library(rstan)
###R version 4.1.1, rstan version 2.21.3###

###how to install package rstan, please see https://github.com/stan-dev/rstan/wiki/RStan-Getting-Started###

setwd("~")###Set working directory, please replace it with your working directory###

####Stan_models###
###α=0.01###
p0.01.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
   real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
 
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  
  tau1 ~ normal(0,0.5);
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*0.01;}
  }
"
###α=0.1###
p0.1.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
   real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
 
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  
  tau1 ~ normal(0,0.5);
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*0.1;}
  }"
###α=0.2###
p0.2.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
   real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
 
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  tau1 ~ normal(0,0.5);
  
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*0.2;}
  }"
###α=0.3###
p0.3.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
  real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  
  tau1 ~ normal(0,0.5);
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*0.3;}
  }"
###α=0.4###
p0.4.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
   real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
 
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  
  tau1 ~ normal(0,0.5);
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*0.4;}
  }"
###α=0.5###
p0.5.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
   real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
 
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  
  tau1 ~ normal(0,0.5);
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*0.5;}
  }"
###α=0.6###
p0.6.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
   real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
 
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  tau1 ~ normal(0,0.5);
  
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*0.6;}
  }"
###α=0.7###
p0.7.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
   real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
 
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  
  tau1 ~ normal(0,0.5);
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*0.7;}
  }"
###α=0.8###
p0.8.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
  real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
 
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  
  tau1 ~ normal(0,0.5);
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*0.8;}
  }"
###α=0.9###
p0.9.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
   real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
 
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  
  tau1 ~ normal(0,0.5);
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*0.9;}
  }"
###α=1###
p1.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
   real mu;          // relative treatment effect (log OR) in RCTs
   real<lower=0> tau;  // the heterogeneity parameter in NRSIs
  real mu1[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;// the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
 
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu1[i]);
       ptrt[i] =inv_logit(mu1[i] +mu+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
  zeta ~normal(0,1);
  
  tau1 ~ normal(0,0.5);
  mu1 ~ normal(0,10);
mu ~ normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      for (i in 1:k)
      {
      target +=normal_lpdf(y[i] | mu,y_se[i]+tau)*1;}
  }"


power.prior.stan <- "data {
  int<lower=1> k;//Number of NRSIs
  real y[k];//Effect in NRSIs
  real<lower=0> y_se[k]; //stdev in NRSIs
  int<lower=0> J;//Number of RCTs
  int<lower=0> n_t[J];//Number of subjects in RCTs, treatment
  int<lower=0> r_t[J];//Number of events, treatment
  int<lower=0> n_c[J];//Number of subjects in RCTs, Control
  int<lower=0> r_c[J];//Number of events, Control
}

parameters {
   real theta;          // relative treatment effect (log OR)
   real<lower=0> tau;  // the heterogeneity parameter
   real<lower=0,upper=1> w1;//down-weight factor for study 1
   real<lower=0,upper=1> w2;//down-weight factor for study 2
   real<lower=0,upper=1> w3;//down-weight factor for study 3
   real<lower=0,upper=1> w4;//down-weight factor for study 4
   real<lower=0,upper=1> w5;//down-weight factor for study 5
   real<lower=0,upper=1> w6;//down-weight factor for study 6
   real<lower=0,upper=1> w7;//down-weight factor for study 7
   real<lower=0,upper=1> w8;//down-weight factor for study 8
   real<lower=0,upper=1> w9;//down-weight factor for study 9
   real<lower=0,upper=1> w10;//down-weight factor for study 10
  real mu[J];//baseline risks in RCTs (log odds)
  real<lower=0> tau1;the heterogeneity parameter in RCTs
 vector[J] zeta;// individual treatment effects in RCTs
  }

