#JAGS Code to fit our covariate adjusted model 
write("data{
 ## Data Construction for the Historical Likelihood ##
	  for (i0 in 1:n0) {
	         for (k in 1:K) {
	            # indicates event-time in interval k
			zed0[i0,k] <- delta0[i0]*step(y0[i0] - kappa[k] - 0.00001)*step(kappa[k+1] - y0[i0]);   
				
		      # length of overlap of y0[i0] with interval k
		      theta0[i0,k] <- (min(y0[i0], kappa[k+1]) - kappa[k])*step(y0[i0] - kappa[k]);      
			
	         }
	   } 
 ## Data Construction for the Current Likelihood ##
	  for (i in 1:n) {
	         for (k in 1:K) {
	            # indicates event-time in interval k
			zed[i,k] <- delta[i]*step(y[i] - kappa[k] - 0.00001)*step(kappa[k+1] - y[i]);   
				
		      # length of overlap of y[i] with interval k
		      theta[i,k] <- (min(y[i], kappa[k+1]) - kappa[k])*step(y[i] - kappa[k]);      
	         }
	   } 
}

model{ 
 ## Historical Likelihoods ##
	  for (i0 in 1:n0) {
	         for (k in 1:K) {
		    # define the likelihood
			mu0[i0,k] <- theta0[i0,k]*exp(alpha0[k]+inprod(beta0[],X0[i0,]))
			zed0[i0,k] ~ dpois(mu0[i0,k]);
	         }
	   } 

 ## Current Likelihoods ##
	  for (i in 1:n) {
	         for (k in 1:K) {			
		    # define the likelihood
			#Use for gamma constant over time
			 mu[i,k] <- theta[i,k]*exp(alpha[k]+inprod(beta[],X[i,])+inprod(gamma[],Z[i,]))
			#Use for time-dependent gamma
			 #mu[i,k] <- theta[i,k]*exp(alpha[k]+inprod(beta[],X[i,])+inprod(gamma[k,],Z[i,]))
			zed[i,k] ~ dpois(mu[i,k]);
	         }
	   } 

	#Vague Priors for Treatment Effect and Historical Log-Hazards
	#Commensurate Priors on Current Log-Hazards
	  for (j in 1:p){
		 beta0[j] ~ dnorm(0,0.0001);
		 beta[j] ~ dnorm(beta0[j],tau[j]);
	  }
	  for (j in 1:q){
		 #Use for constant gamma
		  gamma[j] ~ dnorm(0,0.0001)
		 #Use for time-dependent gamma
		  #gamma[1,j] ~ dnorm(0,0.0001)
		  xi[j] <- 1/(sigmaX[j]*sigmaX[j]);
		  sigmaX[j] ~ dunif(0.01,100);
	  }
	  	 alpha0[1] ~ dnorm(0,0.0001);
	  	 alpha[1] ~ dnorm(alpha0[1], tau[p+1]);
		 v <- tau[p+1]/spike[2];
	  for (k in 2:K) {
		 alpha0[k] ~ dnorm(alpha0[k-1], eta0);
		 alpha[k] ~ dnorm(v*alpha0[k]+(1-v)*alpha[k-1], v*tau[p+1] + (1-v)*eta);
	   #Use for time-dependent gamma
	    #for(j in 1:q){
		 #gamma[k,j] ~ dnorm(gamma[k-1,j],xi[j])
	    #}
	  } 
		#Spike and Slab on Regression Coefficients
	  for (j in 1:p){
		 t[j] ~ dbern(p0);
		 slab[j] ~ dunif(l.slab,u.slab);
		 tau[j] <- (1-t[j])*spike[1] + t[j]*slab[j];
	  }
		#Spike and Slab on Baseline Hazard
		 t[p+1] ~ dbern(p0);
		 slab[p+1] ~ dunif(l.slab,u.slab);
		 tau[p+1] <- (1-t[p+1])*spike[2] + t[p+1]*slab[p+1];

		 eta0 <- 1/(sigma0*sigma0);
		 sigma0 ~ dunif(0.01,100);
		 eta <- 1/(sigma*sigma);
		 sigma ~ dunif(0.01,100);
}","OurModel.txt")