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I want to make a hypothesis test about equality of survival curves. The curves below are from Kaplan-Meier estimate.

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I read in some place that when there are crossing survival curves the Log-rank test it is not appropiate. What test I should use in this case?

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  • $\begingroup$ Are these empiric (not fitted) curves obtained from a simple Kaplan-Meier analysis? Can you provide the number of subjects at-risk along the x-axis? $\endgroup$
    – Todd D
    Commented Oct 2, 2016 at 4:44

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The log rank test can be understood as a score test for a simplified Cox proportional hazards model. The proportional hazards model assumes that the hazards are proportional (shocking, but true). If the Kaplan-Meier curves cross, that implies the hazards are not proportional. In that case, you can fit an extended Cox proportional hazards model. That means that you fit the model with an interaction between your covariates and time, and use a counting process formulation. Then you can test the model as you like. You can find a tutorial on doing this in SAS and R here:

  • Thomas, L., & Reyes, E. (2014). Tutorial: Survival Estimation for Cox Regression Models with Time-Varying Coefficients Using SAS and R. Journal of Statistical Software, 61(Code Snippet 1), 1 - 23. doi:http://dx.doi.org/10.18637/jss.v061.c01
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