BayesianFROC (version 1.0.0)

hits_false_alarms_creator_from_thresholds: Hits and False Alarms Creator

Description

From the parameter of the bi-normal assumptions, hits and false alarms are generated.

Usage

hits_false_alarms_creator_from_thresholds(
  replicate.datset = 3,
  ModifiedPoisson = FALSE,
  mean.truth = 0.6,
  sd.truth = 5.3,
  z.truth = c(-0.8, 0.7, 2.38),
  NL = 259,
  NI = 57,
  summary = TRUE,
  initial.seed = 12345
)

Arguments

replicate.datset

A Number indicate that how many you replicate dataset from user's specified dataset.

ModifiedPoisson

Logical, that is TRUE or FALSE.

If ModifiedPoisson = TRUE, then Poisson rate of false alarm is calculated per lesion, and a model is fitted so that the FROC curve is an expected curve of points consisting of the pairs of TPF per lesion and FPF per lesion.

Similarly,

If ModifiedPoisson = TRUE, then Poisson rate of false alarm is calculated per image, and a model is fitted so that the FROC curve is an expected curve of points consisting of the pair of TPF per lesion and FPF per image.

For more details, see the author's paper in which I explained per image and per lesion. (for details of models, see vignettes , now, it is omiited from this package, because the size of vignettes are large.)

If ModifiedPoisson = TRUE, then the False Positive Fraction (FPF) is defined as follows (\(F_c\) denotes the number of false alarms with confidence level \(c\) )

$$ \frac{F_1+F_2+F_3+F_4+F_5}{N_L}, $$

$$ \frac{F_2+F_3+F_4+F_5}{N_L}, $$

$$ \frac{F_3+F_4+F_5}{N_L}, $$

$$ \frac{F_4+F_5}{N_L}, $$

$$ \frac{F_5}{N_L}, $$

where \(N_L\) is a number of lesions (signal). To emphasize its denominator \(N_L\), we also call it the False Positive Fraction (FPF) per lesion.

On the other hand,

if ModifiedPoisson = FALSE (Default), then False Positive Fraction (FPF) is given by

$$ \frac{F_1+F_2+F_3+F_4+F_5}{N_I}, $$

$$ \frac{F_2+F_3+F_4+F_5}{N_I}, $$

$$ \frac{F_3+F_4+F_5}{N_I}, $$

$$ \frac{F_4+F_5}{N_I}, $$

$$ \frac{F_5}{N_I}, $$

where \(N_I\) is the number of images (trial). To emphasize its denominator \(N_I\), we also call it the False Positive Fraction (FPF) per image.

The model is fitted so that the estimated FROC curve can be ragraded as the expected pairs of FPF per image and TPF per lesion (ModifiedPoisson = FALSE )

or as the expected pairs of FPF per image and TPF per lesion (ModifiedPoisson = TRUE)

If ModifiedPoisson = TRUE, then FROC curve means the expected pair of FPF per lesion and TPF.

On the other hand, if ModifiedPoisson = FALSE, then FROC curve means the expected pair of FPF per image and TPF.

So,data of FPF and TPF are changed thus, a fitted model is also changed whether ModifiedPoisson = TRUE or FALSE. In traditional FROC analysis, it uses only per images (trial). Since we can divide one image into two images or more images, number of trial is not important. And more important is per signal. So, the author also developed FROC theory to consider FROC analysis under per signal. One can see that the FROC curve is rigid with respect to change of a number of images, so, it does not matter whether ModifiedPoisson = TRUE or FALSE. This rigidity of curves means that the number of images is redundant parameter for the FROC trial and thus the author try to exclude it.

Revised 2019 Dec 8 Revised 2019 Nov 25 Revised 2019 August 28

mean.truth

This is a parameter of the latent Gaussian assumption for the noise distribution.

sd.truth

This is a parameter of the latent Gaussian assumption for the noise distribution.

z.truth

This is a parameter of the latent Gaussian assumption for the noise distribution.

NL

Number of Lesions.

NI

Number of Images.

summary

Logical: TRUE of FALSE. Whether to print the verbose summary. If TRUE then verbose summary is printed in the R console. If FALSE, the output is minimal. I regret, this variable name should be verbose.

initial.seed

Replicated datasets are created using a continuous sequence of seeds and its initial seed is specified by this argument. For example, if you choose initial.seed =12300, then the replicated datasets are created from using the sequence of seeds: 12301,12302,12303,12304,<U+2026>

Value

Datasets Including Hits and False Alarms

Details

From the fixed parameters of bi-normal assumptions, we replicate data, that is, we draw the data from the distributions whose parameters are known. Especially, we interest the hits and false alarms since the number of images, lesions and confidence level is same for all replications. So, it is sufficient to check the hits and false alarms.

Examples

# NOT RUN {
 
# }
# NOT RUN {
#================The first example======================================
#      Replication of Data from Fixed ( specified) Parameters.

 a <- hits_false_alarms_creator_from_thresholds(replicate.datset = 1)

#  Extract the first replicated dataset:

 a[[1]]$NL
 a[[1]]$NI
 a[[1]]$f
 a[[1]]$h
 a[[1]]$C


#================The second example======================================
#      Replication of Data from Fixed ( specified) Parameters.

 b <- hits_false_alarms_creator_from_thresholds(replicate.datset = 2)


#  Extract the first replicated dataset:

 b[[1]]$NL
 b[[1]]$NI
 b[[1]]$f
 b[[1]]$h
 b[[1]]$C


#  Extract the second replicated dataset:

 b[[2]]$NL
 b[[2]]$NI
 b[[2]]$f
 b[[2]]$h
 b[[2]]$C


#================The Third example======================================
#      Replication of Data from Fixed ( specified) Parameters.


 c <- hits_false_alarms_creator_from_thresholds(replicate.datset = 3)


#  Extract the first replicated dataset:

 c[[1]]$NL
 c[[1]]$NI
 c[[1]]$f
 c[[1]]$h
 c[[1]]$C


#  Extract the second replicated dataset:

 c[[2]]$NL
 c[[2]]$NI
 c[[2]]$f
 c[[2]]$h
 c[[2]]$C

#  Extract the third replicated dataset:

 c[[3]]$NL
 c[[3]]$NI
 c[[3]]$f
 c[[3]]$h
 c[[3]]$C



# }
# NOT RUN {
# dottest

# }