# AFROC: AF*ROC* curve (alternative free-response *ROC* curve) In BayesianFROC: FROC Analysis by Bayesian Approaches

## Description

An AFROC curve is a plane curve whose area under the curve (AUC) indicates an observer performance ability. In the following, Φ() denotes the cumulative distribution function on the standard Gaussian disribution.

The so-called AFROC curve is defined by

(ξ(t),η(t) ) =(1-e^{-t}, Φ( bΦ^{-1}(\exp(-t) )- a ) )

for all t >0 and some fixed real numbers a,b.

Specifying two real numbers a and b, we can plot an AFROC curve.

The are under the AFROC curve, or breafly AUC, is calculated as follows, whic are used to evaluate how physicians detect lesions in radiographs.

AUC = \int η(t) dξ(t) = \frac{ a }{ √{1+ b^2} }.

Note that the so-called FROC curve can be interpreted as the curve of expectations of data points. On the other hand, AFROC curve cannot be interpreted as the fitted curve, but its AUC is finite. Because AFROC can be obtained by modifying FROC curve, it reflects obeserver performance.

## Usage

 1 AFROC(t, a = 0.14, b = 0.19, x.coordinate.also = FALSE) 

## Arguments

 t A real number which moves in the domain of FROC curve a, b One of the parameter of model which characterize AFROC curve x.coordinate.also Logical, whether a vector of 1-exp(-t) is included in a return value.

## Value

if x.coordinate.also =TRUE, then A list, contains two vectors as x,y cooridinates of the AFROC curve for drawing curves. if x.coordinate.also =FALSE, then return is a vector as y coodinates of the AFROC curve exclueded its x-coordinates. (x coodinates is omitted.)

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 #======================================================================================== # Plot AFROC curve #======================================================================================== tt <- seq(0, 1, length.out = 111) ttt <- stats::runif(1000,0.001,100) t <- c(tt,ttt) a <- AFROC(t,x.coordinate.also=TRUE) plot(a$x,a$y) # We note that the x-coordinates of AFROC curve is not t but x = 1 - exp(-t). # To emphasize that x-coordinates is not t, we prepare the another example #======================================================================================== # Plot AFROC curve #======================================================================================== tt <- seq(0, 1, length.out = 111) ttt <- stats::runif(1000,0.001,100) t <- c(tt,ttt) y <- AFROC(t,x.coordinate.also=FALSE) plot(1-exp(-t),y) Close_all_graphic_devices() # 2020 August 

### Example output

Loading required package: rstan
rstan (Version 2.21.2, GitRev: 2e1f913d3ca3)
For execution on a local, multicore CPU with excess RAM we recommend calling
options(mc.cores = parallel::detectCores()).
To avoid recompilation of unchanged Stan programs, we recommend calling
rstan_options(auto_write = TRUE)

# vignette (or README) URL:  https://CRAN.R-project.org/package=BayesianFROC
# vignette called by R script (internet environment required for TeX)
vignette(package = "BayesianFROC",topic = "Very_Very_Very_Brief_description")

# Demos

demo(demo_for_compilation_of_all_models, package="BayesianFROC");
demo(demo_SBC, package="BayesianFROC");
demo(demo_MRMC, package="BayesianFROC");
demo(demo_srsc, package="BayesianFROC");
demo(demo_stan, package="BayesianFROC");
demo(demo_drawcurves_srsc, package="BayesianFROC");
demo(demo_ppp, package="BayesianFROC");
demo(demo_for_reviewers_of_my_manuscript, package="BayesianFROC");
demo_Bayesian_FROC();
demo_Bayesian_FROC_without_pause();

# Examples
#  A Single reader and A Single Modality

f <- fit_a_model_to(
dataList = BayesianFROC::d,
number_of_parallel_chains_for_MCMC     = 1,
number_of_iterations_for_MCMC = 111,
seed_for_MCMC = 1)

# Posterior Predictive P value of chi square goodness of fit

ppp <- extract_EAP_CI( f,"p_value_logicals",1 )\$p_value_logicals.EAP

#  Mutltiple reader and Mutltiple Modality

f <- fit_a_model_to(
dataList = BayesianFROC::dd,
number_of_parallel_chains_for_MCMC     = 1,
number_of_iterations_for_MCMC = 1111,
seed_for_MCMC = 1234567)

# This package is developed by a some homeless in Japan. Also deseased from MCS as initial toxicant syndet which make him to loss jobs, be a homeless be much lower quality of life.
# With painful life, blood, prurigo nodularis, aches, chronic inflammation, he made this to save his life, but he cannot. I am not interested to Statistics, but Geometry, Differentia geometry, Kodaira-Spencer thoery, pseudo holomorphic curve, Complex differential geometry, symplectic geometry. So,,, Fuck FROC! I hate such a cheap theory! I hate Statistics!

#  SBC for a single reader and a single modality via rstan::sbc

stanModel <- stan_model_of_sbc()

stanModel = stanModel,
ite     = 233,
M       = 11,
epsilon = 0.04,BBB = 1.1,AAA =0.0091,sbc_from_rstan = T)

#  Shiny based  Graphical User Interface for fitting and estimates and drawing curve;

fit_GUI_Shiny()

fit_GUI_Shiny_MRMC()  #for subject-specific random effect model  or MRMC

Ver. 0.  4. 0.   "Such A Couch Potato"
Warning message:
In file(con, "r") : cannot open file '/proc/stat': Permission denied


BayesianFROC documentation built on Jan. 13, 2021, 5:22 a.m.