1) The total number of Gehrig's at-bats for the season in my previous comment should have been 400, not 300 (and, sorry for the duplication)

2) I haven't seen many attempts to actually answer the question in the posting. I'll stick out my neck, after making a couple of simplifying assumptions: ASSUMING that the mortaility frequencies are reflective of the true underlying probabilities, and that the assignment of treatments to patients was otherwise random, I'd use treatment A on men regardless whether they have a history of heart disease, and treatment B on women. (In the real world, where these assumptions don't necessarily hold, I'd have to think a lot harder about the unreliability of the smaller sample sizes, and of course I'd try to find out all I could about further confounding factors, the rules that were used for treatment selection, potential mechanisms underlying the gender and history effects, etc.) Critical comments invited.