### Example: SimulateCorCbmDataset()

Source: https://dpc10ster.github.io/RJafroc/reference/SimulateCorCbmDataset.html

Example usage of SimulateCorCbmDataset with default parameters. The commented-out code shows a long-running example with K1=5000 and K2=5000, which is not run by default.

```r
dataset <- SimulateCorCbmDataset()

# \donttest{
## this takes very long
## dataset <- SimulateCorCbmDataset(K1 = 5000, K2 = 5000)
# }
```

--------------------------------

### Example usage of DfCreateCorCbmDataset

Source: https://dpc10ster.github.io/RJafroc/reference/DfCreateCorCbmDataset.html

Creates a dataset with default parameters. The commented lines show how to set a seed and a long-running example.

```R
## seed <- 1 
## this gives unequal numbers of bins in X and Y conditions for 50/50 dataset
dataset <- DfCreateCorCbmDataset()

# \donttest{
## this takes very long time!! used to show asymptotic convergence of ML estimates 
## dataset <- DfCreateCorCbmDataset(K1 = 5000, K2 = 5000)
# }

```

--------------------------------

### Example: OR-based algorithm with pilot dataset

Source: https://dpc10ster.github.io/RJafroc/reference/SsPowerGivenJK.html

A simple example using the default OR method with a pilot dataset. This is the default behavior when method is not specified.

```r
## EXAMPLE 3: specify 2-modality ROC dataset and use OR-based alg.
res <- SsPowerGivenJK(dataset = dataset02, FOM = "Wilcoxon", effectSize = 0.05, 
J = 6, K = 251)
```

--------------------------------

### Examples: RRRC, FRRC, RRFC power calculations

Source: https://dpc10ster.github.io/RJafroc/reference/SsPowerGivenJK.html

Three examples showing how to compute power for different analysis options (RRRC, FRRC, RRFC) using a pilot dataset and forcing the DBM algorithm with UseDBMHB2004 = TRUE. Each example sets the same parameters but changes analysisOption.

```r
## EXAMPLE 1: RRRC power 
## specify 2-modality ROC dataset and force DBM alg.
res <- SsPowerGivenJK(dataset = dataset02, FOM = "Wilcoxon", effectSize = 0.05, 
J = 6, K = 251, method = "DBM", UseDBMHB2004 = TRUE) # RRRC is default  

## EXAMPLE 1A: FRRC power 
res <- SsPowerGivenJK(dataset = dataset02, FOM = "Wilcoxon", effectSize = 0.05, 
J = 6, K = 251, method = "DBM", UseDBMHB2004 = TRUE, analysisOption = "FRRC") 

## EXAMPLE 1B: RRFC power 
res <- SsPowerGivenJK(dataset = dataset02, FOM = "Wilcoxon", effectSize = 0.05, 
J = 6, K = 251, method = "DBM", UseDBMHB2004 = TRUE, analysisOption = "RRFC")
```

--------------------------------

### SsFrocSampleSize example with dataset04

Source: https://dpc10ster.github.io/RJafroc/reference/SsFrocSampleSize.html

Example call to SsFrocSampleSize using a subset of dataset04, with effectSizeROC 0.03, 5 readers, 100 cases, and a lesion distribution. The example is wrapped in \donttest{} and includes timing output.

```r
# \donttest{
## Examples with CPU or elapsed time > 5s
## user system elapsed
## SsFrocSampleSize 8.102  0.023   8.135

## SsFrocSampleSize(DfExtractDataset(dataset04, trts = c(1,2)), 
## effectSizeROC = 0.03, JPivot = 5, KPivot = 100, lesDistr = c(0.69, 0.2, 0.11))
# }
```

--------------------------------

### Example: Save dataset05 to rocData2.xlsx

Source: https://dpc10ster.github.io/RJafroc/reference/DfWriteExcelDataFile.html

Example call to DfWriteExcelDataFile that saves the dataset05 object to an Excel file named 'rocData2.xlsx'. The example is wrapped in \donttest{} and commented out with #.

```r
# \donttest{
##DfWriteExcelDataFile(dataset = dataset05, fileName = "rocData2.xlsx")
# }
```

--------------------------------

### SimulateFrocDataset example with plotting

Source: https://dpc10ster.github.io/RJafroc/reference/SimulateFrocDataset.html

Example that sets parameters, calls SimulateFrocDataset to generate a dataset, and then plots empirical FROC operating characteristics using PlotEmpOpChrs. The seed is set to 1 for reproducibility.

```r
set.seed(1) 
K1 <- 5;K2 <- 7;
maxLL <- 2;perCase <- floor(runif(K2, 1, maxLL + 1))
mu <- 1;lambda <- 1;nu <- 0.99 ;zeta1 <- -1
I <- 2; J <- 5

frocDataRaw <- SimulateFrocDataset(
  mu = mu, lambda = lambda, nu = nu, zeta1 = zeta1,
  I = I, J = J, K1 = K1, K2 = K2, perCase = perCase )
  
## plot the data
ret <- PlotEmpOpChrs(frocDataRaw, opChType = "FROC")
## print(ret$Plot)
```

--------------------------------

### Examples: Extract paired data with DfExtractCorCbmDataset

Source: https://dpc10ster.github.io/RJafroc/reference/DfExtractCorCbmDataset.html

