I agree that 5/10 survival from the Montefiore coh

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I agree that 5/10 survival from the Montefiore cohort is seems encouraging, but t-tests and binomial tests only make sense if you have good samples to work with. We really don't (yet).

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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.

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But it is completely unclear how the sample for that estimate of p_hat = 88% (not p) that you cite relates to the Montefiore cohort or the S Cal. cohort, and if it is even a little different, your p-values will swing wildly.

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This number was cited in Patterson's paper extracted from the Richardson paper: "Presenting Characteristics, Comorbidities, and Outcomes Among 5700 Patients Hospitalized With COVID-19 in the NewYork City Area" in the section :"Outcomes for Patients Who Were Discharged or Died". The study had 2634 patients in this classification in the NY area (where Montifiore is), so this Cohort is pretty good as a reference.

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Mortality rates for those who received mechanical ventilation in
the 18-to-65 and older-than-65 age groups were 76.4% and 97.2%, respectively.

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Also from CNN (other source).

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(CNN) Nearly all coronavirus patients who needed ventilators in New York's largest health system to help them breathe died, a study found.

Overall, about 20% of Covid-19 patients treated at Northwell Health died, and 88% of those placed on ventilators died, according to the study. A ventilator is a device that forces air into the lungs of patients who cannot breathe on their own because of severe pneumonia or acute respiratory distress syndrome.

https://amp.cnn.com/cnn/2020/04/22/health/cor...index.html

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So, I think the number of P=0.88 (as in probability) is well supported and the sample should reflect the one studied (in New York) and is large for reference.

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I expect the p-values we see from actual, quality data will be somewhere between 0.001 and 0.4

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I am afraid one cannot make any accionable investment decision with this range 0.001= approval; 0.4= not approval.

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I doubt very much that the FDA will be using a fixed and known binomial p in any analyses of the trial data!

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??? What else ?? The Binomial probability distribution is what one uses in cases of failure success trials ... What one does is exactly that: finds a probability from the reference (placebo) cohort and then, calculate how likely is that the results of the "drug" group are due to chance (null hypothesis (H0) that asserts that there is no true difference between the drug, and the alternative, placebo). If this value is less than a reference value (normally 0.05), the null test is discharged and the conclusion is that the drug works. Ho is rejected.

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A binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times. The binomial is a type of distribution that has two possible outcomes (the prefix “bi” means two, or twice).

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In my opinion, it's crazy that a drug with a good safety profile and tantalizing anecdotal stories about effectiveness cannot be tried---except under extraordinary Big Brother oversight---even if the patient and his or her doctor wish to.

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Crazy indeed is maddening. I think the institutions' are failing the people. They should try to help at much faster speed (every day people are dying) and in a more balanced manner. I don't think hey have responded well from any perspective.