# Schoenfled Residua test shows proportionality hazard assumptions holds but Kaplan-Meier plots intersect

"If Kaplan-Meier plots cross each other then proportional hazard assumption does not hold". The issue I am facing is that I got the Kaplam-Meier plot(bleow). We can clearly see that it is overlapping. But when I plot the Schoenfled residual plots, it suggests otherwise because the black solid line is flat(image below). Also the p-values(below) for Schoenfled residual plots are not significant, suggesting that proportional hazard assumption holds

ftest <- cox.zph(fitcox) ftest p as.factor(C)2 0.945 as.factor(C)3 0.922 as.factor(C)4 0.717 GLOBAL 0.915

One may argue that the three hazard ratios are calculated w.r.t. the red plot. Red plot does not intersect the blue and black plots. So it is understandable that proportional hazard assumption holds. But red plot does intersect the green one, although only a little...Is that not enough to violate the proportional hazard assumption?

• If you cannot reject the null hypothesis, it does not mean that it is true. – Michael M Apr 6 at 14:46
• This reasoning accounts for the p-value. What about the Schoenfled residual plots being flat.... – Omar Rafique Apr 6 at 16:37