One could try to reverse engineer their power calculations and assumptions on the study, using a power calculator like here:
https://www2.ccrb.cuhk.edu.hk/stat/proportion/Casagrande.htm
Assuming 80% power used to estimate sample size, with one sided test (H0: P1=P2 vs. Ha: treatment with LL lowers mortality from no treatment / placebo; i.e. P2<P1), the study sample size is approximated by assuming P1=mortality with placebo at 30%, and P2=mortality with LL at 18%. (Gives N=378 sample size, close to 390). So, these might be close to the numbers estimated at trial start to get our sample size and trial powered properly.
When discussing stats, people haven't talked much about confidence intervals or the margin of error in estimating mortality rates in each group, but these are critical when calculating the difference in proportions (absolute difference in mortality in our trial), to prove that it does not include 0. i.e. we want our reduction in risk of death to be less 0%; so a 12% absolute reduction from 0.3 to 0.18 might have a 95%CI from -16% to -8%, which would be good. However if it's only from 0.23 to 0.2 difference in mortality with LL, that -3% might have a 95% CI from -8% to +2%, which is not significant (it could be 8% drop, but it could also be a 2% increase in risk from LL).
From this number, we can also get the number needed to treat to save one life. It is just 1/(P1-P2). If the difference is 12.5%, then we would need to treat 8 people to save one life. They reported this number recently for the UK IL-6 trial. Mortality in their controls was 35.8%; Tocilizumab had 28% and Sarilumab 22.2% death rate. Combined, the reduction was from 35.8% to 27.2%, or a relative reduction of 24%, and absolute of ~8.6%. The number needed to treat to save a life was thus around 12 patients.
https://www.dummies.com/education/math/statis...oportions/
A similar concept for comparing differnce in proportions is the risk ratio or related odds ratio, to prove that it does not include 1.0. i.e. we want our relative risk of death to be less than 1 when using LL, so .18/.30 is 0.6 (or a 40% relative reduction in mortality). The confidence interval of the risk ratio that will tell us if this is significant or not. If reduction is 0.6, with 95%CI from 0.3 to 0.9, then that would be great. If the reduction / RR is 0.8, with 95% CI from 0.3 to 1.3, then that would not be significant.
https://www.cureus.com/articles/39455-whats-t...ard-ratios
Stats are interesting, but I forget everything I may have learned and I'm sure I've mis-stated something above.
https://www2.ccrb.cuhk.edu.hk/stat/proportion/Casagrande.htm
Assuming 80% power used to estimate sample size, with one sided test (H0: P1=P2 vs. Ha: treatment with LL lowers mortality from no treatment / placebo; i.e. P2<P1), the study sample size is approximated by assuming P1=mortality with placebo at 30%, and P2=mortality with LL at 18%. (Gives N=378 sample size, close to 390). So, these might be close to the numbers estimated at trial start to get our sample size and trial powered properly.
When discussing stats, people haven't talked much about confidence intervals or the margin of error in estimating mortality rates in each group, but these are critical when calculating the difference in proportions (absolute difference in mortality in our trial), to prove that it does not include 0. i.e. we want our reduction in risk of death to be less 0%; so a 12% absolute reduction from 0.3 to 0.18 might have a 95%CI from -16% to -8%, which would be good. However if it's only from 0.23 to 0.2 difference in mortality with LL, that -3% might have a 95% CI from -8% to +2%, which is not significant (it could be 8% drop, but it could also be a 2% increase in risk from LL).
From this number, we can also get the number needed to treat to save one life. It is just 1/(P1-P2). If the difference is 12.5%, then we would need to treat 8 people to save one life. They reported this number recently for the UK IL-6 trial. Mortality in their controls was 35.8%; Tocilizumab had 28% and Sarilumab 22.2% death rate. Combined, the reduction was from 35.8% to 27.2%, or a relative reduction of 24%, and absolute of ~8.6%. The number needed to treat to save a life was thus around 12 patients.
https://www.dummies.com/education/math/statis...oportions/
A similar concept for comparing differnce in proportions is the risk ratio or related odds ratio, to prove that it does not include 1.0. i.e. we want our relative risk of death to be less than 1 when using LL, so .18/.30 is 0.6 (or a 40% relative reduction in mortality). The confidence interval of the risk ratio that will tell us if this is significant or not. If reduction is 0.6, with 95%CI from 0.3 to 0.9, then that would be great. If the reduction / RR is 0.8, with 95% CI from 0.3 to 1.3, then that would not be significant.
https://www.cureus.com/articles/39455-whats-t...ard-ratios
Stats are interesting, but I forget everything I may have learned and I'm sure I've mis-stated something above.
