model;

# Calculates posterior distribution of model parameters and the area under curve. y = test

# Based on O'Mally et al. [6] regression method.

{

# likelihood function

for(i in 1:N) {

# The following statement is the regression of y on the disease vector d

y[i]∼dnorm(mu[i],precy[d[i]+1]);

#   yt[i] < −log(y[i]); # logarithmic transformation

# The beta vector are the regression coefficients

mu[i] < −beta[1] + beta[2] × d[i];

}

# prior distributions - non-informative prior; similarly for informative priors

for(i in 1:P) {

beta[i] ∼ dnorm(0, 0.000001);

}

for(i in 1:K) {

precy[i]∼dgamma(0.001, 0.001);

vary[i] < −1.0/precy[i];

}

# calculates area under the curve

la1 < −beta[2]/sqrt(vary[1]); # ROC curve parameters

la2 < −vary[2]/vary[1];

# auc is the area under the ROC curve

auc < −phi(la1/sqrt(1+la2));

}

# Diabetes data

list(K = 2, P = 2, N = 78, y = c(123,129,115,131,119,111,129,127,118,111, 131,118,126,130,122,112,122,128,123,119,132,118,126,136,118,122, 119,117,129,120,125,115,131,123,130,113,128,138,119,118,124,127, 139,120,122,120,114,114,122,127,123,118,131,130,139,125,135,121,124, 109,106,100,88,106,108,110,111,112,94,122,110,113,106,114,101,99,128,106), d = c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))

# the initial values for the simulation

list(beta = c(0,0),precy = c(1,1))