• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.377-387
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• 2015

The area under the ROC curve can be represented by both Mann-Whitney and Wilcoxon rank sum statistics. Consider an ROC surface and manifold equal to three dimensions or more. This paper finds that the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) could be derived as functions of both conditional Mann-Whitney statistics and conditional Wilcoxon rank sum statistics. The nullhypothesis equal to three distribution functions or more are identical can be tested using VUS and HUM statistics based on the asymptotic large sample theory of Wilcoxon rank sum statistics. Illustrative examples with three and four random samples show that two approaches give the same VUS and $HUM^4$. The equivalence of several distribution functions is also tested with VUS and $HUM^4$ in terms of conditional Wilcoxon rank sum statistics.

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.169-174
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• 2013

The ROC curve is drawn with two conditional cumulative distribution functions (or survival functions) of the univariate random variable. In this work, we consider joint cumulative distribution functions of k random variables, and suggest a ROC curve for multivariate random variables. With regard to the values on the line, which passes through two mean vectors of dichotomous states, a joint cumulative distribution function can be regarded as a function of the univariate variable. After this function is modified to satisfy the properties of the cumulative distribution function, a ROC curve might be derived; moreover, some illustrative examples are demonstrated.

• Journal of Veterinary Clinics
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• v.33 no.2
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• pp.97-101
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• 2016

In the field of clinical medicine, diagnostic accuracy studies refer to the degree of agreement between the index test and the reference standard for the discriminatory ability to identify a target disorder of interest in a patient. The receiver operating characteristic (ROC) curve offers a graphical display the trade-off between sensitivity and specificity at each cutoff for a diagnostic test and is useful in assigning the best cutoff for clinical use. In this end, the ROC curve analysis is a useful tool for estimating and comparing the accuracy of competing diagnostic tests. This paper reviews briefly the measures of diagnostic accuracy such as sensitivity, specificity, and area under the ROC curve (AUC) that is a summary measure for diagnostic accuracy across the spectrum of test results. In addition, the methods of creating an ROC curve in single diagnostic test with five-category discrete scale for disease classification from healthy individuals, meaningful interpretation of the AUC, and the applications of ROC methodology in clinical medicine to determine the optimal cutoff values have been discussed using a hypothetical example as an illustration.

• The Korean Journal of Applied Statistics
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• v.32 no.2
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• pp.187-198
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• 2019

Extensive literature exists on how to estimate optimal thresholds based on various accuracy measures using receiver operating characteristic (ROC) and cumulative accuracy profile (CAP) curves. This paper now proposes an alternative measure to represented the specific partial area under the ROC and CAP curves. The relationship between ROC and CAP functions is examined using differential equations of the new defined partial area under curves. In addition, the relationship with the optimal thresholds under conditions of various accuracy measures for the ROC and CAP functions is also derived. We assume there are two kinds of distribution functions composing the mixed distribution as various normal distributions before finding the optimal thresholds. Corresponding type 1 and 2 errors are also explored and discussed under various conditions for accuracy measures.

• Nutrition Research and Practice
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• v.17 no.4
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• pp.641-659
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• 2023

BACKGROUND/OBJECTIVES: The skin is the outermost organ of the human body and plays a protective role against external environmental damages, such as sunlight and pollution, which affect anti-oxidant defenses and skin inflammation, resulting in erythema or skin reddening, immunosuppression, and epidermal DNA damage. MATERIALS/METHODS: The present study aimed to investigate the potential protective effects of red orange complex H extract (ROC) against ultraviolet (UV)-induced skin photoaging in Skh:HR-2 mice. ROC was orally administered at doses of 20, 40, and 80 mg/kg/day for 13 weeks, along with UV irradiation of the mice for 10 weeks. RESULTS: ROC improved UV-induced skin barrier parameters, including erythema, melanin production, transepidermal water loss, elasticity, and wrinkle formation. Notably, ROC inhibited the mRNA expression of pro-inflammatory cytokines (interleukin 6 and tumor necrosis factor α) and melanogenesis. In addition, ROC recovered the UV-induced decrease in the hyaluronic acid and collagen levels by enhancing genes expression. Furthermore, ROC significantly downregulated the protein and mRNA expression of matrix metalloproteinases responsible for collagen degradation. These protective effects of ROC against photoaging are associated with the suppression of UV-induced phosphorylation of c-Jun NH2-terminal kinase and activator protein 1 activation. CONCLUSIONS: Altogether, our findings suggest that the oral administration of ROC exerts potential protective activities against photoaging in UV-irradiated hairless mice.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.987-994
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• 2011