Three example calls showing different ways to specify treatments and readers: two readers in the first modality, one reader across two treatments, and two readers across two treatments. The examples are wrapped in \donttest{}.

```R
# \donttest{
## Extract the paired data corresponding to the second and third readers in the first modality
## from the included ROC dataset
dataset11_23 <- DfExtractCorCbmDataset(dataset05, trts = 1, rdrs = c(2,3))

## Extract the paired data corresponding to the third reader in the first and second treatments
dataset12_33 <- DfExtractCorCbmDataset(dataset05, trts = c(1,2), rdrs = 3)

## Extract the data corresponding to the first reader in the first
## modality paired with the data
## from the third reader in the second modality
## (the bin indices are at different positions in the two arrays)
dataset12_13 <- DfExtractCorCbmDataset(dataset05,
trts = c(1,2), rdrs = c(1,3))
# }
```

--------------------------------

### St usage examples

Source: https://dpc10ster.github.io/RJafroc/reference/St.html

Demonstrates calling St with different datasets, FOMs, and methods. The first three lines show basic usage; the last two are wrapped in \donttest{} to avoid running in examples.

```r
result <- St(dataset02,FOM = "Wilcoxon", method = "DBM")
result <- St(dataset02,FOM = "Wilcoxon", method = "OR")
result <- St(datasetX, FOM = "wAFROC", method = "OR", analysisOption = "RRRC")

# \donttest{
result <- St(dataset05, FOM = "wAFROC")
result <- St(dataset05, FOM = "HrAuc", method = "DBM")
# }
```

--------------------------------

### UtilORVarComp example with jackknife and wAFROC

Source: https://dpc10ster.github.io/RJafroc/reference/UtilORVarComp.html

Example usage of UtilORVarComp with the default jackknife method for FOM 'Wilcoxon' on dataset02, and with FOM 'wAFROC' on datasetX. The commented lines show alternative bootstrap and DeLong calls.

```r
## use the default jackknife for covEstMethod
vc <- UtilORVarComp(dataset02, FOM = "Wilcoxon")

##UtilORVarComp(dataset02, FOM = "Wilcoxon", covEstMethod = "bootstrap", 
##nBoots = 2000, seed = 100)$VarCom 

##UtilORVarComp(dataset02, FOM = "Wilcoxon", covEstMethod = "DeLong")$VarCom

vc <- UtilORVarComp(datasetX, FOM = "wAFROC") 
  
```

--------------------------------

### Install required R packages

Source: https://dpc10ster.github.io/RJafroc/index.html

Use this command at the R Console to install the first two packages listed under Imports in the DESCRIPTION file.

```R
install.packages(c("openxlsx", "ggplot2"))
```

--------------------------------

### RSM_wLLF example call

Source: https://dpc10ster.github.io/RJafroc/reference/RSM_wLLF.html

Example call to RSM_wLLF with sample parameters. The output is 0.34174.

```r
RSM_wLLF(1, 1, 0.9, lesDistr = c(0.5, 0.4, 0.1), relWeights = c(0.7, 0.2, 0.1)) 
#> [1] 0.34174
## 0.34174
```

--------------------------------

### R example: run doBootstrap with parametricFOM=TRUE

Source: https://dpc10ster.github.io/RJafrocBook/sources-of-variability.html

Sets up the input data and calls `doBootstrap` with `parametricFOM=TRUE`, `B=200`, `seed=1`. The output shows the original AUC, mean bootstrap AUC, and standard deviation. The example uses a 2x5 counts table.

```R
parametricFOM <- TRUE
B <- 200;seed <- 1;set.seed(seed)
RocTable = array(dim = c(2,5))
RocTable[1,]  <- c(30,19,8,2,1)
RocTable[2,]  <- c(5,6,5,12,22)

ret <- doBootstrap(parametricFOM, B, seed, RocTable)
OrigAUC <- ret$OrigAUC
meanAUCboot <- ret$meanAUCboot
stdAUCboot <- ret$stdAUCboot

cat("Bootstrap variance estimation:",
    "\nparametricFOM = ", parametricFOM,
    "\nseed = ", seed, 
    "\nB = ", B,
    "\nOrigAUC = ", OrigAUC, 
    "\nmeanAUCboot = ", meanAUCboot, 
    "\nstdAUCboot = ", stdAUCboot, "\n")
```

```R
#> Bootstrap variance estimation: 
#> parametricFOM =  TRUE 
#> seed =  1 
#> B =  200 
#> OrigAUC =  0.8704519 
#> meanAUCboot =  0.8671713 
#> stdAUCboot =  0.04380523
```

