Without going into the philosophical discussion of whether to include or exclude without-event studies in a meta-analysis of binary event data, I am wondering about what options there are in BUGS (I am using OpenBUGS) to actually include without-event studies in a binomial (network) meta-analysis (for example as a sensitivity analysis).
Although studies with a single arm that have no event are not a problem, in a fixed effect setting BUGS is not happy with without-event studies.
# loop over Nobs observation
for(i in 1:Nobs) {
# likelihood
r[i] ~ dbin(p[i],n[i])
# model
logit(p[i]) <- mu[s[i]]+ d[t[i]] - d[b[i]]
}
I had hoped a random effects setting might work, e.g.:
# loop over Nobs observation
for(i in 1:Nobs) {
# likelihood
r[i] ~ dbin(p[i],n[i])
# model
logit(p[i]) <- mu[s[i]]+ delta[i]*(1-equals(t[i],b[i]))
# random effect
delta[i] ~ dnorm(md[i],prec)
# mean of random effects distribution
md[i] <- d[t[i]] - d[b[i]]
}
BUGS still throws an error if I include the 0 event studies without continuity correction. I thought I had done this before successfully, so I am wondering if it is a matter of prior specifications (I am currently using normal vague priors on mu and a uniform on the sd (prec <- pow(sd,-2); sd ~ dunif(0,50)).
Thanks in advance for any advice!
Leon
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