sTeamTraen wrote: ↑Mon Nov 23, 2020 8:59 pm
With those numbers and proportionate numbers of cases, there would be 31 cases with the half dose first and 100 with the full dose first. 90% (62%) efficiency suggests to me that the treatment group had 10% (38%) of the number of cases of the control group. That would mean (3 Tx, 28 control) cases in the half-dose trial and (27 Tx, 73 control) in the full-dose trial, and that would also give the expected (30 Tx, 101 control) in the overall score, for an average efficacy of 70% (i.e., the vaccine prevented 71 out of 101 cases in the treatment group). Assuming equal sample sizes in each group:
My previous post on this (re the AstraZeneca vaccine) contained an error (for the full-dose cohort I had calculated on the basis of the total sample for the study, not the sample for that cohort) and a faulty assumption (i.e., equal numbers of people in each group). It was pointed out to me that in many of the other trials, there have been more people in the treatment group than the control group, so I revised my numbers (and spotted the first error myself while doing so).
Without knowing the exact number in each group we can't determine how many cases there were, but if we assume it's about 2:1 (treatment:control), we could have numbers like this:
Half-dose: Treatment N=1804, 5 cases; Control N=937, 26 cases
1 - ((5/1804)/(26/937)) = 0.9001151 = 90.01151%
Full-dose: Treatment N=6074, 45 cases; Control N=2821, 55 cases
1 - ((45/6074)/(55/2821)) = 0.6200048 = 62.00048%
(Of course, the percentages are unlikely to be anything like as precisely close to an integer as those.)
Still, though, 5 cases is a small number. One case more or fewer would change the effectiveness of the half-dose regime by 2 percentage points. But of course, if the vaccine was 100% effective, we would have 0 cases, and be jumping up and down, even though that's a *very* small number. Maybe a better indication of the sample size problem is having only 26 cases in the control group.