--------------------------------

### UtilLesDistr examples with dataset01, dataset02, datasetCadLroc, array, and dataset11

Source: https://dpc10ster.github.io/RJafroc/reference/UtilLesDistr.html

Five examples showing the output of UtilLesDistr for different inputs: an FROC dataset (dataset01), an ROC dataset (dataset02), an LROC dataset (datasetCadLroc), a custom 1D-array, and a large FROC dataset (dataset11). Each example includes the resulting data frame and comments explaining the output.

```r
res <- UtilLesDistr(dataset01) # FROC dataset
##    lesID       Freq
## 1      1 0.93258427
## 2      2 0.06741573
## In the Excel input file, 93 percent of lesions have lesionID = 1
## and the rest have lesionID = 2


res <- UtilLesDistr(dataset02) # ROC dataset
##       lesID Freq
## 1         1    1
## In the Excel input file all dis. cases have one lesion

res <- UtilLesDistr(datasetCadLroc) # LROC dataset
##       lesID Freq
## 1         1    1
## In the Excel input file all dis. cases have one lesion

res <- UtilLesDistr(c(0.5, 0.3, 0.1, 0.1))
##      lesID Freq
## 1        1  0.5
## 2        2  0.3
## 3        3  0.1
## 4        4  0.1
## An example of array input; 50 percent of the cases have lesionID = 1,
## 30 percent have lesionID = 2, etc.

res <- UtilLesDistr(dataset11) ## big froc dataset
##     lesID        Freq
## 1       1 0.217391304
## 2       2 0.200000000
## 3       3 0.113043478
## 4       4 0.086956522
## 5       5 0.043478261
## 6       6 0.095652174
## 7       7 0.052173913
## 8       8 0.069565217
## 9       9 0.017391304
## 10     10 0.026086957
## 11     11 0.026086957
## 12     12 0.026086957
## 16     16 0.017391304
## 20     20 0.008695652

## TBA!! This dataset has lots of lesions (3D imaging for lung cancer).
## The lesionIDs range from 1 to 20 with a few missing,
## e.g., lesionID = 13 is not present in any diseased case.
## Cases with lesionID = 1 have frequency 0.217, those with lesionID = 16
## have frequency 0.174, those with lesionID = 20 have frequency 0.00870, etc.

```

--------------------------------

### DfSaveDataFile usage examples

Source: https://dpc10ster.github.io/RJafroc/reference/DfSaveDataFile.html

Commented examples of saving dataset02 in MRMC and iMRMC formats with different file extensions and data descriptions.

```r
# \donttest{
## DfSaveDataFile(dataset = dataset02, 
##    fileName = "rocData2.csv", format = "MRMC")
## DfSaveDataFile(dataset = dataset02, 
##    fileName = "rocData2.lrc", format = "MRMC", 
##     dataDescription = "ExampleROCdata1")
## DfSaveDataFile(dataset = dataset02, 
##    fileName = "rocData2.txt", format = "MRMC", 
##     dataDescription = "ExampleROCdata2")
##  DfSaveDataFile(dataset = dataset02, 
##    fileName = "dataset05.imrmc", format = "iMRMC", 
##    dataDescription = "ExampleROCdata3") 
# }
```

--------------------------------

### UtilPseudoValues example calls with wAFROC FOM

Source: https://dpc10ster.github.io/RJafroc/reference/UtilPseudoValues.html

Two example calls: the first extracts the first 10 jackknife FOM values for dataset05, the second computes pseudovalues for datasetX. Both use FOM = "wAFROC".

```r
result <- UtilPseudoValues(dataset05, FOM = "wAFROC")$jkFomValues[1,1,1:10]
result <- UtilPseudoValues(datasetX, FOM = "wAFROC")
```

--------------------------------

### Example: NULL dataset with DBM variance components

Source: https://dpc10ster.github.io/RJafroc/reference/SsPowerGivenJK.html

Shows how to supply variance components when dataset is NULL. The example uses UtilDBMVarComp to obtain variance components and passes them as a list to the ... argument. Note the comments indicate that the right-hand side values should be replaced with actual values.

```r
## EXAMPLE 2: specify NULL dataset & DBM var. comp. & force DBM-based alg.
vcDBM <- UtilDBMVarComp(dataset02, FOM = "Wilcoxon")$VarCom
res <- SsPowerGivenJK(dataset = NULL, FOM = "Wilcoxon", J = 6, K = 251, 
effectSize = 0.05, method = "DBM", UseDBMHB2004 = TRUE, 
list( 
VarTR = vcDBM["VarTR","Estimates"], # replace rhs with actual values as in 4A
VarTC = vcDBM["VarTC","Estimates"], # do:
VarErr = vcDBM["VarErr","Estimates"])) # do:
```

