From threshold, mean and S.D., data of False Alarm are created.
false_and_its_rate_creator_MRMC(
z.truth = BayesianFROC::z_truth,
NI = 333,
NL = 111,
ModifiedPoisson = FALSE,
seed = 12345,
M = 5,
Q = 4,
summary = TRUE
)Vector of dimension = C represents the thresholds of bi-normal assumption.
The number of images.
The number of lesions.
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
The seed for creating a collection of the number of false alarms synthesized by the Poisson distributions using the specified seed.
Number of modalities
Number of readers
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.
Vector for false alarms as an element of list of MRMC data.
In our model, false alarm rate does not depend on the readers or modalities. Thus this sampling function merely synthesizes samples from the Poisson distribution of the same false alarm rate. Of course, this same false rate of the Poisson distributions is not desired one. Since we should assume that each reader with different modality should differ. To accomplish this, we have to assume that threshold parameter of Gaussian assumption should depend on the reader and modality. However, such model does not converge in the Hamiltonian Monte Carlo simulation.
# NOT RUN {
false_and_its_rate_creator_MRMC()
# }
Run the code above in your browser using DataLab