# How do I compare 2 survival curves?

I am comparing the survival of 2 insect larvae under identical conditions. I have the cumulative survival rate (%) for each day. In my case, I have 100% survival on day 0 (start of test) and survival goes down from there. When I plot this for both insects, I get 2 curves with cumulated survival on the Y axis and the number of days since the start of the test on the X axis. What test should I use to see if these curves are significantly different from each other.

Are all larvaes dead i.e. all survival times known? If yes, you can use any suitable two-sample test, e.g. Wilcoxon's rank-sum test (to see if survival times tend to be larger for one type of insect) or Kolmogorov-Smirnov test (to see if your curves are different). Otherwise, if you have censored times, the log-rank test might be more appropriate.

PS: one Michael was faster than the other ;-)

• Not all individuals died, some survived to become adults. But yes, Survival time is known. My raw data looks something like this: Day1 - Survival 100% Day2 - Survival 76% Day 3 - Survival 66% etc. – Stéphane Jun 21 '17 at 20:47
• Usually, raw data would consist of a duration, a status (died or not) and the type per insect. And then use methods from survival analysis as in Michael's answer. If you only have survival rates without any other infos (e.g. numbet of insects per group), you can't do a hypothesis test. – Michael M Jun 21 '17 at 20:54
• So the ''raw'' data I mentionned earlier is already a little ''cooked''? I guess that makes sense. I have the duration, status, and species (type?) for each individual insect observed. This would then be my raw data that I can work with. This seems rather obvious now that I think about it... This is the first time I work with this kind of data so I'm unsure as to what Kaplan-Meier estimates are, but I'll look into it. I had no idea where I was going, hence the vagueness of my question. At least now I have a general direction. Thanks. – Stéphane Jun 21 '17 at 21:08
• Perfect! Without censoring (all larvaes died), it would be classic stats on the durations. It's the censoring that made scientists inventing methods like Kaplan-Meier estimates, log-rank tests and Cox regression. – Michael M Jun 21 '17 at 21:19

If you are using Kaplan-Meier estimates for the survival curves you can use the log rank test for determining whether the two survival curves are different.