Discrete_Survival_with_Cluster_Time

data{
dimY <- dim(y2) # y2 is a matrix with # of rows = subject count, # of columns = number of time points count
N <- dimY[1] # number of observations/subjects (wide format) 
J <- dimY[2] # number of time points
dimX <- dim(X) # dimension of fixed effects matrix
p_x <- dimX[2] # number of fixed effects to include 
}

model
{   
for(i in 1:N){ # for each person
  for(j in 1:J){ # at each time point

# survival model using binary outcome with time as a predictor
y2[i,j] ~ dbern(p[i,j]) # indicator of dropout follows bernoulli with probability p[i,j]
p[i,j] <- ilogit(inprod(X[i,],beta[]) + gamma[clusts[i],j]) # logistic regression with fixed effects (beta)
# and clusts needs to be supplied by the user
# clusts is from the post-processed clusters estimated via the longitudinal clustering algorithm
# there is a gamma_k (k = cluster number) for each time point j
  }
}

# normal priors on fixed effects with tiny precision
for(k in 1:p_x){
beta[k] ~ dnorm(0, 0.01)
}

#J is time point
for(j in 1:J){
# for cluster assignment effects 
for(k in num_clust){ # num clust needs to be provided in the data argument
# num clust is a vector with the numerical names of the cluster (for instance 1, 2, 3,..., 10)
 gamma[k,j] ~ dnorm(0, tau_gam[j]) # tau_gam[j] provides an estimate for how variable hte drop out effects are for that time point j 
    }
tau_gam[j] <- 1/sig_gam[j] # precision
sig_gam[j] ~ dunif(0.1, 50) # on the variance scale
  }
}