--------------------------------

### FitBinormalRoc examples with various datasets

Source: https://dpc10ster.github.io/RJafroc/reference/FitBinormalRoc.html

Examples of fitting the binormal model to different datasets, including an ROC dataset, a binned FROC dataset, single and two interior point data, TONY data, and degenerate ROC data. The examples show how to call the function and print the fitted plot.

```R
# \donttest{
## Test with an included ROC dataset
retFit <- FitBinormalRoc(dataset02);## print(retFit$fittedPlot)


## Test with an included FROC dataset; it needs to be binned
## as there are more than 5 discrete ratings levels
binned <- DfBinDataset(dataset05, desiredNumBins = 5, opChType = "ROC")
retFit <- FitBinormalRoc(binned);## print(retFit$fittedPlot)


## Test with single interior point data
fp <- c(rep(1,7), rep(2, 3))
tp <- c(rep(1,5), rep(2, 5))
dataset <- Df2RJafrocDataset(fp, tp)
retFit <- FitBinormalRoc(dataset);## print(retFit$fittedPlot)

## Test with two interior data points
fp <- c(rep(1,7), rep(2, 5), rep(3, 3))
tp <- c(rep(1,3), rep(2, 5), rep(3, 7))
dataset <- Df2RJafrocDataset(fp, tp)
retFit <- FitBinormalRoc(dataset);## print(retFit$fittedPlot)

## Test with TONY data for which chisqr can be calculated
ds <- DfFroc2Roc(dataset01)
retFit <- FitBinormalRoc(ds, 2, 3);## print(retFit$fittedPlot)
## retFit$ChisqrFitStats
 
## Test with included degenerate ROC data
retFit <- FitBinormalRoc(datasetDegenerate);## print(retFit$fittedPlot)
#> Warning: Data is degenerate; binormal model cannot fit it unambiguously: use CBM or RSM method
# }

 


```

--------------------------------

### SsPowerTable example with OR method

Source: https://dpc10ster.github.io/RJafroc/reference/SsPowerTable.html

Example of sample size calculation using the OR method. The code is wrapped in a donttest block and includes a comment showing expected CPU/elapsed time. The actual call is commented out.

```r
# \donttest{
## Examples with CPU or elapsed time > 5s
##              user    system elapsed
## SsPowerTable 20.033  0.037  20.077    

## Example of sample size calculation with OR method
## SsPowerTable(dataset02, FOM = "Wilcoxon", method = "OR")
# }
```

--------------------------------

### Install RJafroc from GitHub

Source: https://dpc10ster.github.io/RJafroc/index.html

Installs the RJafroc package directly from the dpc10ster GitHub repository using devtools. This triggers compilation of C++ code.

```R
install_github("dpc10ster/RJafroc")
```

--------------------------------

### Output of SsSampleSizeKGivenJ example

Source: https://dpc10ster.github.io/RJafrocQuickStart/froc-sample-size.html

Output from the SsSampleSizeKGivenJ example call, showing ROC-ES, wAFROC-ES, K80RRRC (number of cases needed for 80% power), and Power-wAFROC.

```r
## ROC-ES =  0.035 , wAFROC-ES =  0.0759268 , K80RRRC =  84 , Power-wAFROC =  0.8023879
```

--------------------------------

### Example usage of Util2Intrinsic

Source: https://dpc10ster.github.io/RJafroc/reference/Util2Intrinsic.html

Example showing how to call Util2Intrinsic with sample values and extract the intrinsic parameters. Note that the physical values are only constrained to be positive, so nu_i is not constrained to be between 0 and 1.

```R
mu <- 2;lambda <- 10;nu <- 0.9
lambda_i <- Util2Intrinsic(mu, lambda, nu)$lambda_i 
nu_i <- Util2Intrinsic(mu, lambda, nu)$nu_i 
## note that the physical values are only constrained to be positive, e.g., nu_i is not constrained
## to be between 0 and one.
```

--------------------------------

### Examples of binning datasets with different operating characteristics

Source: https://dpc10ster.github.io/RJafroc/reference/DfBinDataset.html

Demonstrates binning various datasets with different desiredNumBins and opChType values. The first block shows binning dataset02 and dataset05 with ROC, AFROC, and wAFROC, and varying bin counts. The second block shows a longer example that simulates an ROC dataset, bins it, and compares figure of merit before and after binning.

```r
# \donttest{
binned <- DfBinDataset(dataset02, desiredNumBins = 3, opChType = "ROC")
binned <- DfBinDataset(dataset05, desiredNumBins = 4, opChType = "ROC")
binned <- DfBinDataset(dataset05, desiredNumBins = 4, opChType = "AFROC")
binned <- DfBinDataset(dataset05, desiredNumBins = 4, opChType = "wAFROC")
binned <- DfBinDataset(dataset05, opChType = "wAFROC", desiredNumBins = 1)
binned <- DfBinDataset(dataset05, opChType = "wAFROC", desiredNumBins = 2)
binned <- DfBinDataset(dataset05, opChType = "wAFROC", desiredNumBins = 3)
## etc.
# }
 
# \donttest{
## takes longer than 5 sec on OSX
dataset <- SimulateRocDataset(I = 2, J = 5, K1 = 50, K2 = 70, a = 1, b = 0.5, seed = 123)
datasetB <- DfBinDataset(dataset, desiredNumBins = 7, opChType = "ROC")
fomOrg <- as.matrix(UtilFigureOfMerit(dataset, FOM = "Wilcoxon"))
##print(fomOrg)
fomBinned <- as.matrix(UtilFigureOfMerit(datasetB, FOM = "Wilcoxon"))
##print(fomBinned)
##cat("mean, sd = ", mean(fomOrg), sd(fomOrg), "\n")
##cat("mean, sd = ", mean(fomBinned), sd(fomBinned), "\n")
# }

```

--------------------------------

### Example: UtilDBMVarComp with dataset02 and Wilcoxon FOM

Source: https://dpc10ster.github.io/RJafroc/reference/UtilDBMVarComp.html

Example call to UtilDBMVarComp using dataset02 and FOM = 'Wilcoxon'. The result is stored in a variable named 'result'.

```r
result <- UtilDBMVarComp(dataset02, FOM = "Wilcoxon")
```

