#******* jags model of linear dose-response model with binomial likelihood for OR
modelBinLinearDRmetaOR <- function(){
for (i in 1:ns) { ## for each study
# binomial likelihood of number of events in the *refernce* dose level in a study i
r[i,1] ~ dbinom(p[i,1],n[i,1])
# logit parametrization of probabilities at each *refernce* dose level: by that exp(beta)= OR
logit(p[i,1])<- u[i]
for (j in 2:(nd[i])) { ## for each dose
# binomial likelihood of number of events for the *non-refernce* dose in a study i
r[i,j] ~ dbinom(p[i,j],n[i,j])
# logit parametrization of probabilities at each *non-refernce* dose level: by that exp(beta)= OR
logit(p[i,j])<- u[i] + delta[i,j]
delta[i,j] <- beta[i]*(X[i,(j)]-X[i,1])
}
}
# distribution of random effects
for(i in 1:ns) {
beta[i] ~dnorm(beta.pooled,prec.tau)
u[i]~dnorm(0,0.001)
}
# prior distribution for heterogenity
prec.tau<-1/variance
variance<-tau*tau
tau~dnorm(0,1)%_%T(0,)
# prior distribution for the regression coeff beta
beta.pooled ~ dnorm(0,0.001)
}
# xi~dnorm(0,0.1)
# tau.eta~dgamma(5,5)
# tau <- abs(xi)/sqrt(tau.eta)
# log(tau) <- log.tau
# log.tau~ dunif(-20,20)
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