures are evaluated in a simulation study under proportional hazards and five different forms of nonproportional hazards: (1) increasing hazards, (2) decreasing hazards, (3) crossing hazards, (4) diverging hazards, and (5) nonmonotonic hazards. The procedures are compared in the two-sample case corresponding to two groups with different hazard functions. None of the procedures under consideration require partitioning of the survival time axis. Results indicate that the Arjas plot, a plot of estimated cumulative hazard versus number of failures, is superior to the other procedures under almost every form of nonproportional hazards, especially crossing and nonmonotonic hazards. For increasing hazards, the smoothed plot of the ratio of log cumulative baseline hazard rates versus time or the smoothed plot of scaled Schoenfeld residuals versus time perform the best. The Andersen plot performs very poorly for increasing, decreasing, and diverging hazards.
& Khamis, H. J.
(2007). A Comparison of Graphical Methods for Assessing the Proportional Hazards Assumptions in the Cox Model. Journal of Statistics and Applications, 2 (1-4), 1-32.