# How should I compare crossing survival curves?

When survival curves cross, should I use log-rank, HR, or some other method? Does it depend on if they cross at the start of the observation period or at the end?

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then you should consider the wilcoxon test as an alternative to log-rank and maybe restricted mean survival time as replacement for cox regression, or consider cox regression with stratification -see Frank Harrellâ€™s book, there is a brief section on â€śwhat to do when PH failsâ€ť

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There are so many choices and I wouldnâ€™t necessarily use Gehan-Wilcoxon. Many are using the restricted mean survival time but there is no one-number summary that does the trick. I highly recommend that disinterested unbiased experts be consulted in an attempt to find out what really matters to the patient. Is it where they end up? Then the cumulative incidence at the final follow-up time would be preferred. The main descriptive statistic to show is the difference in Kaplan-Meier cumulative incidence curves with confidence bands for the difference.

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Dr Harrell, what are the confidence bands for the difference? What information do they represent?
Can you clarify why these are more informative than the individual confidence intervals of the curves?
I think you mentioned in a blog that intersection of individual confidence intervals doesnâ€™t necessarily mean that there is no difference between curves. Why?

You can have two overlapping 0.95 confidence intervals yet the confidence interval for the difference not include 0.0. This comes from the variance of a difference being the sum of the two variances. You need to actually compute the difference to get the right confidence inteval. And the individual confidence intervals should not even be presented in a randomized trial as there is no population inference for them, since RCTs donâ€™t randomly sample from the population. RCTs are for estimating differences, not per-treatment outcomes.

With crossing curves the right confidence bands (ideally simultaneous confidence bands for the differences across time) you can keep everyone honest and avoid cherry picking a single time at which there seems to be a difference.

Can you please explain again on this real example? â€śAfter a median follow-up of 28.2 months, the percentage of patients surviving without progression was significantly higher in the pola-R-CHP group than in the R-CHOP group (76.7% [95% confidence interval (CI), 72.7 to 80.8] vs. 70.2% [95% CI, 65.8 to 74.6] at 2 yearsâ€ť. These PFS curves are cross in 36 months point. Source: https://www.nejm.org/doi/full/10.1056/NEJMoa2115304