Chapter 7 Exercises
Kidney transplants
Solutions

In Example 7.3.1 (ordered logistic regression model for kidneys for transplantation), add BUGS code to calculate the probability that three or more indicators of organ damage are present after an agonal phase lasting a) 10 minutes, b) 2 hours and c) 12 hours? What are the posterior medians of these probabilities?


model {
for (i in 1:N) {
Score[i] ~ dcat(p[i,])
p[i,1] <- 1 - Q[i,1]
for (r in 2:5) {
p[i,r] <- Q[i,r-1] - Q[i,r]
}
p[i,6] <- Q[i,5]
for (r in 1:5) {
logit(Q[i,r]) <- b.apd*lAPD[i] - c[r]
}
}
   
   logit(p3.10min) <- b.apd*log(10) - c[3]
   logit(p3.2h) <- b.apd*log(2*60) - c[3]
   logit(p3.12h) <- b.apd*log(12*60) - c[3]

for (i in 1:5) {
dc[i] ~ dunif(0, 20)
}
c[1] <- dc[1]
for (i in 2:5) {
c[i] <- c[i-1] + dc[i]
}
b.apd ~ dnorm(0, 1.0E-03)
or.apd <- exp(b.apd)
}

Click arrow for data and initial values

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   p3.10min   0.1854   0.03   5.228E-4   0.1308   0.184   0.2477   501   10000
   p3.12h   0.5296   0.07838   0.001861   0.3772   0.5294   0.6799   501   10000
   p3.2h   0.3661   0.04761   7.603E-4   0.2756   0.3654   0.4628   501   10000
   
From the posterior medians, we estimate a   18%, 37% and 53% probability that there will be three or more indicators of organ damage after agonal phases of 10 minutes, 2 hours and 12 hours respectively.