R/minimal_model_MRMC2.R

In BayesianFROC: FROC Analysis by Bayesian Approaches

foooo  <- function( )  {

    # Make a dataset

    # modality ID
          m <-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3
          ,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5
          ,5,5,5,5,5,5,5,5,5,5,5,5)

    # reader ID

          q <-c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,1,1,1,1
                ,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,1,1,1,1,1,2,2,2
                ,2,2,3,3,3,3,3,4,4,4,4,4)

    # confidence level

          c<-c(5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2
               ,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3,2,1,5,4,3
               ,2,1,5,4,3,2,1,5,4,3,2,1)

    #  FP  ( false alarm)

          f<-c(
             0,4,20,29,21,0,0,6,15,22,1,15,18,31,19,1,2,4,16,17,1,1,21,24,23,1,1,5,30
            ,40,2,19,31,56,42,2,0,2,30,32,1,7,13,28,19,0,1,7,7,31,7,15,28,41,9,0,2,5
            ,24,31,1,4,18,21,23,1,1,0,11,35,6,14,37,36,18,0,2,4,18,25,0,2,19,23,18,0,2
            ,6,10,30,2,25,40,29,24,1,1,4,24,32
          )

    #  TP (hit)
         h<-c(
            50,30,11,5,1,15,29,29,1,0,39,31,8,10,3,10,8,25,45,14,52,25,13,4,1,27,28,29,1
            ,0,53,29,13,2,4,9,16,22,43,14,43,29,11,6,0,18,29,21,0,0,43,29,6,7,1,10,14,19
            ,32,23,61,19,12,9,3,16,29,34,1,0,52,29,10,4,3,10,16,23,43,15,35,29,18,9,0,17,27
             ,24,0,0,34,33,7,13,2,12,16,21,35,15
          )

        C<-5  # the number of confidence levels
        M<-5 # the number of modalities
        Q<-4 # the number of readers
        NI<-199 # the number of images
        NL<-142 # the number of lesions



    # the length of the dataset
        N <-C*M*Q

    # make an array format hits data
        ff <- numeric(N) #Initialization of Cumulative False alarm
        harray<-array(0,dim=c(C,M,Q));

        for(md in 1:M) {
          for(cd in 1:C) {
            for(qd in 1 : Q){
              for(n  in 1:cd){
                ff[cd+(md-1)*C*Q+(qd-1)*C]<-ff[cd+(md-1)*C*Q+(qd-1)*C]+f[n+(md-1)*C*Q+(qd-1)*C]
              }
              harray[cd,md,qd] <- h[cd+(md-1)*C*Q+(qd-1)*C]
            }}}


    # make a data to be passed to sampling()

        data <- list(N=N,Q=Q, M=M,m=m  ,C=C  , NL=NL,NI=NI
                     ,c=c,q=q,
                     h=h, f=f,
                     ff=ff,
                     harray=harray
                     )








    # Make a Stan model





        Stan.model <- rstan::stan_model( model_code="


        data{
          int <lower=0>N;
          int <lower=0>M;
          int <lower=0>C;
          int <lower=0>Q;
          int <lower=0>h[N];
          int <lower=0>f[N];
          int <lower=0>q[N];
          int <lower=0>c[N];
          int <lower=0>m[N];
          int <lower=0>NL;
          int <lower=0>NI;

          int <lower=0>ff[N];
          int <lower=0>harray[C,M,Q];




        }
        transformed data {
          int <lower=0> NX;
           NX = NI;
        }

        parameters{
          real    w;
          real <lower =0  >  dz[C-1];
          real               mu[M,Q];
          real <lower=0>      v[M,Q];
          real <lower=0>      hyper_v[Q];
          real <lower=0,upper=1>A[M];

        }

        transformed parameters {
          real <lower =0>       dl[C];
          real <lower=0,upper=1> ppp[C,M,Q];
          real <lower =0>      l[C];
          real    z[C];
          real                      aa[M,Q];
          real <lower =0>           bb[M,Q];
          real <lower=0,upper=1>    AA[M,Q];
          real deno[C-1,M,Q];
          real hit_rate[C,M,Q];

          z[1]=w;

          for(md in 1 : M) {
            for(qd in 1 : Q) {
              aa[md,qd]=mu[md,qd]/v[md,qd];
              bb[md,qd]=1/v[md,qd];

              for(cd in 1 : C-1) z[cd+1] = z[cd] + dz[cd];
              ppp[C,md,qd] = 1- Phi((z[C] -mu[md,qd])/v[md,qd]);

              for(cd in 1 : C-1) ppp[cd,md,qd] = Phi((z[cd+1] -mu[md,qd])/v[md,qd])  - Phi((z[cd ] -mu[md,qd])/v[md,qd]);



              for(cd in 1 : C) l[cd] = (-1)*log(Phi(z[cd]));
              dl[C] = fabs(l[C]-0);
              for(cd in 1:C-1) dl[cd]= fabs(l[cd]-l[cd+1]);




            }
          }

          for(md in 1 : M) {
            for(qd in 1 : Q) {
              AA[md,qd]=Phi(  (mu[md,qd]/v[md,qd])/sqrt((1/v[md,qd])^2+1)  );//Measures of modality performance
            }}




          for(md in 1 : M) {
            for(qd in 1 : Q) {
              deno[C-1,md,qd]=1-ppp[C,md,qd];
              for(cd in 3:C){  deno[c[cd],md,qd]=deno[c[cd-1],md,qd]-ppp[c[cd-1],md,qd];  }
            }}


          for(md in 1 : M) {
            for(qd in 1 : Q) {
              for(cd in 1:C-1){
                hit_rate[cd,md,qd]=ppp[cd,md,qd]/deno[cd,md,qd];
              }
              hit_rate[C,md,qd]=ppp[C,md,qd];

            }}



        }






        model{
            int s=0;


            for(qd in 1 : Q) {
              for(md in 1 : M) {
                target += normal_lpdf( AA[md,qd]|A[md],hyper_v[qd]);
              }  }
            for(n in 1:N) {
              target +=   poisson_lpmf(ff[n]|l[c[n]]*NX);
            }




            for(qd in 1 : Q) {
              for(md in 1 : M) {
                s=0;
                for(cd in 1 : C){
                   target += binomial_lpmf(harray[cd,md,qd]  |  NL-s, hit_rate[c[cd],md,qd]  );
                  s = s + harray[cd,md,qd]; }
                }}








              w ~  uniform(-3,3);
              for(cd in 1:C-1) dz[cd] ~  uniform(0.001,7);
              for(md in 1 : M) { for(qd in 1 : Q) {
                mu[md,qd] ~ uniform(-11,11);
                v[md,qd] ~ uniform(0.01,11);

              }}





          }

        ")



    #  Fit a model to data




        fit  <-  rstan::sampling(
          object= Stan.model, data=data,  verbose = FALSE,
          seed=1234567, chains=1, warmup=111, iter=1111
          , control = list(adapt_delta = 0.9999999,
                           max_treedepth = 15)
          # ,init = initial
        )

        rstan::traceplot(fit,pars=c("w"))
        rstan::check_hmc_diagnostics(fit)






    # MCMC fails if the seed is changed.
        fit  <-  rstan::sampling(
          object= Stan.model, data=data,  verbose = FALSE,
          seed=1, chains=1, warmup=111, iter=122
          , control = list(adapt_delta = 0.9999999,
                           max_treedepth = 15)
          ,init = 0.2
        )

        rstan::traceplot(fit,pars=c("w"))
        rstan::check_hmc_diagnostics(fit)
}#function