왜정규분포를 이용한 ROC 곡선에 대한 베이지안 모형

국문 초록 (Abstract)

질병 진단을 위한 진단검사의 결과는 연속형 또는 순서형 자료로 주어질 수 있는데, 일반적으로 진단검사의 정확도는 특성화 곡선과 곡선하면적으로 나타낼 수 있다. 임상적으로 유용한 진단검사는 임의로 선택한 실제 질병이 없는 경우의 검사 결과보다 실제 질병이 있는 경우의 검사 결과가 더 크게 나오는 경우인데, 이런 경우 특성화 곡선은 적절하다고 정의한다. 본 연구에서는 진단검사의 결과가 순서형 자료로 주어지는 경우 적절한 특성화 곡선을 추정하기 위해 확률적 순서화 방법을 이용하고자 한다. 그리고 순서형 변수에 대한 잠재변수의 분포가 치우친 경우를 고려하기 위하여 잠재변수의 분포를 왜정규분포로 가정하여 특성화 곡선과 곡선하면적을 추정할 수 있는 베이지안 모형을 소개하고, 이를 실제 자료에 적용하고자 한다.

다국어 초록 (Multilingual Abstract)

The results of diagnostic tests for disease diagnosis are measured by continuous or ordinal data. The performance of diagnostic tests usually be summarized using the receiver operating characteristic (ROC) curve and the area under the curve. The diagnostic tests are clinically useful when the test results in the diseased group are higher than those in the non-diseased group, in which case the ROC curve is called a proper ROC curve. In this study, we consider the skew normal distribution for the latent variables of ordinal data and the stochastic ordering methods to estimate the proper ROC curve in Bayesian model, and apply them to the real data.

목차 (Table of Contents)

• 요약
• 1. 서론
• 2. 왜정규분포를 이용한 ROC 곡선에 대한 베이지안 모형
• 3. 자료분석
• 4. 결론
• References
• Abstract

참고문헌 (Reference)

1 Mossman, D., "Using dual beta distributions to create"Proper"ROC curves based on rating category data" 36 : 349-365, 2016

2 Azzalini, A., "The skew-normal and related families" Cambridge University Press 2014

3 Hanley, J. A., "The robustness of the"binormal"assumptions used in fitting ROC curves" 8 : 197-203, 1988

4 홍종선, "TROC 곡선과 정확도 측도들" 한국데이터정보과학회 29 (29): 861-872, 2018

5 Hughes, G., "Symmetry properties of bi-normal and bi-gamma receiver operating characteristic curves are described by Kullback-Leibler divergences" 15 : 1342-1356, 2013

6 Metz, C. E., "Some practical issues of experimental design and data analysis in radiological ROC studies" 24 : 243-245, 1989

7 Jang, E. J., "Small area estimation of receiver operating characteristic curves for ordinal data under stochastic ordering" 25 : 1858-1871, 2020

8 홍종선, "ROC 곡선 일반화 함수와 AUC" 한국데이터정보과학회 31 (31): 477-488, 2020

9 Dorfman, D. D., "Proper receiver operating characteristic analysis : The bigamma model" 4 : 138-149, 1996

10 Gelman, A., "Prior distribution for variance parameters in hierarchical models" 1 : 515-533, 2006

11 Azzalini, A., "Package ‘sn’"

12 Wang, C., "Nonparametric estimation of ROC curves based on Bayesian models when the true disease state is unknown" 12 : 128-146, 2007

13 Gelfand, A. E., "Nonparametric Bayesian modeling for stochastic order" 53 : 865-876, 2001

14 Hanson, T. E., "Modelling stochastic order in the analysis of receiver operating characteristic data : Bayesian non-parametric approaches" 57 : 207-225, 2008

15 Metz, C. E., "Maximum likelihood estimation of receiver operating characteristic(ROC)curves from continuously-distributed data" 17 : 1033-1053, 1998

16 Dorfman, D. D., "Maximum likelihood estimation of parameters of signal detection theory and determination of confidence intervals : Rating method data" 6 : 487-496, 1969

17 Azzalini, A., "Further results on a class of distributions which includes the normal ones" 46 : 199-208, 1986

18 Swets, J. A., "Form of empirical ROCs in discrimination and diagnostic tasks : implications for theory and measurement of performance" 99 : 181-198, 1986

19 Van Dyke, C. W., "Cine MRI in the diagnosis of thoracic aortic dissection" 1993

20 Nandram, B., "Bayesian predictive inference of a finite population proportion under selection bias" 11 : 1-21, 2013

21 Spiegelhalter, D. J., "Bayesian measures of model complexity and fit (with discussion)" 64 : 583-539, 2002

22 장은진, "Bayesian hierarchical model for the estimation of proper receiver operating characteristic curves using stochastic ordering" 한국통계학회 26 (26): 205-216, 2019

23 Nandram, B., "Bayesian analysis of a ROC curve for categorical data using a skew-binormal model" 11 : 369-384, 2018

24 Peng, F., "Bayesian analysis of ROC curves using Markov-chain Monte Carlo methods" 16 : 404-411, 1996

25 Geweke, J., "Bayesian Statistics, 4" Claredon Press 169-194, 1992

26 Hwang, B. S., "An integrated Bayesian nonparametric approach for stochastic and variability orders in ROC curve estimation : An application to endometriosis diagnosis" 110 : 923-934, 2015

27 Gelman, A., "A weakly informative default prior distribution for logistic and other regression models" 2 : 1360-1383, 2008

28 Nandram, B., "A nonparametric Bayesian prediction interval for a finite population mean" 86 : 1-17, 2016

29 Ishwaran, H., "A general class of hierarchical ordinal regression models with applications to correlated ROC analysis" 28 : 731-750, 2000

30 Azzalini, A., "A class of distributions which includes the normal ones" 12 : 171-178, 1985

31 Johnson, T. D., "A Bayesian hierarchical approach to multirater correlated ROC analysis" 25 : 1858-1871, 2006

32 Nandram, B., "A Bayesian benchmarking of the Scott-Smith model for small areas" 81 : 1593-1608, 2011

33 Metz, C. E., ""Proper"binormal ROC curves : Theory and maximum-likelihood estimation" 43 : 1-33, 1999