# Fit the contaminated binormal model (CBM) to selected treatment and reader in an ROC dataset Fit the CBM-predicted ROC curve for specified treatment and reader ```r FitCbmRoc(dataset, trt = 1, rdr = 1) ``` ## Arguments - `dataset`: The dataset containing the data - `trt`: The desired treatment, default is 1 - `rdr`: The desired reader, default is 1 ## Returns The return value is a list with the following elements: - **mu**: The mean of the visible diseased distribution (the non-diseased) has zero mean - **alpha**: The proportion of diseased cases where the disease is visible - **zetas**: The cutoffs, zetas or thresholds - **AUC**: The AUC of the fitted ROC curve - **StdAUC**: The standard deviation of AUC - **NLLIni**: The initial value of negative LL - **NLLFin**: The final value of negative LL - **ChisqrFitStats**: The chisquare goodness of fit results - **covMat**: The covariance matrix of the parameters - **fittedPlot**: A `ggplot2` object containing the fitted operating characteristic along with the empirical operating points. Use `print()` to display the object ## Details In CBM ratings from diseased cases are sampled from a mixture distribution with two components: (1) distributed normal with mean $mu$ and unit variance with integrated area $alpha$, and (2) from a unit-normal distribution with integrated area $1-alpha$. Ratings for non-diseased cases are sampled from a unit-normal distribution. The `ChisqrFitStats` consists of a list containing the chi-square value, the p-value and the degrees of freedom. ## Note This algorithm is very robust, much more so than the binormal model. ## Examples ```r ## 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 ``` ## References Dorfman DD, Berbaum KS (2000) A contaminated binormal model for ROC data: Part II. A formal model, Acad Radiol, 7:6, 427--437.

FitCbmRoc function