# The zip file contains the WinBUGS code to fit the shared parameter model to the HERS data and the R code to perform G-computation in the sensitivity analysis for the HERS data analysis. 

# 1. SPM_model.txt: The WinBUGS model file to fit the SPM to the HERS data
# 2. postsample.Rdata: posterior samples of  model parameters for the SPM fitted to the HERS data; to be used in G-computation. 
# 3. EV_skewednormaldist.R:  R function to calculate the mean and Variance for a multivariate skewed normal disrtribution
# 4. G-computation.R: R functions to perform the G-computation (using approxmiations and exact values of the posterior variance of random slopes).
# 5.  summary-G-computation.R: R code to summarize the G-computation results for sensitivity analysisd[i],1]+randombi[numsubjid[i],2]*lonx1[i]
    }
  
  
### drop-out  process;
   for(j in 1:M) ### M is the number of subjects;
   {
     
      onesD[j]<-1   ### ones trick;
      for(kd in 1:numK)
      {
        quantD[j,kd]<-phi(lambdaD2[j,kd])
       ##### NB: 1-step() to avoid confusion on threshhold;  avoid numerical problems in probit
       lambdaD2[j,kd]<-lambdaD[j,kd]*step(lambdaD[j,kd]+7)*step(7-lambdaD[j,kd])+(-7)*(1-step(lambdaD[j,kd]+7))+7*(1-step(7-lambdaD[j,kd])) 
       ##### survDx1-survDx5: baseline covariates
       ##### survDvisit: visits
       ##### survalphaD[1:9]: regression coefficients
       ##### survgammaD[1:2]: \gamma parameters linking the outcome and dropout processes
       lambdaD[j,kd]<-(survalphaD[1]+survalphaD[2]*survDx1[j]+survalphaD[3]*survDx2[j]+survalphaD[4]*survDx3[j]+survalphaD[5]*survDx4[j]+survalphaD[6]*survDx5[j]+survalphaD[7]*survDvisit[kd]+survalphaD[8]*pow(survDvisit[kd],2)+survalphaD[9]*survDvisit[kd]*survDx5[j]+survgammaD[1]*randombi[j,1]+survgammaD[2]*randombi[j,2])
      }
       ##### survD: observed dropout time
       ##### survdeltaD: dropout indicator 1=dropout, 0=completer 
       probD[j]<-(prod(quantD[j,1:survD[j]])*pow((1-quantD[j,survD[j]]),survdeltaD[j])/pow(quantD[j,(survD[j])],survdeltaD[j]))*survdeltaD[j]+(1-survdeltaD[j])*prod(quantD[j,1:11])
  
      onesD[j]~dbern(probD[j])
  
     
  
  #### random effects;
  randombi[j,1]~dnorm(0,taub1)  ## random intercept;
  randombi[j,2]<-theta12*randombi[j,1]+e2[j]  ## random slope: var(b2)=theta21^2*var(b1)+var(e2)
  e2[j]~dnorm(0,taub2)
}


#####################################
### prior;

### lonalphaP: number of fixed effects in longitudinal model;
for(p1 in 1:lonalphaP)
{lonalpha[p1]~dnorm(0,1.0E-2)}
### survalphaDP= number of regression coefficients  in the dropout model ;
for(p2 in 1:survalphaDP)
{survalphaD[p2]~dnorm(0,0.25)}
### survgammaDP: number of gamma parameters;
for(p3 in 1:survgammaDP)
{survgammaD[p3]~dnorm(0,0.25)}


###### variance parameters for random effects;
taub1<-1/(sigmab11*sigmab11)
taub2<-1/(sigmab22*sigmab22)
sigmab11~dunif(0,5)
sigmab22~dunif(0,5)
theta12~dnorm(0,1.0E-2)

###### error variance
tauepsilon~dgamma(0.001,0.001)
sigma2epsilon<-1/tauepsilon

sigma2b11<-1/taub1  ## variance of random intercepts
sigma2b22<-sigma2b11*pow(theta12,2)+1/taub2  ### variance of random slopes

sigma2b12<-theta12*sigma2b11 #### covariance
rho12<-theta12*sqrt(sigma2b11)/sqrt(sigma2b22) #### correlation; 
}