Wednesday, March 30, 2005
Don't Do It Code Blue!
Via Michelle Malkin, I see where the radiologist who is running Code Blue Blog has put forth the following wager:
So let's analyze this gambling situation. If the neurologist guesses 60 or more cases correctly as either PVS or not PVS, the the neurologist quadruples his/her money (maybe 5 times - I'm not certain what distinction code blue is drawing on neurologist/bioethicist).
To prove my point I am offering $100,000 on a $25,000 wager for ANY neurologist (and $125,000 for any neurologist/bioethicist) involved in Terri Schiavo's case--including all the neurologists reviewed on television and in the newspapers who can accurately single out PVS patients from functioning patients with better than 60% accuracy on CT scans.
I will provide 100 single cuts from 100 different patient's brain CT's. All the neurologist has to do is say which ones represent patients with PVS and which do not.
If the neurologist can be right 6 out of 10 times he wins the $100,000.
Now if the neurologist was an untrained monkey, there would be a fifty-fifty chance of getting each diagnosis correct and the odds of getting 60 or more correct would be approximately 2.8%. Quadruple the return, and you have an expectation of getting 11.2% of your wager back. Those are indeed bad odds. However, that's for monkeys.
We're talking humans here, neurologists to be precise. If they only have a probability of just 56.13%, then they'll break even. Any higher and they'll make money.
Now cause I'm a dork, I plotted the probability of guessing right for 60 or more scans versus the probability of guessing any one scan correctly. As I show below, the neurologists need to only be able to guess right a little better than 56% of the time to come out ahead.
However, we can be more precise as to exactly how well the neurologists will have to do.
From the Journal of Neurology, we know that the occurence of misdiagnosis of PVS has been measured at 37% (that's disturbingly high which is what I think is Code Blue's motivation).
But that's just the probability of false alarm (the probability of diagnosing PVS when not PVS). We also have to factor in the probability of a miss (the probability of not diagnosing PVS when the patient really does have PVS).
Given that the break even point for Code Blue is when the neurologists guess right 56% of the time, we can figure out what the probability of a miss will have to be for code blue to make money (assuming that horrendous 37% false alarm rate is maintained). This miss probability can be found by solving the following equation:
For the sake of argument, let's assume that Code Blue chooses his samples so that half are PVS and half are not. Then that expression above becomes:
So assuming with this half and half assumption and with the assumption that the neurologists will continue with a 37% false alarm rate (saying it's PVS when it's not), then when the neurologists say the scan isn't PVS, at least 50.7% ot the time the neurologists would have to be wrong for Code Blue to make money.
Code Blue makes excellent points 1) that radiologists are the ones trained to take first looks at the scans, not neurologists and 2) that PVS is misdiagnosed ALOT.
But if Code Blue wants to hang onto his money, he shouldn't make this wager...