`FitCorCbm.Rd`

Fit the Correlated Contaminated Binormal Model (CORCBM)
to a paired ROC dataset.
The **ROC** dataset has to be formatted as a
**single modality**, **two-reader** dataset, even though the actual
pairing may be different, see details.

`FitCorCbm(dataset)`

- dataset
A

**paired ROC**dataset

A list containing three objects:

- fitCorCbmRet
list(

`FPCounts`

,`TPCounts`

,`muX`

,`muY`

,`alphaX`

,`alphaY`

,`rhoNor`

,`rhoAbn2`

,`zetaX`

,`zetaY`

,`covMat`

,`fixParam`

)- stats
list(

`aucX`

,`aucX`

,`stdAucX`

,`stdAucY`

,`stdErr`

,`areaStat`

,`areaPval`

)- fittedPlot
The fitted plot with operating points, error bars, for both conditions

The conditions (X, Y) can be two readers interpreting images in the same
modality, the same reader interpreting images in different treatments, or
different readers interpreting images in 2 different treatments. Function
`DfExtractCorCbmDataset`

can be used to construct a dataset suitable for
`FitCorCbm`

. With reference to the returned values, and assuming R bins
in condition X and L bins in conditon Y,
`FPCounts`

is the R x L matrix containing the counts for non-diseased cases,
`TPCounts`

is the R x L matrix containing the counts for diseased cases;
`muX`

,`muY`

,`alphaX`

,`alphaY`

,`rhoNor`

,`rhoAbn2`

are
the CORCBM parameters; `aucX`

,`aucX`

are the AUCs in the two conditions;
`stdAucX`

,`stdAucY`

are the corresponding standard errors;`stdErr`

contains the standard errors of the parameters of the model; `areaStat`

,
`areaPval`

,`covMat`

are the area-statistic, the p-value and the covariance
matrix of the parameters. If a parameter approaches a limit, e.g., `rhoNor`

= 0.9999, it is held constant at near the limiting value and the covariance matrix
has one less dimension (along each edge) for each parameter that is held constant.
The indices of the parameters held fixed are in `fitCorCbmRet$fixParam`

.

Zhai X, Chakraborty DP (2017) A bivariate contaminated binormal model for robust fitting of proper ROC curves to a pair of correlated, possibly degenerate, ROC datasets. Medical Physics. 44(6):2207--2222.