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ROC analysis with multiple classes and multiple tests: Methodology and its application in microarray studies. (English) Zbl 1143.62083
Summary: The accuracy of a single diagnostic test for binary outcomes can be summarized by the area under the receiver operating characteristic (ROC) curve. The volume under the surface and hypervolume under the manifold have been proposed as extensions for multiple class diagnosis. However, the lack of simple inferential procedures for such measures has limited their practical utility. Part of the difficulty is that calculating such quantities may not be straightforward, even with a single test. The decision rule used to generate the ROC surface requires class probability assessments, which are not provided by the tests. We develop a method based on estimating the probabilities via some procedure, for example, multinomial logistic regression. Bootstrap inferences are proposed to account for variability in estimating the probabilities and perform well in simulations. The ROC measures are compared to the correct classification rate, which depends heavily on class prevalences. An example of tumor classification with microarray data demonstrates that this property may lead to substantially different analyses. The ROC-based analysis yields notable decreases in model complexity over previous analyses.

MSC:
62P10 Applications of statistics to biology and medical sciences; meta analysis
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62N02 Estimation in survival analysis and censored data
62G09 Nonparametric statistical resampling methods
62G05 Nonparametric estimation
62N03 Testing in survival analysis and censored data
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