Log-rank test appropriate?


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
In my opinion, multiple crossing (similar course) of the curves indicates that both groups experience similar disease course in terms of survival and log-rank test results are in line with this (non significant). You can try to prove there is some kind of difference using other types of tests (early difference with Wilcoxon test, difference in distribution of survival times using Kolmogorov-Smirnov test...). However log-rank test is gold standard for univariate comparison of survival curves over whole study period as far as I'm informed. I belive problem arises with interpreting hazard ratios if log-rank test becomes significant even when curves cross. But maybe someone more informed on this subject could better clarify this issue.
Hope this helps


Omega Contributor
I don't use a lot of survival analysis, but I believe their is a proportion equality assumption that crossing curves is referenced in regards to. But I always assumed that was for gratuitous slope differences where confidence intervals separate, not insignificant crossing. Though, I am not positive of this.

I agree with Markica85 that if there are wild shifts between the two group's curves than there is a chance that at some selected time of follow-up the groups may differ. However, you need to realize you are finding this after looking at your data results and that may be biasing you to test it and that may not have been your a priori plan.