transformed parameters {
 real pctrl[J];
 real ptrt[J];
 for (i in 1:J)
      {pctrl[i] =inv_logit(mu[i]);
       ptrt[i] =inv_logit(mu[i] +theta+zeta[i]*tau1);}
}
model
 {
//prior distributions
     tau ~ normal (0, 0.5);
w1~beta(4,1);//Fralick et al. (2017)-Moderate risk of bias
w2~beta(1.5,1);//Wang et al. (2017)-Serious risk of bias
w3~beta(4,1);//kim et a. (2018)-Moderate risk of bias
w4~beta(4,1);//Ueda et a. (2018)-Moderate risk of bias
w5~beta(1.5,1);//Wang et al. (2019)-Serious risk of bias
w6~beta(1.5,1);//Wang et al. (2019)-Serious risk of bias
w7~beta(1.5,1);//Wang et al. (2019)-Serious risk of bias
w8~beta(1.5,1);//Wang et al. (2019)-Serious risk of bias
w9~beta(4,1);//Douros et a. (2020)-Moderate risk of bias
w10~beta(4,1);//McGurnaghan et a. (2019)-Moderate risk of bias
  tau1 ~ normal(0,0.5);
  mu ~ normal(0,10);
 zeta ~normal(0,1);
theta~normal(0,2.82);
  r_c ~ binomial(n_c,pctrl);
  r_t ~ binomial(n_t,ptrt);
      target +=normal_lpdf(y[1] | theta,y_se[1]+tau)*w1;
 target +=normal_lpdf(y[2] | theta,y_se[2]+tau)*w2;
 target +=normal_lpdf(y[3] | theta,y_se[3]+tau)*w3;
 target +=normal_lpdf(y[4] | theta,y_se[4]+tau)*w4;
 target +=normal_lpdf(y[5] | theta,y_se[5]+tau)*w5;
 target +=normal_lpdf(y[6] | theta,y_se[6]+tau)*w6;
 target +=normal_lpdf(y[7] | theta,y_se[7]+tau)*w7;
 target +=normal_lpdf(y[8] | theta,y_se[8]+tau)*w8;
 target +=normal_lpdf(y[9] | theta,y_se[9]+tau)*w9;
 target +=normal_lpdf(y[10] | theta,y_se[9]+tau)*w10;
  }
"

set.seed(2023)
###RCT data###
meta.data.rct <- as.data.frame(matrix(NA, 7,4))
colnames(meta.data.rct) <- c("rtrt","ntrt","rctrl","nctrl")
meta.data.rct$rtrt <- c(0,1,1,0,1,1,1)
meta.data.rct$ntrt <- c(735,447,1652,233,888,985,205)
meta.data.rct$rctrl <- c(1,0,1,1,0,0,0)
meta.data.rct$nctrl <- c(549,233,1050,230,437,247,209)
k.rct <- dim(meta.data.rct)[1]


  
###RWE data###
k.rwe <- 10


R <- k.rwe###the number of NRSIs
M <- k.rct###the number of RCTs
y_nrsi <- log(c(2.12,2.06,0.85,1.73,1.44,1.32,2.48,1.31,3.62,0.53))###log-or for RWE study
y_se_nrsi <- c((log(3.38)-log(1.33))/(2*1.96),(log(3.61)-log(1.17))/(2*1.96),(log(1.40)-log(0.52))/(2*1.96),(log(3.63)-log(0.82))/(2*1.96),
               (log(1.68)-log(1.23))/(2*1.96),(log(1.81)-log(0.96))/(2*1.96),(log(4.03)-log(1.53))/(2*1.96),(log(1.61)-log(1.07))/(2*1.96),
               (log(4.50)-log(2.91))/(2*1.96),(log(0.92)-log(0.31))/(2*1.96))


##power prior##
pp.data <- list(J =M, n_t=meta.data.rct$ntrt, r_t=meta.data.rct$rtrt,n_c=meta.data.rct$nctrl,r_c=meta.data.rct$rctrl,k=R,y=y_nrsi,y_se=y_se_nrsi)
fit.p0.01 <- stan(model_code  = p0.01.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.p0.1 <- stan(model_code  = p0.1.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.p0.2 <- stan(model_code  = p0.2.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.p0.3 <- stan(model_code  = p0.3.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.p0.4 <- stan(model_code  = p0.4.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.p0.5 <- stan(model_code  = p0.5.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.p0.6 <- stan(model_code  = p0.6.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.p0.7 <- stan(model_code  = p0.7.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.p0.8 <- stan(model_code  = p0.8.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.p0.9 <- stan(model_code  = p0.9.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.p1 <- stan(model_code  = p1.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))
fit.pp <- stan(model_code  = power.prior.stan, data = pp.data,chains = 4,iter = 5000, cores=4,control=list(adapt_delta = 0.99))

