I am comparing survival between two groups distinguished by a single factor. The survival curves converge at both ends (near time 0 and near the maximum time) but never cross, and R's survival::cox.zph() test also indicates that the proportional hazards assumption does not hold.
Given the lack of proportional hazards, is the difference in median survival (calculated with R's survival::survfit()) still a valid measure quantifying the differences in survival?
Since the differences converge at both ends, far from the median, would the best measure of the survival difference be the hazard ratio expressed as a function of time t?
What measure would you recommend using to quantify this difference for nontechnical stakeholders?
Thanks so much!