Dear all,

I’m new to Stan. The following paragraph is my Stan code for the hierarchical survival model. But I had trouble running my model (about ~ 8 days for iter=10000, warm up=5000, N=35000). Now, I want to run my model by with-in chain parallelization method with reduce_sum (25.1 Reduce-sum | Stan User’s Guide).

How can I run my model using this method? Can anyone help me to change my codes in RSTAN?

Thank you in advance!

My Stan code is as below (N=35000, province=31, num=12):

```
'''
functions{
real icar_normal_lpdf(vector phi, int province, int[] node1, int[] node2) {
return -0.5 * dot_self(phi[node1] - phi[node2]);
}
// defines the log survival
vector log_S (vector t, real shape,vector scale){
vector[num_elements(t)] log_S;
for (i in 1:num_elements(t)){
log_S[i] = log(1- ((scale [i]*(t[i])^shape)/ (1+(scale [i]*(t[i])^shape)))); // county is a vector that shows the location of patients with dim = num_elements(t)
}
return log_S;
}
//defines the log pdf
vector log_f (vector t,real shape,vector scale){
vector[num_elements(t)] log_f;
for (i in 1:num_elements(t)){
log_f[i] =log((scale[i]*shape*t[i]^(shape-1))/((1+(scale[i]*t[i]^shape))^2));
}
return log_f;
}
//defines the log-likelihood for right censored data
real surv_loglogistic_lpdf(vector t,vector d, real shape,vector scale){
vector[num_elements(t)] log_lik;
real prob;
log_lik = d .* log_f(t, shape, scale)+ (1 - d) .* log_S(t, shape, scale);
prob = sum(log_lik);
return prob;
}
real partial_sum(array[] int y_slice,
int start, int end,vector d,
real shape, vector scale) {
return surv_loglogistic_lpdf(y_slice | d, shape, scale);
}
}
//data block
data{
int <lower=0> province;
int <lower=0> N;
int <lower=0> num;
int <lower=0> number;
int <lower =0 , upper = province> county[N];
matrix [N,number] respon;
int<lower=0> N_edges;
int<lower=1, upper=province> node1[N_edges]; // node1[i] adjacent to node2[i]
int<lower=1, upper=province> node2[N_edges]; // and node1[i] < node2[i]
}
//parameters block
parameters{
vector [num] beta;
real <lower=0> sigma;//scale parameter sigma=1/shape
vector <lower=0> [province] sigma1;
vector[province] w1; // random effect (CAR)
vector[province] theta; // heterogeneous effects
}
// transformed parameters block
transformed parameters{
vector [num] time_ratio;
//vector[N] linpred;
vector[N] lambdaa;
real <lower=0> alpha = 1 / sigma;
time_ratio = exp(beta);
lambdaa = exp ((-respon[,7:18] * beta - w1[county] - theta[county]) / sigma);
}
// model block
model{
target += normal_lpdf(beta | 0, 1000);
//target += student_t_lpdf(sigma| 3,0,1);
target += gamma_lpdf(alpha | 0.001, 0.001);
w1 ~ icar_normal_lpdf(province, node1, node2);
sum(w1) ~ normal(0, 0.001 * province);
target += normal_lpdf(theta| 0, sigma1);
target += student_t_lpdf(sigma1| 3,0,1);
respon[,4] ~ surv_loglogistic//model for the data
}
// generated quantities block
generated quantities{
vector[N] log_lik;//log-likelihood
{ for(n in 1:N){
log_lik[n] = respon[n,6] * (log((exp ((-respon[n,7:18] * beta - w1[county[n]] - theta[county[n]])*alpha)*alpha*respon[n,4]^(alpha-1)) / ((1+(exp ((-respon[n,7:18] * beta - w1[county[n]] - theta[county[n]])*alpha)*(respon[n,4])^(alpha)))^2))) + (1-respon[n,6]) * ( log(1- ((exp ((-respon[n,7:18] * beta - w1[county[n]] - theta[county[n]])*alpha)*(respon[n,4])^alpha) / (1+(exp ((-respon[n,7:18] * beta - w1[county[n]] - theta[county[n]])*alpha)*(respon[n,4])^alpha)))));}
}
}
'''
```