Installation

Available from CRAN with the following R script, which installs the released version of BayesianFROC .

              install.packages("BayesianFROC")
              
              
#     Pleaes execute it from the R console or the R studio console.

Shiny Based GUIs

A single reader and a single modaity case

                           library(BayesianFROC)
                           BayesianFROC::fit_GUI_Shiny()

Multiple Readers and Mutiple Modalities Case

                           library(BayesianFROC)
                           BayesianFROC::fit_GUI_Shiny_MRMC()

For details

• See vignettes (For package size restriction (< 5Mb), it is omitted.)

• A pre-print of the author: Bayesian Models for Free-response Receiver Operating Characteristic Analysis

Goal of this package BayesianFROC

Comparison of modality. In some context, modality is imaging methods: MRI, CT, PET,…etc, and the another context, if images are taken for treatment (case) group and untreatment (or another treatment) (control) group, then modality means efficacy of treatment.

• Fitting: data is the following two type
  • Single Reader and Single Modality case.
  • Multiple Reader and Multiple modality case (MRMC)
• Comparison of the modalities by AUC (the area under the AFROC curve).

Example

• Build Data
  • Convert from Jafroc data
  • make a dataset
• Fit
  • draw FROC curves using a fitted model object
  • Calculates AUCs
• Validation
  • goodness of fit
  • posterior predictive p value (PPP)
  • SBC
  • comparison of truth by replicating datasets from true model

This is an example dataset;

where hit means True Positive: TP and false alarm means False Positive: FP.

#0) To avoid the following error in Readme file,
#I have to attach the Rcpp. 
#I do not know why such error occur withou Rcpp. 
#This error occurs only when I run the following R scripts from readme.

#Error
#in do.call(rbind,sampler_params) :second argument must be a list Calles:<Anonymous>...get_divergent_iterations ->sampler_param_vector =. do.call Execution halted

 library(Rcpp)  # This code can remove the above unknown error, if someone know why the error occur, please tell me.




 library(BayesianFROC)


#1) Build  data for singler reader and single modality  case.




  dataList <- list(c=c(3,2,1),     # c is ignored, can omit.
              h=c(97,32,31),
              f=c(1,14,74),
              NL=259,
              NI=57,
              C=3)





#  where,
#        c denotes confidence level, each components indicates that 
#                3 = Definitely lesion,
#                2 = subtle,  
#                1 = very subtle
#        h denotes number of hits 
#          (True Positives: TP) for each confidence level,
#        f denotes number of false alarms
#          (False Positives: FP) for each confidence level,
#        NL denotes number of lesions (signal),
#        NI denotes number of images,


  
  
  
  
  
  
  
  
  
  
  
  
  
#2) Fit the FROC model.


 
   fit <- BayesianFROC::fit_Bayesian_FROC(
     
            # data to which we fit a model                 
                dataList = dataList,
                                        
            # The number of MCMC chains                         
                     cha = 4,
            
            # The number of MCMC samples for each chains                         
                    ite  = 11111,
                    
            # The number of warming up of MCMC simulation for each chains           
                     war = 1111,
            
            # Show verbose summary and MCMC process
                 summary = TRUE
                                                         )

                  
                  
                  
                  
                  
                  

#  validation of fit via alculation of p -value of the chi square goodness of fit, which is 
#  calculated by integrating with  predictive posterior measure.
                  
                  
            BayesianFROC::ppp(
              fit
              )
                   
                   # The auhor thinks it is not correctly programmed, so it needs validaton of programing

                                     
                  

Jafroc (a software)

In order to apply this package to a dataset formulated for Jafroc, use the following code;

     dataList <- convertFromJafroc(
                                  No.of.Modalities =5,
                                  No.of.readers    =4,
                                  No.of.confidence.levels = 5
                                    )

where it requires to specify the number of modalities, readers, confidence levels.

The FROC curve

Using the fitted model object fit of class stanfitExtended, we can draw the FROC curve (or AFROC curve) as follows;

# new.imaging.device = FALSE  is used to include the output image 
# in this README file, so I recommand new.imaging.device = TRUE
BayesianFROC::DrawCurves(fit,
                         new.imaging.device = FALSE)

If you want to draw the curve in white background, then use the followings

# new.imaging.device = FALSE  is used to include the output image 
# in this README file, so I recommand new.imaging.device = TRUE.

BayesianFROC::DrawCurves(fit,
                         Colour = FALSE,
                         new.imaging.device = FALSE)

Excuting the above code, an imaging device will appears in which there are circles indicating the so-called False Positive Fractions (FPFs) and True Positive Fractions (TPFs). In addition, an FROC curve is plotted. FROC curve thorough exactly the expected points of FPFs and TPFs. Thus we can intuitively confirm the goodness of fit by comparing the circles and the curve. Ha,… someone reads this boring vignettes? My right arm ache bothering me for 20 months. Ha,… I want to die. I developed theory and package, but this research cannot make me happy, cannot change anything about my poor life… ha.

Latent Distributions

Hit rates are determined the areas of signal Gaussian between thresholds,

and false alarm rate are defined by the areas of differential logarithmic cumulative Gaussian between thresholds.

