This software is much easier than using my old stats book, thanks!
I played with the one-tailed test and came up with the same results you previously shared (i.e., 9 dead in 17 placebo patients would require 9 or fewer dead in Leronimab patients for 95% confidence).
I also changed the hits on placebo to see the change in Leronimab patients to achieve p<0.05 (>95% one-tailed confidence level). The results show that as the placebo numbers get worse (more dead), the number of allowed dead patients receiving Leronimab increases can increase by a higher number while still complying with p<0.05. For example, if the placebo dead increased by 1 from 9 to 10 patients, the number of Leronimab patients could increase by 2 from 9 to 11 patients, while still maintaining the required statistical significance.
Conversely, a decrease in the number of dead among placebo patients would require a larger decrease in the number of dead Leronimab patients to satisfy p<0.05. For example, if the number of dead placebo patients decreased by 3 from 9 to 6, the number of dead Leronimab patients would have to decrease by 5 from 9 to 4 to achieve p<0.05.
I think that the main takes from this are: 1) The worse the placebo results, the better for Leronimab, which would still need to prove efficacy, and 2) The results are not linear over larger ranges, but are approximately linear over narrow ranges.
I have to admit that I feel a bit sad to realize that we are playing with numbers that involve mortality, but it is the nature of the trials and it may help save many lives in the future.
Thank you again and let me know if you find errors in my analysis.
