Restricted time window for survival analysis using Kaplan Meier estimates

Question

I am kinda new to statistics, so I have a question about survival analysis using Kaplan Meier estimates. In my samples (tumors), I think a certain feature has a positive prognostic impact (better overall survival) only in the short term i.e., it has a positive impact in the first 24 months after diagnosis, but after this time the feature becomes detrimental, and patients with it die sooner than the others. In other words: in the 24-month time window after diagnosis, patients with the feature tend to die in the later portion of the window, but those with the feature who survive after 24 months, do not live much longer. I have previous information to say this is biologically plausible.

I cannot perform U Mann-Whitney test because some data are censored. If I use Kaplan Meier estimates, as I am doing, is it acceptable to restrict the analysis to a specific time window (in my case, ≤24 months), and then running the log-rank test? Or is there another method? Thank you in advance for your answers.

Answer 1

It looks like you have a case of crossing hazard rates. The group with the feature you describe has a lower hazard rate in the first 24 months as compared to the group without this feature, and then after 24 months the hazard rates cross wherein the group with the feature has a higher hazard rate. The log-rank test has optimal power to detect difference in hazard rates between the 2 groups when the hazard curves do not cross. If they do cross, then early positive differences may be cancelled out by later negative differences and may lead to a misleading conclusion that there is no difference between the two groups. What you need is a test that has the power to detect crossing hazard rates, like the Renyi type tests. Refer to Sections 7.7 and 7.8 in Chapter 7 of the Klein Moescheberger book for a description of such tests.