I am currently working on a small (29 patients) retrospective analysis of patients undergoing a certain treatment. One of the main parameters is the progression-free survival, which exhibited some censored data; thus, its median was estimated using the Kaplan-Meier method. For the sake of exploratory analysis, I formed two subgroups and compared them to each other using the log-rank (Mantel-Cox) test. However, the two survival curves crossed each other multiple time and the log-rank test revealed no significant difference (p = 0.85). In literature, crossing survival curves are a contraindication for the used statistical test, as for instance when the first group has better prognosis in the beginning while the second is prone to exhibit improved survival after some time. In my opinion, the findings in my study may be due to the small case number and probably the lack of significance between the subgroup differences. Nevertheless, I am not sure whether the log-rank test is appropriate in this situation as the curves still cross multiply - what is, in my eyes, rather attributable to the small case number and not to non proportional hazard ratios. Can someone tell me whether I chose the right test in this context?

Thank you very much!

Kind regards