• The Korean Journal of Applied Statistics
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• 제32권4호
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• pp.593-605
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• 2019

Significant literature exists on the area under the ROC curve (AUC) and the volume under the ROC surface (VUS) which are statistical measures of the discriminant power of classification models. Whereas the partial AUC is restricted on the false positive rate, the two-way partial AUC is restricted on both the false positive rate and true positive rate, which could be more efficient and accurate than partial AUC. The two-way partial AUC was suggested as more efficient and accurate than the partial AUC. Partial VUS as well as the three-way partial VUS were also developed for the ROC surface. A proposed AUC is expressed in this paper with probability and integration using two truncated distribution functions restricted on both the false positive rate and true positive rate. It is also found that this AUC has a relation with the two-way partial AUC. The three-way partial VUS for the ROC surface is also related to the VUS using truncated distribution functions. These AUC and VUS are represented and estimated in terms of Mann-Whitney statistics. Their parametric and non-parametric estimation methods are explored based on normal distributions and random samples.

• The Korean Journal of Applied Statistics
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• 제33권5호
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• pp.541-553
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• 2020

The receiver operating characteristic (ROC) curve is expressed as both sensitivity and specificity; in addition, some optimal thresholds using the ROC curve are also represented with both sensitivity and specificity. In addition to the sensitivity and specificity, the expected usefulness function is considered as disease prevalence and usefulness. In particular, partial the area under the ROC curve (AUC) on a certain range should be compared when the AUCs of the crossing ROC curves have similar values. In this study, partial AUCs representing high sensitivity and specificity are proposed by using sensitivity and specificity lines, respectively. Assume various distribution functions with ROC curves that are crossing and AUCs that have the same value. We propose a method to improve the discriminant power of the classification models while comparing the partial AUCs obtained using sensitivity and specificity lines.

• Journal of the Korean Data and Information Science Society
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• 제26권6호
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• pp.1367-1375
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• 2015

Consider the linear growth models for longitudinal data analysis. Several kind of linear growth models are selected such as time-effect and random-effect models as well as a dummy variable included model. In this work, simulation data are generated with normality assumption, and both binormal ROC curve and AUC are obtained and compared for various linear growth models. It is found that ROC curves have different shapes and AUC increase slowly, as values of the covariance increase and the time passes for random-effect models. On the other hand, AUC increases very fast as values of covariance decrease. When the covariance has positive value, we explored that the variances of random-effect models increase and the increment of AUC is smaller than that of AUC for time-effect models. And the increment of AUC for time-effect models is larger than the increment for random-effect models.

• The Korean Journal of Applied Statistics
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• 제26권6호
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• pp.977-985
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• 2013

Many situations are classified into more than two categories in real world. In this work, we consider ROC surface and VUS, which are graphical representation methods for classification models with three categories. The standard criteria of AUC for the probability of default based on Basel II is extended to the VUS for ROC surface; therefore, the standardized criteria of VUS for the classification model is proposed. The ranges of AUC, K-S and mean difference statistics corresponding to VUS values for each class of the standard criteria are obtained. The standard criteria of VUS for ROC surface can be established by exploring the relationships of these statistics.

• Communications for Statistical Applications and Methods
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• 제17권2호
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• pp.275-292
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• 2010

Receiver operating characteristic(ROC) curves can be used to assess the accuracy of tests measured on ordinal or continuous scales. The most commonly used measure for the overall diagnostic accuracy of diagnostic tests is the area under the ROC curve(AUC). When two ROC curves are constructed based on two tests performed on the same individuals, statistical analysis on differences between AUCs must take into account the correlated nature of the data. This article focuses on confidence interval estimation of the difference between paired AUCs. We compare nonparametric, maximum likelihood, bootstrap and generalized pivotal quantity methods, and conduct a monte carlo simulation to investigate the probability coverage and expected length of the four methods.

