# How to interpret Kaplan-Meier curves intersecting at tail end?

I performed a CoxPH analysis on a sample dataset that yielded the following results:

Univariate analysis: 0.40 (0.20 - 0.88). P value: 0.02 Multivariate analysis: 0.44 (0.24 - 0.94). P value: 0.03

I then ran a KM analysis on the same dataset that yielded a statistically significant plot added below

I just want to confirm if my results are still valid/statistically significant as I am uncertain how to interpret the fact that the tail ends of the KM curve tend to cross over (I believe that the curves are ideally supposed to remain separate in order for the findings to be statistically meaningful). Would appreciate any advice in this regard.

• I would prefer to start in the blue group, if I had to decide. Even if out of the 94 people you observed the last two surviving were red. Those two represent the special case, not the usual. Jan 31 at 20:52
• Hello, can you give more details on what the numbers for univariate and multivariate analysis mean? Are those hazard ratios? Or log-hazards? Feb 1 at 12:32

First, I wouldn't use the phrase "statistically significant plot". It's the estimator that is significant (or, in other cases, not significant). All three estimators that you show are significant at 0.05.

Second, and more importantly, the plot shows what is going on and it's worth taking time to look at it carefully. The fact that the blue line is above (and often far above) the red line for almost the whole time shows that group B has a higher chance of survival up to about 40 months (you may want to add more time ticks to the x axis). Then they switch. But looking at the data beneath the plot, we see that, even at 24 months, the number at risk is getting small. You can add a column for 36 months to get another estimate. That means that the switch is about a very small data set. Looking at the ticks on the lines, that final drop in the blue curve seems to be just one person.

Therefore, I would not worry about the crossing.

You wrote:

(I believe that the curves are ideally supposed to remain separate in order for the findings to be statistically meaningful)

Well, OK, sure. That would be nice. And if the groups were bigger at the time of the crossing, then I think you would want more analysis. Maybe there are important changes in risk over time. Right now, though, you have very minimal evidence of any such changes.

If you flip a coin 3 times and get 2 heads, that's not much evidence of anything. And that is (roughly) what is happening at thee right end of your graph.

• Show confidence band for the difference in the two estimates, which will better help us to know how much we don’t know. Feb 1 at 13:22