False rate

# new.imaging.device = FALSE  is used to include the output image 
# in this README file, so I recommand new.imaging.device = TRUE

BayesianFROC::draw_bi_normal_version_UP(
    fit,new.imaging.device = F,
    dark_theme = T,
    hit.rate = F,
    false.alarm.rate = T,
    both.hit.and.false.rate = F)

Hit rate

# new.imaging.device = FALSE  is used to include the output image 
# in this README file, so I recommand new.imaging.device = TRUE

BayesianFROC::draw_bi_normal_version_UP(
    fit,new.imaging.device = F,
    dark_theme = T,
    hit.rate = T,
    false.alarm.rate = F,
    both.hit.and.false.rate = F)

One will see that the bi normal assumption is wrong in the FROC context, and instead of bi normal assumption, we use two latent distributions, one is Gaussian for signal and another is the differential logarithmic Gaussian introduced first by the author of this package. For details, see vignettes of this package.

Modality Comparison

By fitting hierarchical Bayesian model, we can get the characteristics such as AUCs for each imaging modality (MRI,PET,CT,etc) to compare modalities.

Using the data object named BayesianFROC::dataList.Chakra.Web representing multiple modality data, we will fit the model to data by the following R script. For letting the running time be short, we take small MCMC iteration, that is, ite =222 which is too small to obtain reliable estimates. I think it should be ite =33333 for actual data analysis or compatible result with Jafroc.

The author try to remove eval=FALSE, but it cause stopping of knitr, so I can not include the following code. The following code sometimes crash R session, so,… it is heavy for README file??

#0) To avoid the following error I have to attach the Rcpp. I do not know why such error occur withou Rcpp.
#Error in do.call(rbind,sampler_params) :second argument must be a list Calles:<Anonymous>...get_divergent_iterations ->sampler_param_vector =. do.call Execution halted

library(Rcpp)  # This code can remove the above unknown error, if someone know why the error occur, please tell me.


library(BayesianFROC)



dataList <- dataList.Chakra.Web

fitt <- BayesianFROC::fit_Bayesian_FROC(
  
  # data of multiple reader and multiple case (modalities)
 dataList =   dataList,
  
  # iteration of MCMC
  ite = 1111 # Should be ite = 33333
 )

Now, we obtain the fitted model object named fit which is an S4 object of class stanfitExtended inherited from stanfit of the rstan package..

Transform of S4 Class to apply other packages

To apply the functions of other package such as rstan or ggmcmc, …, etc in which there are functions for object of class stanfit, e.g., rstan::stan_trace(), rstan::stan_dens(),rstan::check_hmc_diagnostics(),…etc, we have to change the class of the fitted model object by the following manner:

 fit.stan <- methods::as(fit, "stanfit")

Then the above object fit.stan is an object of the class stanfit and thus we can apply the function of rstan package as rstan::stan_dens(fit.stan).

Prepare pipe operator (redundant)

# First, get pipe operator
`%>%` <- utils::getFromNamespace("%>%", "magrittr")

Change the class to stanfit

# Change the class from stanfitExtended to stanfit
fit.stan <- methods::as(fit,"stanfit")

trace plot for object of class stanfit

# Change the class from stanfitExtended to stanfit
#fit.stan <- methods::as(fit,"stanfit")


# Plot about MCMC samples of paremeter name "A", reperesenting AUC
ggmcmc::ggs(fit.stan) %>% ggmcmc::ggs_traceplot(family  = "A")

posterior density of parameter A stored in an object of class stanfit

The following plot indicates that maximal posterior estimator (MAP) is very unstable in each chain in this iteration. By drawing more samples, it become stable?

# Change the class from stanfitExtended to stanfit
#fit.stan <- methods::as(fit,"stanfit"
                        
                        
ggmcmc::ggs(fit.stan) %>% ggmcmc::ggs_density(family    = "A")

Auto correlation for an object of class stanfit

# Change the class from stanfitExtended to stanfit
# fit.stan <- methods::as(fit,"stanfit")


ggmcmc::ggs(fit.stan) %>% ggmcmc::ggs_autocorrelation(family    = "A")

How ggmcmc painted using these colors was amazing!

package shinystan

For fitted model object fit.stan of class stanfit, there is a GUI viewer

# Change the class from stanfitExtended to stanfit
fit.stan <- methods::as(fit,"stanfit")


shinystan::launch_shinystan(fit.stan)

Goodness of fit via posterior predictive p value

Evaluates a p value of chi square goodness of fit. In addition, the scatter plot are drawn which shows the replicated datasets from the posterior predictive p value of the data which is used to create a fitted model object fit.

BayesianFROC::ppp(fit)

In previous release, my program for ppp was wrong, so in the current version I fixed.

SBC

Validation of model via Simulation Based Calibration (SBC)

Talts, S., Betancourt, M., Simpson, D., Vehtari, A., and Gelman, A. (2018). Validating Bayesian Inference Algorithms with Simulation-Based Calibration. arXiv preprint arXiv:1804.06788

BayesianFROC::Simulation_Based_Calibration_single_reader_single_modality_via_rstan_sbc()

Errors of estimates decrease monotonically with respect to sample size.

The author investigate the sample size for reliable estimates. Accracy of estimates are depend on the sample size. Large sample size leads us to small error. However, in practical perspective, the number of images or lesions has limitation. The author thinks it is better to obtain 100 images or lesions. And 100 images or lesions gives us the error 0.01 in AUC.

X axis is sample size and Y axis is error of estimates.

BayesianFROC::error_srsc_error_visualization(a)

X axis is sample size and Y axis is variance of estimates.

BayesianFROC::error_srsc_variance_visualization(a)