# Hierarchical Model for effect of HbA1c on CHF
# Model based on article by Mukherjee

model
{
  for (i in 1:2545)       # Loop over 2545 Matched Sets
  {
  numerator[i]<-exp(beta1*hba1c_7_8[i,1] + beta2*hba1c_8_9[i,1]
                    + beta3*hba1c_9_10[i,1] + beta4*hba1c_10[i,1])

 for (j in 1:J[i])

 {
  denominator[i,j]<-exp(beta1*hba1c_7_8[i,j] + beta2*hba1c_8_9[i,j]
                     + beta3*hba1c_9_10[i,j] + beta4*hba1c_10[i,j])
 }
  likelihood[i]<-numerator[i]/sum(denominator[i, 1:J[i]])

}

 beta1  ~  dnorm(0, 0.01) I(-2, 2)   #  Prior for beta1
 beta2  ~  dnorm(0, 0.01) I(-2, 2)   #  Prior for beta2
 beta3  ~  dnorm(0, 0.01) I(-2, 2)   #  Prior for beta3
 beta4  ~  dnorm(0, 0.01) I(-2, 2)   #  Prior for beta4

#  Create Odds Ratios

or.hba1c_7_8 <- exp(beta1)
or.hba1c_8_9 <- exp(beta2)
or.hba1c_9_10 <- exp(beta3)
or.hba1c_10 <- exp(beta4)

 for (i in 1:2545) {
                 ones[i] <- 1
                 p[i] <- likelihood[i]
                 ones[i] ~ dbern(p[i])
 }

}


# Inits

list(beta1=0.5, beta2=0.5, beta3=0.5, beta4=0.5)

# Results

node                 mean       sd         MC error     2.5%        median    97.5%     start     sample
beta1                0.02872    0.05431    0.00117      -0.0771     0.02821   0.1343    5001      5000
beta2                0.3046     0.06069    0.001468      0.1844     0.3047    0.4222    5001      5000
beta3                0.2553     0.08108    0.001523      0.09364    0.2559    0.4089    5001      5000
beta4                0.2986     0.08536    0.001567      0.1308     0.2989    0.4637    5001      5000
likelihood[1]        0.5        0.0        1.414E-12     0.5        0.5       0.5       5001      5000
likelihood[100]      0.08736    0.00168    4.105E-5      0.0841     0.08736   0.0905    5001      5000
likelihood[1000]     0.07867    0.00275    7.025E-5      0.07344    0.07865   0.0842    5001      5000
or.hba1c_10          1.353      0.1153     0.002107      1.14       1.348     1.59      5001      5000
or.hba1c_7_8         1.031      0.05604    0.001211      0.9258     1.029     1.144     5001      5000
or.hba1c_8_9         1.359      0.08253    0.001998      1.203      1.356     1.525     5001      5000
or.hba1c_9_10        1.295      0.1049     0.001977      1.098      1.292     1.505     5001      5000