It is well understood that the optimal classification decision variable is the likelihood ratio or any monotonic transformation of the likelihood ratio. An automated classifier which maps from an input space to one of the likelihood ratio family of decision variables is an optimal classifier or "ideal observer." Artificial neural networks (ANNs) are frequently used as classifiers for many problems. In the limit of large training sample sizes, an ANN approximates a mapping function which is a monotonic transformation of the likelihood ratio, i.e., it estimates an ideal observer decision variable. A principal disadvantage of conventional ANNs is the potential over-parameterization of the mapping function which results in a poor approximation of an optimal mapping function for smaller training samples. Recently, Bayesian methods have been applied to ANNs in order to regularize training to improve the robustness of the classifier. The goal of training a Bayesian ANN with finite sample sizes is, as with unlimited data, to approximate the ideal observer. We have evaluated the accuracy of Bayesian ANN models of ideal observer decision variables as a function of the number of hidden units used, the signal-to-noise ratio of the data and the number of features or dimensionality of the data. We show that when enough training data are present, excess hidden units do not substantially degrade the accuracy of Bayesian ANNs. However, the minimum number of hidden units required to best model the optimal mapping function varies with the complexity of the data.

We have developed a model for FROC curve fitting that relates the observer's FROC performance not to the ROC performance that would be obtained if the observer's responses were scored on a per image basis, but rather to a hypothesized ROC performance that the observer would obtain in the task of classifying a set of "candidate detections" as positive or negative. We adopt the assumptions of the Bunch FROC model, namely that the observer's detections are all mutually independent, as well as assumptions qualitatively similar to, but different in nature from, those made by Chakraborty in his AFROC scoring methodology. Under the assumptions of our model, we show that the observer's FROC performance is a linearly scaled version of the candidate analysis ROC curve, where the scaling factors are just given by the FROC operating point coordinates for detecting initial candidates. Further, we show that the likelihood function of the model parameters given observational data takes on a simple form, and we develop a maximum likelihood method for fitting a FROC curve to this data. FROC and AFROC curves are produced for computer vision observer datasets and compared with the results of the AFROC scoring method. Although developed primarily with computer vision schemes in mind, we hope that the methodology presented here will prove worthy of further study in other applications as well.

BackgroundMUC1 protein is highly expressed in lung cancer. The cytoplasmic domain of MUC1 (MUC1-CD) induces tumorigenesis and resistance to DNA-damaging agents. We characterized MUC1-CD-induced transcriptional changes and examined their significance in lung cancer patients.MethodsUsing DNA microarrays, we identified 254 genes that were differentially expressed in cell lines transformed by MUC1-CD compared to control cell lines. We then examined expression of these genes in 441 lung adenocarcinomas from a publicly available database. We employed statistical analyses independent of clinical outcomes, including hierarchical clustering, Student's t-tests and receiver operating characteristic (ROC) analysis, to select a seven-gene MUC1-associated proliferation signature (MAPS). We demonstrated the prognostic value of MAPS in this database using Kaplan-Meier survival analysis, log-rank tests and Cox models. The MAPS was further validated for prognostic significance in 84 lung adenocarcinoma patients from an independent database.ResultsMAPS genes were found to be associated with proliferation and cell cycle regulation and included CCNB1, CDC2, CDC20, CDKN3, MAD2L1, PRC1 and RRM2. MAPS expressors (MAPS+) had inferior survival compared to non-expressors (MAPS-). In the initial data set, 5-year survival was 65% (MAPS-) vs. 45% (MAPS+, p < 0.0001). Similarly, in the validation data set, 5-year survival was 57% (MAPS-) vs. 28% (MAPS+, p = 0.005).ConclusionsThe MAPS signature, comprised of MUC1-CD-dependent genes involved in the control of cell cycle and proliferation, is associated with poor outcomes in patients with adenocarcinoma of the lung. These data provide potential new prognostic biomarkers and treatment targets for lung adenocarcinoma.

The likelihood ratio, or ideal observer, decision rule is known to be optimal for two-class classification tasks in the sense that it maximizes expected utility (or, equivalently, minimizes the Bayes risk). Furthermore, using this decision rule yields a receiver operating characteristic (ROC) curve which is never above the ROC curve produced using any other decision rule, provided the observer's misclassification rate with respect to one of the two classes is chosen as the dependent variable for the curve (i.e., an "inversion" of the more common formulation in which the observer's true-positive fraction is plotted against its false-positive fraction). It is also known that for a decision task requiring classification of observations into N classes, optimal performance in the expected utility sense is obtained using a set of N − 1 likelihood ratios as decision variables. In the N-class extension of ROC analysis, the ideal observer performance is describable in terms of an (N 2 − N − 1)-parameter hypersurface in an (N 2 − N)-dimensional probability space. We show that the result for two classes holds in this case as well, namely that the ROC hypersurface obtained using the ideal observer decision rule is never above the ROC hypersurface obtained using any other decision rule (where in our formulation performance is given exclusively with respect to between-class error rates rather than within-class sensitivities).

The purpose of this study is to investigate whether computerized analysis using three-class Bayesian artificial neural network (BANN) feature selection and classification can characterize tumor grades (grade 1, grade 2 and grade 3) of breast lesions for prognostic classification on DCE-MRI. A database of 26 IDC grade 1 lesions, 86 IDC grade 2 lesions and 58 IDC grade 3 lesions was collected. The computer automatically segmented the lesions, and kinetic and morphological lesion features were automatically extracted. The discrimination tasks-grade 1 versus grade 3, grade 2 versus grade 3, and grade 1 versus grade 2 lesions-were investigated.Step-wise feature selection was conducted by three-class BANNs. Classification was performed with threeclass BANNs using leave-one-lesion-out cross-validation to yield computerestimated probabilities of being grade 3 lesion, grade 2 lesion and grade 1 lesion. Two-class ROC analysis was used to evaluate the performances. We achieved AUC values of 0.80 ± 0.05, 0.78 ± 0.05 and 0.62 ± 0.05 for grade 1 versus grade 3, grade 1 versus grade 2, and grade 2 versus grade 3, respectively. This study shows the potential for (1) applying three-class BANN feature selection and classification to CADx and (2) expanding the role of DCE-MRI CADx from diagnostic to prognostic classification in distinguishing tumor grades.