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    Comparative assessment of three common algorithms for estimating the variance of the area under the nonparametric receiver operating characteristic curve

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    The area under the receiver operating characteristic (ROC) curve is often used to summarize and compare the discriminatory accuracy of a diagnostic test or modality,and to evaluate the predictive power of statistical models for binary outcomes. Parametric maximum likelihood methods for Þtting of the ROC curve provide direct estimates of the area under the ROC curve and its variance. Nonparametric methods, on the other hand, provide estimates of the area under the ROC curve, but do not directly estimate its variance. Three algorithms for computing the variance for the area under the nonparametric ROC curve are commonly used, although ambiguity exists about their behavior under diverse study conditions. Using simulated data, we found similar asymptotic performance between these algorithms when the diagnostic test produces results on a continuous scale, but found notable differences in small samples, and when the diagnostic test yields results on a discrete diagnostic scale. Copyright 2002 by Stata Corporation.receiver operating characteristic (ROC )curve,trapezoidal rule, sensitivity,specificity,discriminatory accuracy,predictive power

    One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve

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    We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class of the Totally Asymmetric Oslo model, thereby identifying a large universality class of directed sandpiles. We map the avalanche size to the area under a Brownian curve with an absorbing boundary at the origin, motivating us to solve this Brownian curve problem. Thus, we are able to determine the moment generating function for the avalanche-size probability in this universality class, explicitly calculating amplitudes of the leading order terms.Comment: 24 pages, 5 figure

    Part 5: Receiver Operating Characteristic Curve and Area under the Curve

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    Multiple diagnostic tools are used by emergency physicians,every day. In addition, new tools are evaluated to obtainmore accurate methods and reduce time or cost of conventionalones. In the previous parts of this educationalseries, we described diagnostic performance characteristicsof diagnostic tests including sensitivity, specificity, positiveand negative predictive values, and likelihood ratios. Thereceiver operating characteristics (ROC) curve is a graphicalpresentation of screening characteristics. ROC curve is usedto determine the best cutoff point and compare two or moretests or observers by measuring the area under the curve(AUC). In this part of our educational series, we explain ROCcurve and two methods to determine the best cutoff value