--------------------------------

### Example 5A: Compute power with hard-coded DBM variance components

Source: https://dpc10ster.github.io/RJafroc/reference/SsPowerGivenJK.html

Calls SsPowerGivenJK with method='DBM' and explicit numeric values for KStar, VarR, VarC, VarTR, VarTC, VarRC, and VarErr. This is the hard-coded version of Example 5.

```R
res <- SsPowerGivenJK(dataset = NULL, J = 6, K = 251, effectSize = 0.05, 
method = "DBM", FOM = "Wilcoxon",
list(KStar = 114,
VarR = 0.00153499935,
VarC = 0.02724923428,
VarTR = 0.00020040252,
VarTC = 0.01197529621,
VarRC = 0.01226472859,
VarErr = 0.03997160319))
```

--------------------------------

### R: kableExtra table with collapse_rows

Source: https://dpc10ster.github.io/RJafrocFrocBook/index.html

Example of creating a table with kableExtra, using collapse_rows and kable_styling options.

```R
kbl(dfA, caption = "….", booktabs = TRUE, escape = FALSE) %>% collapse_rows(columns = c(1, 3), valign = "middle") %>% kable_styling(latex_options = c("basic", "scale_down", "HOLD_position"), row_label_position = "c")
```

--------------------------------

### RSM_pdfN example with output

Source: https://dpc10ster.github.io/RJafroc/reference/RSM_pdfN.html

Example call to RSM_pdfN with z = c(1,2) and lambda = 1, producing the density values 0.20647131 and 0.05277653.

```r
RSM_pdfN(c(1,2),1)
#> [1] 0.20647131 0.05277653
```

--------------------------------

### DfReadDataFile examples for reading various data formats

Source: https://dpc10ster.github.io/RJafroc/reference/DfReadDataFile.html

Demonstrates reading ROC, FROC, and LROC data files in different formats (JAFROC, MRMC, iMRMC). The first example reads an LROC file with newExcelFileFormat=TRUE. The remaining examples are wrapped in \donttest{} and show reading .xlsx, .csv, and .imrmc files.

```r
fileName <- system.file("extdata", "toyFiles/ROC/rocCr.xlsx",
package = "RJafroc", mustWork = TRUE)
rdrArr1D <- DfReadDataFile(fileName, newExcelFileFormat = TRUE)


# \donttest{
fileName <- system.file("extdata", "Roc.xlsx",
package = "RJafroc", mustWork = TRUE)
RocDataXlsx <- DfReadDataFile(fileName)

fileName <- system.file("extdata", "RocData.csv",
package = "RJafroc", mustWork = TRUE)
RocDataCsv<- DfReadDataFile(fileName, format = "MRMC")

fileName <- system.file("extdata", "RocData.imrmc",
package = "RJafroc", mustWork = TRUE)
RocDataImrmc<- DfReadDataFile(fileName, format = "iMRMC")

fileName <- system.file("extdata", "Froc.xlsx",
package = "RJafroc", mustWork = TRUE)
FrocDataXlsx <- DfReadDataFile(fileName, sequentialNames = TRUE)
# }
```

--------------------------------

### Example: Simulate FROC dataset and verify AUC equivalence

Source: https://dpc10ster.github.io/RJafroc/reference/SimulateFrocFromLrocDataset.html

Example usage of SimulateFrocFromLrocDataset with datasetCadLroc. It computes the LROC AUC and the FROC HrAuc, then uses testthat::expect_equal to verify they are equal.

```R
frocDataset <- SimulateFrocFromLrocDataset(datasetCadLroc)
lrocAuc <- UtilFigureOfMerit(datasetCadLroc, FOM = "Wilcoxon")
frocHrAuc <- UtilFigureOfMerit(frocDataset, FOM = "HrAuc")   
testthat::expect_equal(lrocAuc, frocHrAuc)
```

--------------------------------

### Example: Calculate FOMs for ROC, FROC, and cross-modality datasets

Source: https://dpc10ster.github.io/RJafroc/reference/UtilFigureOfMerit.html

Three example calls: one for ROC data with FOM = "Wilcoxon", one for FROC data using the default wAFROC FOM, and one for a cross-modality dataset with FOM = "wAFROC".

```r
res <- UtilFigureOfMerit(dataset02, FOM = "Wilcoxon") # ROC data
res <- UtilFigureOfMerit(dataset01) # FROC dataset, default wAFROC FOM
res <- UtilFigureOfMerit(datasetX, FOM = "wAFROC")
```

--------------------------------

### Convert DBM to OR variance components with example output

Source: https://dpc10ster.github.io/RJafroc/reference/UtilDBM2ORVarCom.html

Example usage of UtilDBM2ORVarCom with dataset02 and Wilcoxon FOM, showing the resulting OR variance components. Also includes a related conversion back using UtilOR2DBMVarCom.

```r
DBMVarCom <- St(dataset02, FOM = "Wilcoxon", method = "DBM")$ANOVA$VarCom
UtilDBM2ORVarCom(114, DBMVarCom)
#>             VarCom      Rhos
#> VarR  0.0015349993        NA
#> VarTR 0.0002004025        NA
#> Cov1  0.0003466137 0.4320314
#> Cov2  0.0003440748 0.4288668
#> Cov3  0.0002390284 0.2979333
#> Var   0.0008022883        NA

ORVarCom <- St(dataset02, FOM = "Wilcoxon", method = "OR")$ANOVA$VarCom
UtilOR2DBMVarCom(114, ORVarCom)
#>           Estimates
#> VarR   0.0015349993
#> VarC   0.0272492343
#> VarTR  0.0002004025
#> VarTC  0.0119752962
#> VarRC  0.0122647286
#> VarErr 0.0399716032
```

