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An Anthology of Parametric ROC Models
Abstract
In the context of classification problems, ROC curve has gained its importance in classified fields. The so called parametric form of ROC curve, namely, Binormal ROC model was developed by assuming normal distributions. However, the practical situations in classifying individuals/objects demanded new forms of ROC models. The present paper brings out an insight into the theoretical development of different parametric forms of ROC models and its measures.
Keywords
References
Tanner, J. W. P., and Swets, J. A. A decision making theory of visual detection. Psychol Rev 1954; 61: 401–409. http://dx.doi.org/10.1037/h0058700
Peterson, W. W., Birdsall, T. G., and Fox, W. C. The theory of signal detectability. Transactions of the IRE Professional Group on Information Theory, PGIT 1954; 2(4): 171–212.
Swets, J. A. Signal Detection Theory and ROC Analysis in Psychology and Diagnostics: Collected Papers, Lawrence Erlbaum Associates, New Jersey; 1996.
Green, D. M., and Swets, J. A. Signal Detection theory and Psychophysics. New York, NY: Wiley; 1966.
Drury, C. G., and Fox, J. G. Human reliability in quality control. New York, NY: Halsted; 1975.
Swets, J. A. Egilance: Relationships among theory, physiological correlates and operational performance. New York, NY: Plenum; 1977.
Krzanowski, W. J., and Hand, D. J. ROC curves for continuous data, Monographs on Statistics and Applied Probability. New York, NY: CRC Press, Taylor and Francis Group; 2009.
Swets, J. A., Tanner, W. G. P. J., and Birdsall, T. Decision processes in perception. Psychol Rev 1961; 68: 301–340.http://dx.doi.org/10.1037/h0040547
Linker, E., Moore, M. E., and Galanter, E. Taste thresholds, detection models, and disparate results. Journal of Experimental Psychology 1964; 67(1): 59–66. http://dx.doi.org/10.1037/h0046687
Egan, J. P., Greenberg, G. Z., and Schulman, A. I. Receiver Operating characteristics, signal detectability and the method of free response. J. Acoust. Soc. Am. 1961; 33: 993–1007. http://dx.doi.org/10.1121/1.1908935
Sekuler, R. W. Signal detection, choice response times, and visual backward masking. Canadian Journal of Psychology/Revue Canadienne de Psychologie 1965; 19(2): 118–132. http://dx.doi.org/10.1037/h0082895
Norman, D. A. Sensory thresholds and response bias. J. Acoust. Soc. Am. 1963; 35(9): 1432–1441. http://dx.doi.org/10.1121/1.1918708
Lusted, L. B. Signal detectability and medical decision making. Science 1971; 171: 1217–1219.
Centor, R. M. Signal Detectability: The Use of ROC curves and Their Analyses. Med Decis Making 1991; 11: 102–106.
Zweig, M. H., and Campbell, G. Receiver operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clinical Chemistry 1993; 39(4): 561–577.
Obuchowski, N. A. Receiver Operating Characteristic Curves and their use in Radiology. Radiology 2003; 229(1): 3–8. http://dx.doi.org/10.1148/radiol.2291010898
Fawcett, T. An introduction to ROC analysis. Pattern Recognition Letters 2006; 27(8): 861–874.
Brown, C. D., and Davis, H. T. Receiver operating characteristics curves and related decision measures: A tutorial. Chemometrics and Intelligent Laboratory Systems 2006; 80(1): 24–38.
Cook, N. R. Statistical Evaluation of Prognostic versus Diagnostic Models: Beyond the ROC curve. Clinical Chemistry 2008; 54(1): 17–23.
Metz, C. E. ROC analysis in medical imaging: a tutorial review of the literature. Radiol Phys Technol 2008; 1: 2–12.
Gonclaves, L., Subtil, A., Oliveira, M. R., et. al. ROC curve Estimation: An Overview. Revstat – Statistical Journal 2014; 12(1): 1–20.
Swets, J. A., and Pickett, R. M. Evaluation of Diagnostic Systems: Methods from Signal Detection Theory. New York, NY: Academic Press; 1982.
Bamber, D. The Area above the Ordinal Dominance Graph and the Area below the ROC Graph. Journal of Mathematical Psychology 1975; 12: 387–415.
Dorfman and Alf. Maximum Likelihood Estimation of parameters of signal detection theory – a direct solution. Psychometrika 1968; 33: 117 – 124.
Dorfman, D. D., and Alf, E. Maximum likelihood estimation of parameters of signal-detection theory and determination of confidence intervals - Rating-method data. Journal of Mathematical Psychology 1969; 6(3): 487–496.
Metz, C. E. Basic principles of ROC analysis. Seminars in Nuclear Medicine 1978; 8: 283–298.
Hanley, J. A, McNeil, B. J. The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 1982; 143(1): 29–36. http://dx.doi.org/10.1148/radiology.143.1.7063747
Centor, R. M., and Schwartz, J.S. An Evaluation of Methods for Estimating the Area Under the Receiver Operating Characteristic (ROC) Curve. Med Decis Making 1985; 5: 149–156.
