I have an experiment, where I compare two groups over time in frames of the time to event analysis. The Kaplan-Meier curves cross 3 times.
It means, that the hazards ratios switch to the opposite side multiple times. So, the problem is not even in non-constant HR, but even worse - the interpretation varies from period to period. Like on the picture below.
I am interested in 2 analyses: the Cox regression (with just single 2-level categorical group) to get the HR and the CI for it and the curve comparison test.
Normally, I would run the Cox model and get the HR and the p-value (equivalent to long-rank in this case).
But here I have multiple HRs. What should I do?
- Run separate Cox / KM analysis in each period determined by the moment of crossing? But within each period the curves do not diverge from each other, as the PH suggests, but rather first diverge and then converge (to cross each other). So the PH assumption is still violated!
I could "manually" find the moments of crossing, R has such function and split the analysis by those periods.
employ time dependent covariate? I mean group x time interaction? But how to interpret such model?
regarding the statistical test, I can imagine a test, that is not fooled by the turning hazards ratios and reporting that "in overall the two curves differ, regardless of the nature of the difference". But what kind of test can do that?
Is there any other, better method to handle such analysis? I know the AFT model doesn't need the PH assumption, but still - how will it handle the "race" between the two curves?
Please note, I am aware, that missing covariate could cause that, but I have no additional information in my data set. Only the basic survival data I need to summarize somehow.
Let's assume the difference reported naively with the log rank is stat. significant. So saying "if there is no significant difference, your problem diminishes". The curves diverge far from each other to then meet each other and cross.