replicate_MRMC_dataList: MRMC: Replicates Datasets From Threshold, Mean and S.D.

Description

Make several datasets from a given model parameter.

Usage

replicate_MRMC_dataList(
  replication.number = 2,
  initial.seed = 123,
  mu.truth = BayesianFROC::mu_truth,
  v.truth = BayesianFROC::v_truth,
  z.truth = BayesianFROC::z_truth,
  NI = 200,
  NL = 142,
  ModifiedPoisson = TRUE,
  summary = FALSE
)

Arguments

replication.number

A positive integer, specifying number of replicated datasets by this function. For fixed number of lesions, images, the dataset of hits and false alarms are replicated, and the number of replicated datasets are specified by this variable.

initial.seed

The variable initial.seed is used to replicate datasets. That is, if you take initial.seed = 1234, then the seed 1234, 1235, 1236, 1237, 1238, .... etc are for the first replication, the second replication, the third replication, .... etc. If the n-th model does not converge for some n, then such model has no mean and thus the non-convergent models are omitted to calculate the errors.

mu.truth

array of dimension (M,Q). Mean of the signal distribution of bi-normal assumption.

v.truth

array of dimension (M,Q). Standard Deviation of represents the signal distribution of bi-normal assumption.

z.truth

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

Number of Images.

Number of Lesions.

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

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.

Value

A list, each component is also a list, representing an FROC dataset.

Examples

Run this code

# NOT RUN {
#========================================================================================
#                Visualization of replicated datasets synthesized by default values
#========================================================================================



#  Replicates datasets from a model with user specified parameters (now, it is default).
         a <-replicate_MRMC_dataList()


# Calculates FPF and TPF and plot it for the first replicatec dataset

         plot_FPF_and_TPF_from_a_dataset(a[[1]])


# Calculates FPF and TPF and plot it for the second replicatec dataset

         plot_FPF_and_TPF_from_a_dataset(a[[2]])



         # Reviesed 2019 Oct 9



# }

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Description

Usage

Arguments

Value

Examples