--------------------------------

### Compute pnorm and qnorm for threshold example

Source: https://dpc10ster.github.io/RJafrocBook/binary-task-model.html

Shows two R examples: pnorm(0.75) returns 0.773, and 2*qnorm(pnorm(zeta)) returns 1.5. These illustrate the relationship between sensitivity, specificity, and the separation parameter.

```R
pnorm(0.75) # example 1
#> [1] 0.773
2*qnorm(pnorm(zeta)) # example 2
#> [1] 1.5
```

--------------------------------

### RSM_pdfD example with three lesion distribution values

Source: https://dpc10ster.github.io/RJafroc/reference/RSM_pdfD.html

Example call to RSM_pdfD with z=c(1,2), mu=1, lambda=1, nu=0.5, and lesion distribution c(0.2,0.3,0.5). Output shows pdf values.

```R
RSM_pdfD(c(1,2),1,1,0.5, c(0.2, 0.3, 0.5))
#> [1] 0.3636117 0.2830817
```

--------------------------------

### UtilMeanSquares usage examples

Source: https://dpc10ster.github.io/RJafroc/reference/UtilMeanSquares.html

Two example calls: one using the default method "DBM" with FOM = "Wilcoxon" on dataset02, and another using method = "OR" with FOM = "wAFROC" on dataset05. Both assign the result to a variable named 'result'.

```r
result <- UtilMeanSquares(dataset02, FOM = "Wilcoxon")
result <- UtilMeanSquares(dataset05, FOM = "wAFROC", method = "OR")
```

--------------------------------

### FitCbmRoc examples with various datasets

Source: https://dpc10ster.github.io/RJafroc/reference/FitCbmRoc.html

Examples of using FitCbmRoc with included ROC data, degenerate data, single and two interior point data, and data with zero counts. Also shows retrieving the ChisqrFitStats output.

```r
# \donttest{
## CPU time 8.7 sec on Ubuntu (#13)
## Test with included ROC data
retFit <- FitCbmRoc(dataset02);## print(retFit$fittedPlot)

## Test with included degenerate ROC data (yes! CBM can fit such data)
retFit <- FitCbmRoc(datasetDegenerate);## print(retFit$fittedPlot)

## Test with single interior point data
fp <- c(rep(1,7), rep(2, 3))
tp <- c(rep(1,5), rep(2, 5))
dataset <- Df2RJafrocDataset(fp, tp)
retFit <- FitCbmRoc(dataset);## print(retFit$fittedPlot)

## Test with two interior data points
fp <- c(rep(1,7), rep(2, 5), rep(3, 3))
tp <- c(rep(1,3), rep(2, 5), rep(3, 7))
dataset <- Df2RJafrocDataset(fp, tp)
retFit <- FitCbmRoc(dataset);
## print(retFit$fittedPlot)

## Test with included ROC data (some bins have zero counts)
retFit <- FitCbmRoc(dataset02, 2, 1);## print(retFit$fittedPlot)

## Test with TONY data for which chisqr can be calculated
ds <- DfFroc2Roc(dataset01)
retFit <- FitCbmRoc(ds, 2, 3);## print(retFit$fittedPlot)
retFit$ChisqrFitStats
#> $chisq
#> [1] 1.449787
#> 
#> $pVal
#> [1] 0.4843762
#> 
#> $df
#> [1] 2
#> 
# }
```

--------------------------------

### Example call to SsSampleSizeKGivenJ with NULL dataset

Source: https://dpc10ster.github.io/RJafrocQuickStart/froc-sample-size.html

Example call to SsSampleSizeKGivenJ with dataset set to NULL, specifying J=6, effectSize=effectSizewAFROC, and a list of variance components (JStar, KStar, VarTR, Cov1, Cov2, Cov3, Var). Returns the number of cases needed for 80% power.

```r
ret2 <- SsSampleSizeKGivenJ(
  dataset = NULL, 
  J = 6, 
  effectSize = effectSizewAFROC, 
  list(JStar = JStar, 
       KStar = KStar, 
       VarTR = varTR_wafroc,
       Cov1 = Cov1_wafroc,
       Cov2 = Cov2_wafroc,
       Cov3 = Cov3_wafroc,
       Var = Var_wafroc))
```

--------------------------------

### Example: Convert intrinsic to physical RSM parameters

Source: https://dpc10ster.github.io/RJafroc/reference/Util2Physical.html

Example usage of Util2Physical. Sets mu, lambda_i, and nu_i, then extracts the physical lambda and nu values. Note that physical values are constrained to be positive and nu must obey 0 <= nu <= 1.

```R
mu <- 2;lambda_i <- 20;nu_i <- 1.1512925 
lambda <- Util2Physical(mu, lambda_i, nu_i)$lambda 
nu <- Util2Physical(mu, lambda_i, nu_i)$nu 
## note that only the physical values are only constrained to be positive
## the physical variable nu must obey 0 <= nu <= 1
```