parameter.fit.p0.01 <- extract(fit.p0.01, permuted = TRUE)
parameter.fit.p0.1 <- extract(fit.p0.1, permuted = TRUE)
parameter.fit.p0.2 <- extract(fit.p0.2, permuted = TRUE)
parameter.fit.p0.3 <- extract(fit.p0.3, permuted = TRUE)
parameter.fit.p0.4 <- extract(fit.p0.4, permuted = TRUE)
parameter.fit.p0.5 <- extract(fit.p0.5, permuted = TRUE)
parameter.fit.p0.6 <- extract(fit.p0.6, permuted = TRUE)
parameter.fit.p0.7 <- extract(fit.p0.7, permuted = TRUE)
parameter.fit.p0.8 <- extract(fit.p0.8, permuted = TRUE)
parameter.fit.p0.9 <- extract(fit.p0.9, permuted = TRUE)
parameter.fit.p1 <- extract(fit.p1, permuted = TRUE)
parameter.fit.pp <- extract(fit.pp, permuted = TRUE)


p0.01.theta <- parameter.fit.p0.01$mu
p0.1.theta <- parameter.fit.p0.1$mu
p0.2.theta <- parameter.fit.p0.2$mu
p0.3.theta <- parameter.fit.p0.3$mu
p0.4.theta <- parameter.fit.p0.4$mu
p0.5.theta <- parameter.fit.p0.5$mu
p0.6.theta <- parameter.fit.p0.6$mu
p0.7.theta <- parameter.fit.p0.7$mu
p0.8.theta <- parameter.fit.p0.8$mu
p0.9.theta <- parameter.fit.p0.9$mu
p1.theta <- parameter.fit.p1$mu
pp.theta <- parameter.fit.pp$theta

p0.01.theta.median <-  quantile(p0.01.theta,0.5);p0.01.theta.l <-  quantile(p0.01.theta,0.025);p0.01.theta.u <-  quantile(p0.01.theta,0.975)
p0.1.theta.median <-  quantile(p0.1.theta,0.5);p0.1.theta.l <-  quantile(p0.1.theta,0.025);p0.1.theta.u <-  quantile(p0.1.theta,0.975)
p0.2.theta.median <-  quantile(p0.2.theta,0.5);p0.2.theta.l <-  quantile(p0.2.theta,0.025);p0.2.theta.u <-  quantile(p0.2.theta,0.975)
p0.3.theta.median <-  quantile(p0.3.theta,0.5);p0.3.theta.l <-  quantile(p0.3.theta,0.025);p0.3.theta.u <-  quantile(p0.3.theta,0.975)
p0.4.theta.median <-  quantile(p0.4.theta,0.5);p0.4.theta.l <-  quantile(p0.4.theta,0.025);p0.4.theta.u <-  quantile(p0.4.theta,0.975)
p0.5.theta.median <-  quantile(p0.5.theta,0.5);p0.5.theta.l <-  quantile(p0.5.theta,0.025);p0.5.theta.u <-  quantile(p0.5.theta,0.975)
p0.6.theta.median <-  quantile(p0.6.theta,0.5);p0.6.theta.l <-  quantile(p0.6.theta,0.025);p0.6.theta.u <-  quantile(p0.6.theta,0.975)
p0.7.theta.median <-  quantile(p0.7.theta,0.5);p0.7.theta.l <-  quantile(p0.7.theta,0.025);p0.7.theta.u <-  quantile(p0.7.theta,0.975)
p0.8.theta.median <-  quantile(p0.8.theta,0.5);p0.8.theta.l <-  quantile(p0.8.theta,0.025);p0.8.theta.u <-  quantile(p0.8.theta,0.975)
p0.9.theta.median <-  quantile(p0.9.theta,0.5);p0.9.theta.l <-  quantile(p0.9.theta,0.025);p0.9.theta.u <-  quantile(p0.9.theta,0.975)
p1.theta.median <-  quantile(p1.theta,0.5);p1.theta.l <-  quantile(p1.theta,0.025);p1.theta.u <-  quantile(p1.theta,0.975)
pp.theta.median <-  quantile(pp.theta,0.5);pp.theta.l <-  quantile(pp.theta,0.025);pp.theta.u <-  quantile(pp.theta,0.975)

median.value <- c(p0.01.theta.median,p0.1.theta.median,p0.2.theta.median,p0.3.theta.median,p0.4.theta.median,p0.5.theta.median,p0.6.theta.median,p0.7.theta.median,p0.8.theta.median,
                  p0.9.theta.median,p1.theta.median,pp.theta.median)

