Quote:Well, 11 patients are not a whole lot, of course. But one has to use the information one has. For me is better to use 11 patients than no patients at all.
I'd take a good (meaning representative) sample of n = 11 over a bad large sample that does not look like the target population. But that's only half the problem. You need a good sample to compare it to. "88%" is guaranteed to be wrong, but we don't know how wrong or in what direction. I wouldn't put much faith in that number AT ALL. The problem is that for that number to make any sense, the population it is derived from has to be the same that the 10 (or 11) are derived from. And, no, I mean "population" in the statistical sense (patient condition and treatment), not in the demographic sense (e.g. NY area). Otherwise the statistics are bunk.
Did the patients that the 88% estimate (not fixed reality --- critical distinction in statistics!) come from have the condition (severity of condition, length of time since initial infection, prior treatment, age, comorbidities), the same treatment, and the same measure of mortality (in the study you cite, the odds of mortality are calculated as fatalities:discharges. What about the fates of the patients who were living but still in the hospital? Same as in the Montefiore cohort? No idea. These are crucial questions, which is part of the reason clinical trials are so blinkin' hard to set up. Unless they are carefully dealt with, the "statistics" are garbage if you try to make inference beyond your sample.
And my objection to your "what FDA does" comment is not that there's anything wrong with the binomial distribution (one might even say that my entire professional life as a statistician for the past 8 years or so has been working with elaborations of binomial RVs...and other discrete distributions for the 17 years before that!), but that there's a world of difference between a two-sample test and a one-sample test, and they will certainly use two-sample tests.
3
