BayesianFROC (version 1.0.0)

metadata_srsc_per_image: Create metadata for MRMC data.

Description

The so-called false positive fraction (FPF) and the true positive fraction (TPF) are calculated from the number of hits (True Positives: TPs) and the number of false alarms (False Positives: FPs)

Usage

metadata_srsc_per_image(dataList, ModifiedPoisson)

Arguments

dataList

A list, should include m,q,c,h,f,NL,C,M,Q which means

c should be created by c <-c(rep(C:1)), where C is the number of confidence levels. So, you should write down your hits and false alarms vector so that it is compatible with this automatically created c vector.

h means the number of hits

f means the number of false alarm

NL means the Total number of lesions for all images

C means the highest number of confidence level

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

Value

A metadata such as number of cumulative false alarms and hits to create and draw the curve.

Details

From data of number of hits (True Positive: TP) and false alarms (False Positive: FP), we calculate the number of cumulative false positives (FPF) and cumulative hits (TPF).

Because there are three subscripts, reader, modality, and image, we create array format and vector format etc...

Examples

# NOT RUN {
#========================================================================================
#                      TP and FP
#========================================================================================


        dat  <- BayesianFROC::dataList.Chakra.Web



#========================================================================================
#              Calculates  TPF and FPF from TP and FP
#========================================================================================


             metadata_srsc_per_image(dat)






# Revised 2019 Nov.


# }
# NOT RUN {
# dottest
# }