l.value <- c(p0.01.theta.l,p0.1.theta.l,p0.2.theta.l,p0.3.theta.l,p0.4.theta.l,p0.5.theta.l,p0.6.theta.l,p0.7.theta.l,p0.8.theta.l,
             p0.9.theta.l,p1.theta.l,pp.theta.l)

u.value <- c(p0.01.theta.u,p0.1.theta.u,p0.2.theta.u,p0.3.theta.u,p0.4.theta.u,p0.5.theta.u,p0.6.theta.u,p0.7.theta.u,p0.8.theta.u,
             p0.9.theta.u,p1.theta.u,pp.theta.u)

p0.01 <- length(which( p0.01.theta >0))/length(p0.01.theta)
p0.1 <- length(which( p0.1.theta >0))/length(p0.1.theta)
p0.2 <- length(which( p0.2.theta >0))/length(p0.2.theta)
p0.3 <- length(which( p0.3.theta >0))/length(p0.3.theta)
p0.4 <- length(which( p0.4.theta >0))/length(p0.4.theta)
p0.5 <- length(which( p0.5.theta >0))/length(p0.5.theta)
p0.6 <- length(which( p0.6.theta >0))/length(p0.6.theta)
p0.7 <- length(which( p0.7.theta >0))/length(p0.7.theta)
p0.8 <- length(which( p0.8.theta >0))/length(p0.8.theta)
p0.9 <- length(which( p0.9.theta >0))/length(p0.9.theta)
p1 <- length(which( p1.theta >0))/length(p1.theta)
pp <- length(which( pp.theta >0))/length(pp.theta)
p.value <- c(p0.01,p0.1,p0.2,p0.3,p0.4,p0.5,p0.6,p0.7,p0.8,p0.9,p1,pp)

result.data <- round(cbind(median.value,l.value,u.value,p.value),2)


###plot###
or_dataset <- data.frame(Model=c("0.01","0.1","0.2","0.3","0.4","0.5","0.6","0.7","0.8","0.9","1","Random"),Median=result.data[,1],lower=result.data[,2],upper=result.data[,3])
or_dataset$Model <- factor(or_dataset$Model,levels = c("0.01","0.1","0.2","0.3","0.4","0.5","0.6","0.7","0.8","0.9","1","Random"))

annotation_log_or <- data.frame(
  
  x=c(1.5,1.5,1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5,  1.5, 1.5, 1.5, 1.5, 1.75,1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75, 1.75,1.75,1.75,1.75,1.75,2.1,2.05,2.05, 2.05, 2.05, 2.05, 2.05, 2.05, 2.05, 2.05, 2.05, 2.05, 2.05),
  
  y = c(12.5,12,11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1,12.5,12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1,12.5,12,11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1),
  
  label=c('Median',  '0.34','0.43','0.43','0.43','0.42','0.41','0.40', '0.39', '0.36','0.32', '0.26', '0.03',
          '95% CrI','(-0.21-0.86)','(0.06-0.80)','(0.02-0.81)','(-0.02-0.82)','(-0.05-0.85)','(-0.12-0.88)','(-0.20-0.91)','(-0.30-0.96)','(-0.41-1.01)','(-0.56-1.07)','(-0.79-1.20)','(-1.30-1.40)',
          'P(log-OR>0)','0.90','0.98','0.98','0.97','0.96','0.94','0.92','0.89','0.85','0.79','0.70','0.52'))
Figure.s2 <- ggplot(or_dataset, aes(Median, Model)) + geom_point(size=1) +
  
  geom_errorbarh(aes(xmax =upper, xmin = lower),height = 0.1,size=0.5)+
  
  geom_vline(aes(xintercept=0))+
  
  scale_x_continuous(limits=c(-1.5, 2.1)) +
  
  xlab('Log odds ratio (μ)') + ylab("Alpha used for power prior ") + theme_bw() + geom_text(data=annotation_log_or,aes(x=x,y=y,label=label),size=4)+
  
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),axis.title = element_text(size = 15,face = "bold",color = "black"),
        axis.text.y = element_text(size=10, face = "bold",color = "black"), axis.text.x = element_text(size=10, face = "bold",color = "black"))

ggsave(Figure.s2, filename = "~\\Figure_s2.png", dpi = 300, height =24, width =28, units = "cm")