I estimated the Bayesian posterior using a skeptical prior (mean no effect, standard deviation extending 5% past MCID) and methods proposed in this paper. As you suggested the probability of HR<1 was 0.95, with a HR of 0.78 95% Certainty Interval 0.59-1.04.

I’d argue this is strong evidence for adopting the capillary refill time as the target end-point, instead of the more invasive and less direct measure of tissue hypoperfusion given by lactate.

Limitation: This method assumes normal distributions of the parameters.

**R Code** (Please point out if there are any errors so I can use again)

*Update: Code has been refined with help from @BenYAndrew

#Calculating MCID#

#Here I am using the estimated reductions from the power calculation to get an OR for the MCID (may need to be converted to RR instead of OR)#

n < - 420 #Sample size

a <- 0.3 * n #Intervention and Outcome

b <- 0.45 * n #Control and Outcome

c <- n - a #Intervention No Outcome

d <- n - b #Control No Outcome

MCID <- ((a+0.5) * (d+0.5))/((b+0.5) * (c+0.5))

*#Hazard Ratio*

HR <- 0.75

UCI <- 1.02

*#Calculate Prior*

#Skeptical prior mean estimate

#Calculating skeptical prior SD estimate for 5% probability of exceeding projected estimate

z <- qnorm(0.05)

prior.theta <- log(1)

prior.sd <- (log(MCID)-prior.theta)/z

#Enthusiastic Prior

prior.theta <- log(MCID)

prior.sd <- (log(1.05)-log(MCID))/qnorm(0.975)

*#Calculate Likelihood*

L.theta <- log(HR)

L.sd <- (log(UCI)-log(HR))/qnorm(0.975)

*#Calculate Posterior*

post.theta <- ((prior.theta/prior.sd^2)+(L.theta/L.sd^2))/((1/prior.sd^2)+(1/L.sd^2))

post.sd <- sqrt(1/((1/prior.sd^2)+(1/L.sd^2)))

#Calculate posterior median effect and 95% certainty interval

cbind(exp(qnorm(0.025, post.theta,post.sd, lower.tail = T)), exp(qnorm(0.5, post.theta,post.sd)), exp(qnorm(0.975, post.theta,post.sd)))

#Calculate probability benefit (HR < 1.0)

pnorm(log(1), post.theta,post.sd, lower.tail=T)

*# Plot the prior density*

mu.plot <- seq(-2,2,by=0.025)

prior <- dnorm(mu.plot, prior.theta, prior.sd)

likelihood <- dnorm(mu.plot, L.theta, L.sd)

posterior <- dnorm(mu.plot, post.theta, post.sd)

plot(exp(mu.plot), exp(prior),

type=“l”, col=“black”, lty=3,

xlim=c(0,1.5),

ylim=c(1,15),

lwd=2,

xlab=“Hazard Ratio”,

ylab=“Probability Density”)

#likelihood

lines(exp(mu.plot), exp(likelihood), col=“green”,lwd=2,lty = 2)

#posterior

lines(exp(mu.plot), exp(posterior), col=“red”,lwd=2)

abline(v=1, col = “gray”)

legend(“topleft”,

col=c(“black”,“green”,“red”),

lty=c(3,2,1),

lwd=2, #line width = 2

legend=c(“Prior”, “Likelihood”, “Posterior”))