--------------------------------

### R: kableExtra table with caption

Source: https://dpc10ster.github.io/RJafrocFrocBook/index.html

Example of creating a table with kableExtra, using collapse_rows and kable_styling options, with a specific caption.

```R
kbl(x12, caption = "Summary of optimization results using wAFROC-AUC.", booktabs = TRUE, escape = FALSE) %>% collapse_rows(columns = c(1), valign = "middle") %>% kable_styling(latex_options = c("basic", "scale_down", "HOLD_position"), row_label_position = "c")
```

--------------------------------

### R output: doBootstrap with seed=2

Source: https://dpc10ster.github.io/RJafrocBook/sources-of-variability.html

Shows the output of the same bootstrap example but with `seed=2`. The mean and standard deviation change slightly, illustrating sampling variability.

```R
#> Bootstrap variance estimation: 
#> parametricFOM =  TRUE 
#> seed =  2 
#> B =  200 
#> OrigAUC =  0.8704519 
#> meanAUCboot =  0.8673155 
#> stdAUCboot =  0.03815402
```

--------------------------------

### Get lesion distribution vector with UtilLesionDistrVector()

Source: https://dpc10ster.github.io/RJafrocQuickStart/quick-start-froc.html

Calls UtilLesionDistrVector(x) to obtain the lesion distribution vector. The function returns an array with two columns: the first column contains the distinct non-zero lesion counts (14 in this example), and the second column contains the fraction of diseased cases with that number of lesions. The second column sums to unity.

```R
lesDistr <- UtilLesionDistrVector(x)
lesDistr
#>  [1] 0.217391304 0.200000000 0.113043478 0.086956522 0.043478261 0.095652174
#>  [7] 0.052173913 0.069565217 0.017391304 0.026086957 0.026086957 0.026086957
#> [13] 0.017391304 0.008695652
```

--------------------------------

### Example: Convert LROC dataset and compare AUCs

Source: https://dpc10ster.github.io/RJafroc/reference/DfLroc2Froc.html

Converts datasetCadLroc to FROC, then computes the LROC Wilcoxon AUC and the FROC HrAuc to verify equivalence.

```r
frocDataset <- DfLroc2Froc(datasetCadLroc)
lrocAuc <- UtilFigureOfMerit(datasetCadLroc, FOM = "Wilcoxon")
frocHrAuc <- UtilFigureOfMerit(frocDataset, FOM = "HrAuc")   

```

--------------------------------

### Set parameters for confidence interval example

Source: https://dpc10ster.github.io/RJafrocBook/rsm.html

Defines the number of samples K=100 and lambda values for two readers. The output prints the parameters.

```R
K <- 100
lambdaP <- c(1,2)
cat ("K = ", K, ", lambdaP 1st reader = ", lambdaP[1], ", lambdaP 2nd reader = ", lambdaP[2],"\n")
```

```R
## K =  100 , lambdaP 1st reader =  1 , lambdaP 2nd reader =  2
```

--------------------------------

### Test RJafroc installation with PlotCbmFit

Source: https://dpc10ster.github.io/RJafroc/index.html

Run this R code after installing RJafroc to verify the installation. It creates a CBM fit plot and prints it, which should display two ROC plots in the Plots window.

```R
cbmPlot <- PlotCbmFit(c(1, 2), c(0.5, 0.5))
print(cbmPlot)
```

--------------------------------

### RSM_FPF example call

Source: https://dpc10ster.github.io/RJafroc/reference/RSM_FPF.html

Example usage of RSM_FPF with a z-vector and lambda=1, showing the computed FPF values.

```r
RSM_FPF(c(-Inf,0.1,0.2,0.3),1)
#> [1] 0.6321206 0.3688250 0.3434394 0.3175654
```

--------------------------------

### RSM_TPF example usage

Source: https://dpc10ster.github.io/RJafroc/reference/RSM_TPF.html

Example call to RSM_TPF with a lesion distribution and a z-vector, showing the resulting TPF values.

```r
lesDistr <- c(0.1,0.3,0.6)
RSM_TPF(c(-Inf,0.1,0.2,0.3), 1, 1, 0.9, lesDistr)
#> [1] 0.9949968 0.9627697 0.9545997 0.9445033
```

--------------------------------

### Example: OR method with pilot dataset and with variance components

Source: https://dpc10ster.github.io/RJafroc/reference/SsSampleSizeKGivenJ.html

Two calls that should give identical results. The first uses a pilot dataset directly; the second uses variance components obtained from UtilORVarComp. Both produce KRRRC = 170 and powerRRRC = 0.8016186.

```r
## the following two should give identical results
SsSampleSizeKGivenJ(dataset02, FOM = "Wilcoxon", effectSize = 0.05, J = 6, method = "OR")
#>   KRRRC powerRRRC
#> 1   170 0.8016186

a <- UtilORVarComp(dataset02, FOM = "Wilcoxon")$VarCom
KStar <- length(dataset02$ratings$NL[1,1,,1])
SsSampleSizeKGivenJ(dataset = NULL, J = 6, effectSize = 0.05, method = "OR", 
   list(KStar = KStar, 
   VarTR = a["VarTR",1], 
   Cov1 = a["Cov1",1], 
   Cov2 = a["Cov2",1], 
   Cov3 = a["Cov3",1], 
   Var = a["Var",1]))
#>   KRRRC powerRRRC
#> 1   170 0.8016186
```

