A little decision analysis goes a long way

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In the House episode Maternity, there's an epidemic in the hospital, with two really sick babies and four others getting sick. As usual, the House team can't figure out what kind of infection it is. The two leading candidates are MRSA and pseudomonas, so they prescribe vancomycin for the MRSA and aztreonam for the pseudomonas. Of course, something goes wrong, in this case that both babies start to experience renal failure, but since both drugs can cause renal failure, they don't know which one to stop.

House's oh-so-clever response is to take each baby off one drug and see what happens. Naturally, the hospital administrator and lawyer are freaked out and want him to get informed consent, which means telling both sets of parents that the other baby is getting a different treatment. House refuses because then they wouldn't consent, which obviates the point of the trial. Or does it? Let's work through the logic chain, using only baby A. If we take it off vancomycin and it gets better. Bingo, aztreonam works. On the other hand, if it dies, then we know that aztreonam doesn't work. Now, we don't know that the other works, but we know what doesn't, so the only choice is to use the other drug. Problem solved.

So, informationally it doesn't matter whether you take the patients off different drugs or the same drug. From a cost/benefit perspective it doesn't matter to the parents either. If you really have no idea which drug will work, then you shouldn't care which drug your baby is on--and it doesn't matter what the other one is on. There's a 50% chance of death either way. Superficially, you might be able to see why doctors would want to take the babies off different drugs: if you believe the problem is one of the two bacteria, then this lets you save one of them. But consider that it also makes it very likely that one of them will die. If you take them off the same drug, then there's a 50% chance that both will die and 50% chance one will live: expected value, one death, same as if you take them off different drugs. Of course, there are risk models where a 50% chance of 2X is worse than X, but that mostly requires nonlinearity of preference, which doesn't seem appropriate here.

Of course, at the end of the day it turns out that the problem is neither MRSA nor pseudomonas, which just goes to show that decision models are only as good as the data you feed into them.

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While I really like House as a TV show, it's basically a clinic (get it?) on the decision making fallacies typically exhibited by doctors.

While professionally I'm appalled that they depict (probably accurately) one of the world's best diagnosticians using such poor decision making procedures, it would be really boring to have a TV show where a comptuter spits out the best answers.

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