Description Usage Arguments Details Value Examples
The socalled 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)
1  metadata_to_fit_MRMC(dataList, ModifiedPoisson = FALSE)

dataList 
A list, consisting of the following R objects:
The detail of these dataset, please see the example datasets, e.g. 
ModifiedPoisson 
Logical, that is If Similarly, If 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 \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 \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 ( or as the expected pairs of FPF per image and TPF per lesion ( If On the other hand, if So,data of FPF and TPF are changed thus, a fitted model is also changed whether Revised 2019 Dec 8 Revised 2019 Nov 25 Revised 2019 August 28 
To fit a model to data, we need a hit data and false data formulated by both an array and a vector.
It also calculates the socalled False Positive Fractions (FPF) (resp. True Positive Fractions (TPF) ) which are cumulative sums of false alarms (resp. hits) over number of lesions or images.
From data of number of hits and false alarms, we calculate the number of cumulative false positives and hits per image or lesion, in other words, False Positive Fraction (FPF) and True Positive Fraction (TPF). Since there are three subscripts, reader, modality, and image, we can create array format or vector format etc...
Abbreviations
FPF: false positive fraction
TPF: true positive fraction
hit : True Positive = TP
false alarms: False Positive = FP
The traditionaly, the socalled FPF;False Positive Fraction and TPT:True Positive Fraction are used. Recall that our data format:
A single reader and a single modality case
——————————————————————————————————
NI, NL  confidence level  No. of false alarms  No. of hits 
(FP:False Positive)  (TP:True Positive)  
       
definitely present  5  F_5  H_5 
probably present  4  F_4  H_4 
equivocal  3  F_3  H_3 
subtle  2  F_2  H_2 
very subtle  1  F_1  H_1 
—————————————————————————————————
FPF is defined as follows;
FPF(5):= \frac{F_5}{NI},
FPF(4):= \frac{F_4+F_5}{NI},
FPF(3):= \frac{F_3+F_4+F_5}{NI},
FPF(2):= \frac{F_2+F_3+F_4+F_5}{NI},
FPF(1):= \frac{F_1+F_2+F_3+F_4+F_5}{NI}.
TPF is defined as follows;
TPF(5):= \frac{H_5}{NL},
TPF(4):= \frac{H_4+H_5}{NL},
TPF(3):= \frac{H_3+H_4+H_5}{NL},
TPF(2):= \frac{H_2+H_3+H_4+H_5}{NL},
TPF(1):= \frac{H_1+H_2+H_3+H_4+H_5}{NL}.
A list, which includes arrays and vectors. A metadata such as number of cumulative false alarms and hits to create and draw the curve.
The False Positive Fraction (FPF) and True Positive Fraction (TPF) are also calculated.
The components of list I rediscover it at 2019 Jun 18, I am not sure it is useful? 2019 Dec 8
harray
An array of hit, dimension [C,M,Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
farray
An array of false alarms, dimension [C,M,Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
hharray
An array of cumulative hits, dimension [C,M,Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
ffarray
An array of cumulative false alarms, dimension [C,M,Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
hharrayN
An array of TPF, dimension [C,M,Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
ffarrayN
An array of FPF, dimension [C,M,Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
h
An vector of hit, dimension [C*M*Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
f
An vector of false alarms, dimension [C*M*Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
hh
An vector of cumulative hits, dimension [C*M*Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
ff
An vector of cumulative false alarms, dimension [C*M*Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
hhN
An vector of TPF, dimension [C*M*Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
ffN
An vector of FPF, dimension [C*M*Q]
, where C,M,Q
are a number of confidence level, modalities, readers, respectively.
Revised Nov. 21
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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63  #========================================================================================
# First, we prepare the data endowed with this package.
#========================================================================================
dat < get(data("dataList.Chakra.Web"))
#========================================================================================
# #Calculate FPFs and TPFs and etc.
#========================================================================================
a < metadata_to_fit_MRMC(dat)
#Now, we get a metadata object named "a".
#========================================================================================
# Check of Definiion
#========================================================================================
a$hh/dat$NL == a$hhN
# Since all of aboves are TRUE, the hhN is a TPF per NL.
#========================================================================================
# Plot a FPFs and TPFs
#========================================================================================
#'
FPF = a$ffN
TPF = a$hhN
dark_theme()
plot(FPF,TPF)
#========================================================================================
# Plot a FPFs and TPFs via ggplot
#========================================================================================
length(dat$f)==length(FPF)
q < dat$q
m < dat$m
df < data.frame(FPF,
TPF,
m,
q
)
# ggplot2::ggplot(df, aes(x =FPF, y = TPF, colour = q, group = m)) + ggplot2::geom_point()
# Revised 2019 Jun 18, Revised 2019 Sept 9

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