Is it valid to compare 'time to separation of curves' between 2 Kaplan-Meier curves?

Suppose one has 2 placebo-controlled clinical drug trials (drug X vs placebo; and drug Y vs placebo).

And suppose one creates a Kaplan-Meier plot for time to some event (eg, disease progression) for drug X vs placebo, and one creates another similar K-M plot for drug Y vs placebo.

Would it then be valid to compare the 2 K-M graphs (at least qualitatively, by eye) and say: drug X seems to separate from placebo faster than drug Y separates from placebo, so drug X seems to have a more rapid effect?

I think something like this is sometimes done in the literature, but I've seen a paper which stated that one cannot make such inferences from Kaplan-Meier graphs.

• Is there censoring (dropout, other disease)? Do you assume that it is the same for both trials? – martin Aug 7 '13 at 9:28
• Yes, I'm envisaging a situation with censoring, since that's quite common in such clinical trials. And the censoring would not be the same in each study arm – user2503 Aug 8 '13 at 15:05

In general this is an unsafe practice. What would be needed is a simultaneous confidence interval for the difference in two survival curves. It is easy to get non-simultaneous (pointwise) confidence bands (e.g., in R rms package survdiffplot function). An example is in http://biostat.mc.vanderbilt.edu/wiki/pub/Main/StatGraphCourse/graphscourse.pdf p. 15.