#******* jags model of linear dose-response model with binomial likelihood for RR
modelBinLinearDRmetaRR <- function(){
for (i in 1:ns) { ## for each study
# binomial likelihood of number of events in the *reference* dose level in a study i
r[i,1] ~ dbinom(p[i,1],n[i,1])
# log parametrization of probabilities at each *reference* dose level: by that exp(beta)= RR
log(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])
# log parametrization of probabilities at each *non-reference* dose level: by that exp(beta)= RR
log(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.beta)
u[i]~dnorm(0,0.001)%_%T(,0)
}
# prior distribution for heterogenity
prec.beta<-1/variance
variance<-tau*tau
tau~ dnorm(0,1)%_%T(0,)
# prior distribution for the regression coeff beta
beta.pooled ~ dnorm(0,0.001)
}
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