• The Korean Journal of Applied Statistics
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• 제35권1호
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• pp.35-47
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• 2022

The receiver operating characteristic (ROC) curve was developed to quantify the classification ability of marker values (covariates) on the response variable and has been extended to survival data with diverse missing data structure. When survival data is understood as binary data (status of being alive or dead) at each time point, the ROC curve expressed at every time point results in time-dependent ROC curve and time-dependent area under curve (AUC). In particular, a follow-up study brings the change of cohort and incomplete data structures such as censoring and competing risk. In this paper, we review time-dependent ROC estimators under several contexts and perform simulation to check the performance of each estimators. We analyzed a dementia dataset to compare the prognostic power of markers.

• Communications for Statistical Applications and Methods
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• 제22권3호
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• pp.223-232
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• 2015

The area under the ROC curve (AUC), the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) are defined and interpreted with probability that measures the discriminant power of classification models. AUC, VUS and HUM are expressed with the summation and integration notations for discrete and continuous random variables, respectively. AUC for discrete two random samples is represented as the nonparametric Mann-Whitney statistic. In this work, we define conditional Mann-Whitney statistics to compare more than two discrete random samples as well as propose that VUS and HUM are represented as functions of the conditional Mann-Whitney statistics. Three and four discrete random samples with some tie values are generated. Values of VUS and HUM are obtained using the proposed statistic. The values of VUS and HUM are identical with those obtained by definition; therefore, both VUS and HUM could be represented with conditional Mann-Whitney statistics proposed in this paper.

• Journal of the Korean Data and Information Science Society
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• 제25권3호
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• pp.473-483
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• 2014

Even though the ROC manifold for more than three dimensional space which is an extension of the ROC curve and surface has difficulty to represent graphically, the hypervolume under the ROC manifold (HUM) statistic can be defined and obtained based on AUC and VUS measures for the ROC curve and the ROC surface. Hence the definition and characteristics of the HUM for four dimensional space are studied in this work. By extension of the standard criterion of AUC for probabilities of default based on Basel II, the 13 classes of standard criterion of HUM are proposed in order to discriminate four classification models and some application methods are discussed. In order to explore the standard criterion of HUM whose values are obtained from various distributions, ternary plot is used and explained.

• Journal of the Institute of Electronics Engineers of Korea CI
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• 제45권6호
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• pp.179-186
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• 2008

In this paper we analyse the effects of Bayesian algorithm in teaming class imbalance problems and compare the performance evaluation methods. The teaming performance of the Bayesian algorithm is evaluated over the class imbalance problems generated by priori data distribution, imbalance data rate and discrimination complexity. The experimental results are calculated by the AUC(Area Under the Curve) values of both ROC(Receiver Operator Characteristic) and PR(Precision-Recall) evaluation measures and compared according to imbalance data rate and discrimination complexity. In comparison and analysis, the Bayesian algorithm suffers from the imbalance rate, as the same result in the reported researches, and the data overlapping caused by discrimination complexity is the another factor that hampers the learning performance. As the discrimination complexity and class imbalance rate of the problems increase, the learning performance of the AUC of a PR measure is much more variant than that of the AUC of a ROC measure. But the performances of both measures are similar with the low discrimination complexity and class imbalance rate of the problems. The experimental results show 4hat the AUC of a PR measure is more proper in evaluating the learning of class imbalance problem and furthermore gets the benefit in designing the optimal learning model considering a misclassification cost.

• Communications for Statistical Applications and Methods
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• 제29권5호
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• pp.533-545
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• 2022

Collection of data on several variables, especially in the field of medicine, results in the problem of measurement errors. The presence of such measurement errors may influence the outcomes or estimates of the parameter in the model. In classification scenario, the presence of measurement errors will affect the intrinsic cum summary measures of Receiver Operating Characteristic (ROC) curve. In the context of ROC curve, only a few researchers have attempted to study the problem of measurement errors in estimating the area under their respective ROC curves in the framework of univariate setup. In this paper, we work on the estimation of area under the multivariate ROC curve in the presence of measurement errors. The proposed work is supported with a real dataset and simulation studies. Results show that the proposed bias-corrected estimator helps in correcting the AUC with minimum bias and minimum mean square error.