On October 1, 2021, Merck announced the result of an interim analysis of the efficacy of antiviral drug Molnupiravir for the treatment of covid-19 patients (https://www.merck.com/news/merck-and-ridgebacks-investigational-oral-antiviral-molnupiravir-reduced-the-risk-of-hospitalization-or-death-by-approximately-50-percent-compared-to-placebo-for-patients-with-mild-or-moderat). The trial was designed as a parallel RCT with two groups: Molnupiravir and Placebo. The key data are as follows:

In this analysis, we estimate the probability that Molnupiravir reduced the risk of hospitalization or death by at least 50%. The method of analysis is based on the Beta-Binomial model.

Traditional analysis

library(epiR)
## Warning: package 'epiR' was built under R version 4.0.2
## Loading required package: survival
## Package epiR 1.0-15 is loaded
## Type help(epi.about) for summary information
## Type browseVignettes(package = 'epiR') to learn how to use epiR for applied epidemiological analyses
## 
dd = c(28, 385-28, 53, 377-53)
dat = matrix(dd, nrow=2, byrow=T)
epi.2by2(dat, method = "cohort.count")
##              Outcome +    Outcome -      Total        Inc risk *        Odds
## Exposed +           28          357        385              7.27      0.0784
## Exposed -           53          324        377             14.06      0.1636
## Total               81          681        762             10.63      0.1189
## 
## Point estimates and 95% CIs:
## -------------------------------------------------------------------
## Inc risk ratio                               0.52 (0.33, 0.80)
## Odds ratio                                   0.48 (0.30, 0.78)
## Attrib risk *                                -6.79 (-11.15, -2.42)
## Attrib risk in population *                  -3.43 (-7.56, 0.71)
## Attrib fraction in exposed (%)               -93.30 (-198.74, -25.08)
## Attrib fraction in population (%)            -32.25 (-53.99, -13.58)
## -------------------------------------------------------------------
##  Test that OR = 1: chi2(1) = 9.232 Pr>chi2 = 0.00
##  Wald confidence limits
##  CI: confidence interval
##  * Outcomes per 100 population units

Bayesian analysis of hospitalization

n = 100000
n1 = 385; n2 = 377 
x1 = 28;  x2 = 53 
a1 = 1; b1 = 1; a2 = 1; b2 = 1
p1 = rbeta(n, x1+a1, n1-x1+b1)
p2 = rbeta(n, x2+a2, n2-x2+b2)
rr = p1/p2
plot(density(rr))

quantile(1-rr, c(0.025, 0.50, 0.975))
##      2.5%       50%     97.5% 
## 0.2015564 0.4751597 0.6629467
table(rr < 0.50)
## 
## FALSE  TRUE 
## 58685 41315

Bayesian analysis of deaths

n = 100000
n1 = 385; n2 = 377 
x1 = 0;  x2 = 8 
a1 = 1; b1 = 1; a2 = 1; b2 = 1
p1 = rbeta(n, x1+a1, n1-x1+b1)
p2 = rbeta(n, x2+a2, n2-x2+b2)
rr = p1/p2
plot(density(rr))

quantile(1-rr, c(0.025, 0.50, 0.975))
##      2.5%       50%     97.5% 
## 0.5048196 0.9212117 0.9972351
table(rr < 0.50)
## 
## FALSE  TRUE 
##  2428 97572