From the point view of credit evaluation whose population is divided into the default and non-default state, two methods are considered to estimate conditional distribution functions: one is to estimate under the assumption that the data is followed the mixture normal distribution and the other is to use the kernel density estimation. The parameters of normal mixture are estimated using the EM algorithm. For the kernel density estimation, five kinds of well known kernel functions and four kinds of the bandwidths are explored. In addition, the corresponding ROC functions are obtained based on the estimated distribution functions. The goodness-of-fit of the estimated distribution functions are discussed and the performance of the ROC functions are compared. In this work, it is found that the kernel distribution functions shows better fit, and the ROC function obtained under the assumption of normal mixture shows better performance.

• The Korean Journal of Applied Statistics
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• v.32 no.4
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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.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.27 no.2
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• pp.7-13
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• 1997

조직학적으로 유용성이 입증된 산탈회법을 이용한 인접면 비교적 초기 치아 우식의 병소를 형성하여 진단율을 조사하였다. 산 용액을 이용하여 20개 인접면 치아우식을 20개 소구치에 형성하였고, 37개 인접면 치아우식을 30개 대구치에 형성하였다. 건전한 소구치 20개, 대구치 30개를 포함하여 총 96개 치아를 4개씩 나누어 24개의 블록을 형성하였고, 각각 2개 블록의 교합면을 교합시켜서, 교익촬영을 하였다. 촬영 결과를 36명의 치과의사들이인접면 치아우식의 유무를 기록하고, 동시에 및 ROC 분석을 위한 5 개 범주의 판독 기준으로 판독하여 기록하였다. 인접면 치아우식증 유, 무만으로 판독한 결과 진단의 sensitivity는 0.71, specificity는 0.78 이였다. ROC 분석 한 결과의 곡선도표 아래부분의 평균 면적은 약 0.806 이였다. 치아우식증 유무만으로 진단한 결과는 특정한 sensitivity와 specificity 만을 나타내지만, ROC 분석 결과는 주관적 진단 기준과 구별되는 고유의 진단 능력을 표시하는 1-specificity(False Positive)의 변화에 따른 sensitivity(True Positive)의 변화를 연속적으로 나타내어 주었다.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.523-537
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• 2011

A receiver operating characteristic (ROC) curve plots the true positive rate of a classier against its false positive rate, both of which are accuracy measures of the classier. The ROC curve has several interesting geometrical properties, including concavity which is a necessary condition for a classier to be optimal. In this paper, we study the nonparametric maximum likelihood estimator (NPMLE) of a concave ROC curve and its modification to reduce bias. We characterize the NPMLE as a solution to a geometric programming, a special type of a mathematical optimization problem. We find that the NPMLE is close to the convex hull of the empirical ROC curve and, thus, has smaller variance but positive bias at a given false positive rate. To reduce the bias, we propose a modification of the NPMLE which minimizes the $L_1$ distance from the empirical ROC curve. We numerically compare the finite sample performance of three estimators, the empirical ROC curve, the NMPLE, and the modified NPMLE. Finally, we apply the estimators to estimating the optimal ROC curve of the variance-threshold classier to segment a low depth of field image and to finding a diagnostic tool with multiple tests for detection of hemophilia A carrier.

• The Korean Journal of Applied Statistics
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• v.26 no.6
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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.