Estimating three-class ideal observer decision variables for computerized detection and classification of mammographic mass lesions

We are using Bayesian artificial neural networks (BANNs) to classify mammographic masses in schemes for computer-aided diagnosis, and we are extending this methodology to a three-class classification task. We investigated whether a BANN can estimate ideal observer decision variables to distinguish malignant, benign, and false-positive computer detections. Five features were calculated for 63 malignant and 29 benign computer-detected mass lesions, and for 1049 false-positive computer detections, in 440 mammograms randomly divided into a training and testing set. A BANN was trained on the training set features and applied to the testing set features. We then used a known relation between three-class ideal observer decision variables and that used by a two-class ideal observer when two of three classes are grouped into one class, giving one decision variable for distinguishing malignant from nonmalignant detections, and a second for distinguishing true-positive from false-positive computer detections. For comparison, we grouped the training data into two classes in the same two ways and trained two-class BANNs for these two tasks. The three-class BANN decision variables were essentially identical in performance to the specifically trained two-class BANNs, with the average difference in area under the ROC curves being less than 0.0035 and no differences in area being statistically significant. Thus, the BANN outputs obey the same theoretical relationship as do the three-class and two-class ideal observer decision variables, which is consistent with the claim that the three-class BANN output can provide good estimates of the decision variables used by a three-class ideal observer