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.
My only criticism is that you never really explain why you would do as you say. Perhaps it is as Daniel Burfoot said here, that for each person you are simply using the best information that you have?
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.
My only criticism is that you never really explain why you would do as you say. Perhaps it is as Daniel Burfoot said here, that for each person you are simply using the best information that you have?