--------------------------------

### Set up lesion distribution parameters

Source: https://dpc10ster.github.io/RJafrocBook/rsm.html

Defines the number of cases per lesion count (K2) and the lesion counts (Lk), along with success probabilities for two readers. Prints the parameters to verify setup.

```R
K2 <- c(97,2,1);Lk <- c(1,2,3);nuP1 <- 0.5;nuP2 <- 0.9;
samples1 <- array(dim = c(sum(K2),length(K2)))
cat("K2[1] =", K2[1],", K2[2] =", K2[2],", K2[3] =", K2[3], ", nuP1 =", nuP1, ", nuP2 =", nuP2, "\n")
```

```R
## K2[1] = 97 , K2[2] = 2 , K2[3] = 1 , nuP1 = 0.5 , nuP2 = 0.9
```

--------------------------------

### Example: Calculate PROPROC AUC

Source: https://dpc10ster.github.io/RJafroc/reference/UtilAucPROPROC.html

Example usage of UtilAucPROPROC with c1 = 0.2 and da = 1.5, returning the AUC value 0.8558655.

```r
c1 <- .2;da <- 1.5
UtilAucPROPROC(c1,da)
#> [1] 0.8558655
```

--------------------------------

### Example: Calculate CBM AUC

Source: https://dpc10ster.github.io/RJafroc/reference/UtilAucCBM.html

Example usage of UtilAucCBM with mu = 2 and alpha = 0.8, returning the AUC value 0.8370803.

```R
mu <- 2;alpha <- 0.8
UtilAucCBM(mu,alpha)
#> [1] 0.8370803
```

--------------------------------

### RSM_LLF example call

Source: https://dpc10ster.github.io/RJafroc/reference/RSM_LLF.html

Example call to RSM_LLF with z = c(1,2), mu = 1, nu = 0.5, and the resulting output.

```r
RSM_LLF(c(1,2),1,0.5)
#> [1] 0.25000000 0.07932763
```

--------------------------------

### Example 4: Compute power using OR variance components from dataset

Source: https://dpc10ster.github.io/RJafroc/reference/SsPowerGivenJK.html

Computes JStar and KStar from dataset02, obtains OR variance components via UtilORVarComp, and calls SsPowerGivenJK with a NULL dataset. The variance components are passed as a list with named elements VarTR, Cov1, Cov2, Cov3, and Var.

```R
JStar <- length(dataset02$ratings$NL[1,,1,1])
KStar <- length(dataset02$ratings$NL[1,1,,1])
vcOR <- UtilORVarComp(dataset02, FOM = "Wilcoxon")$VarCom
res <- SsPowerGivenJK(dataset = NULL, FOM = "Wilcoxon", effectSize = 0.05, J = 6, 
K = 251, list(JStar = JStar, KStar = KStar, 
   VarTR = vcOR["VarTR","Estimates"], # replace rhs with actual values as in 4A
   Cov1 = vcOR["Cov1","Estimates"],   # do:
   Cov2 = vcOR["Cov2","Estimates"],   # do:
   Cov3 = vcOR["Cov3","Estimates"],   # do:
   Var = vcOR["Var","Estimates"]))
```

--------------------------------

### Example: Simulate an LROC dataset using RSM

Source: https://dpc10ster.github.io/RJafroc/reference/SimulateLrocDataset.html

Sets a seed, defines parameters, simulates an FROC dataset, and converts it to an LROC dataset using DfFroc2Lroc.

```r
set.seed(1)
  K1 <- 5; K2 <- 5; mu <- 2; lambda <- 1; lesionVector <- rep(1, 5); nu <- 0.8; zeta1 <- -3
  frocData <- SimulateFrocDataset(mu, lambda, nu, zeta1, I = 2, J = 5, K1, K2, lesionVector)
  lrocData <- DfFroc2Lroc(frocData)
```

--------------------------------

### Run doCalSimulator() with parametric AUC and print results

Source: https://dpc10ster.github.io/RJafrocBook/sources-of-variability.html

Sets up a ROC counts table and calls doCalSimulator() with parametricFOM=TRUE, seed=1, and P=2000. The returned mu, sigma, zetas, meanAUC, and stdAUC are stored in variables.

```R
parametricFOM <- TRUE
seed <- 1
set.seed(seed)
P <- 2000
RocCountsTable = array(dim = c(2,5))
RocCountsTable[1,]  <- c(30,19,8,2,1)
RocCountsTable[2,]  <- c(5,6,5,12,22)
ret <- doCalSimulator(P, parametricFOM, RocCountsTable)
mu <- ret$mu
sigma <- ret$sigma
zetas <- ret$zetas
meanAUC_1_2000 <- ret$meanAUC
stdAUC_1_2000 <- ret$stdAUC
```