# Distance metric for survival functions?

Similar to this question, I would like a good metric for the distance between multiple ecdfs. However, in this case I have survival functions that are right-censored.

Question

Is there a metric that is commonly used with survival functions?

• If not, is there any metric that weights divergence at earlier values of $t$ more than later values? Early failures are much less desirable than later ones, so it seems natural to devise a metric with such a property.

• If not, does it make sense to devise one, and does anyone have any pointers for doing this? I have some intuition that cdfs might naturally penalize early failures, but I don't know enough about the subject to get from there to a metric.
• Have you considered having a look at the log-rank test that compares two Kaplan-Meier curves? – ocram Mar 24 '13 at 15:11

This metric has the added bonus of being readily available in R as the survdiff function in the survival package. Some citations (and the R implemenation) point at the Harrington and Fleming $G^\rho$ family of tests, where $\rho = 1$ gives the Peto-Peto test described above.