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I am wondering how to correctly interpret Kaplan Meier Curves, the log-rank test respectively. I calculated a log-rank test to compare two survival curves and got an insignificant p-value from this. My medians of the two curves are 527 (Ci.: 445, 682) and 832 (Ci.: 404, 1332).

Does the insignificant log-rank test mean that there is no statistical difference between the medians or is this not a valid interpretation?

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The logrank test is distinct from the Kaplan-Meier estimator. Here are some problems with your approach:

  1. You put yourself into a hypothesis testing framework without thinking of the ultimate analytic goal. In most cases estimation is more useful than hypothesis testing, the latter being more of a signal detection exercise.
  2. The logrank test is just a special case of the Cox proportional hazards model and nothing is gained by using this special case, especially since the Cox model allows you to adjust for baseline covariates whereas the logrank test does not.
  3. The median is a very noisy estimator.
  4. The confidence intervals for the individual medians are irrelevant to your goal.
  5. Compute confidence limits for the difference or ratio of the two unknown medians instead.
  6. Keep in mind that the Cox/logrank approach does not test for medians so the use of medians is just to illustrate one property of the distributions.

Depending on your goals I recommend concentrating on confidence bands for the difference in two Kaplan-Meier esetimates, over time. And here is a way to effectively show this band superimposed with the two K-M curves.

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