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.