# Fit the binormal model to selected treatment and reader in an ROC dataset Fit the binormal model-predicted ROC curve for a dataset. This is the R equivalent of ROCFIT or RSCORE ```r FitBinormalRoc(dataset, trt = 1, rdr = 1) ``` ## Arguments - `dataset`: The ROC dataset - `trt`: The desired treatment, default is 1 - `rdr`: The desired reader, default is 1 ## Returns The returned value is a list with the following elements: - **a**: The mean of the diseased distribution; the non-diseased distribution is assumed to have zero mean - **b**: The standard deviation of the non-diseased distribution. The diseased distribution is assumed to have unit standard deviation - **zetas**: The binormal model cutoffs, zetas or thresholds - **AUC**: The binormal model fitted ROC-AUC - **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 the binormal model ratings (more accurately the latent decision variables) from diseased cases are sampled from $N(a,1)$ while ratings for non-diseased cases are sampled from $N(0,b^2)$. To avoid clutter error bars are only shown for the lowest and uppermost operating points. An FROC dataset is internally converted to a highest rating inferred ROC dataset. To many bins containing zero counts will cause the algorithm to fail; so be sure to bin the data appropriately to fewer bins, where each bin has at least one count. ## Examples ```r ## 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) ``` ## References Dorfman DD, Alf E (1969) Maximum-Likelihood Estimation of Parameters of Signal-Detection Theory and Determination of Confidence Intervals - Rating-Method Data, Journal of Mathematical Psychology 6, 487-496. Grey D, Morgan B (1972) Some aspects of ROC curve-fitting: normal and logistic models. Journal of Mathematical Psychology 9, 128-139.

FitBinormalRoc function