Hanley, J. A. The Robustness of the Binormal Assumptions Used in Fitting ROC curves. Med Decis Making 1988; 8(3): 197–203.
Cantor, S. B., and Kattan, M. W. Determining the Area under the ROC curve for a Binary Diagnostic Test. Med Decis Making 2000; 20(4): 468–470.
Faraggi, D., and Reiser, B. Estimation of the area under the ROC curve. Statistics in Medicine 2002; 21(20): 3093–3106.
Qin, G., and Zhou, X. H. Empirical likelihood inference for the area under the ROC curve. Biometrics 2006; 62(2): 613–622.
Vishnu Vardhan, R. and Sarma, K.V.S. Estimation of the Area under the ROC curve using Confidence Intervals of Mean. ANU Journal of Physical Sciences 2010; 2(1): 29–39.
Suresh Babu, N., Vishnu Vardhan, R. and Sarma K.V.S. On the Comparison of Binormal ROC curves using Confidence Interval of Means. International Journal of Statistics and Analysis 2011; 3(1): 213–221.
Vishnu Vardhan, R. and Balaswamy, S. Improved Methods for Estimating Areas under the Receiver Operating Characteristic Curves: A Confidence Interval Approach. International Journal of Green Computing 2013; 4(2): 58–75.
Goddard, M. J., and Hinberg, I. Receiver operating characteristic (ROC) curves and non-normal data: An empirical study. Statistics in Medicine 1990; 9: 325–337.
England, W. L. An Exponential Model used for optimal threshold selection on ROC curves. Med Decis Making 1988; 8(2): 120–131.
Campbell, G., and Ratnaparkhi, M.V. An application of lomax distributions in receiver operating characteristic (ROC) curve analysis. Communications in Statistics – Theory and Methods 1993; 22(6): 1681–1687.
Hussain, E. The ROC curve Model from Generalized Exponential Distribution. Pakistan Journal of Operations Research 2011; 2: 323–330.
Hussain, E. The Bi-Gamma ROC curve in a straightforward manner. Journal of Basic and Applied Sciences 2012; 8: 309–314.
Vishnu Vardhan, R., Sudesh Pundir and Sameera, G. Estimation of Area under the ROC curve Using Exponential and Weibull Distributions. Bonfring International Journal of Data Mining 2012; 2(2): 52–56.
Balaswamy, S., Vishnu Vardhan, R. and Rao. M. B. A Divergence Measure for STROC curve in Binary Classification. Journal of Advanced Computing 2014; 3(2): 68–81.
Douglas Mossman and Hongying Peng. Using Dual Beta Distributions to Create Proper ROC curves Based on Rating Category Data. Med Decis Making 2015; DOI: 10.1177/0272989X15582210.
Vishnu Vardhan, R. and Kiruthika, C. Properties and the use of Half Normal Distribution in ROC curve Analysis. IAPQR Transactions 2015; 39(2): 169–179.
Balaswamy, S., Vishnu Vardhan, R. and Sarma, K.V.S. The Hybrid ROC curve and its Divergence Measures for Binary Classification, International Journal of Statistics in Medical Research 2015; 4(1): 94–102.
Balaswamy, S. and Vishnu Vardhan, R. Interface between the ratio β with Area under the ROC curve and Kullback-Leibler Divergence under the combination of Half Normal and Rayleigh distributions. American Journal of Biostatistics 2015; 5(2): 69–77.
Balaswamy, S. and Vishnu Vardhan, R. Estimation of Confidence Intervals of a GHROC curve in the presence of Scale and Shape parameters. Research Journal of Mathematical and Statistical Sciences 2015; 3(10): 4–11.
Balaswamy, S. and Vishnu Vardhan, R. Confidence Interval Estimation of an ROC curve: An application of Generalized Half Normal and Weibull distributions. Journal of Probability and Statistics 2015; Article ID 934362, 8 pages. http://dx.doi.org/10.1155/2015/934362
Perkins, N. J. and Schisterman, E. F. The Youden Index and Optimal Cut Point Corrected for Measurement Error. Biometrical Journal 2005; 47: 428–441.
Schisterman, E.F., Perkins, N.J., Aiyi Liu, et. al. Optimal Cut point and Its Corresponding Youden Index to Discriminate Individuals Using Pooled Blood Samples. Epidemiology 2005; 16: 73–81.
Shannon, C. E. and Weaver, W. W. A Mathematical Theory of Communication. The Bell System Technical Journal. University of Illinois Press, Urbana; 1949.
Fisher, R. A. On the Mathematical Foundations of Theoretical Statistics. Philosophical Transactions of the Royal Society A 1922; 222: 309–368. http://www.jstor.org/stable/91208
Kullback, S., and Leibler, R. A. On Information and Sufficiency. The Annals of Mathematical Statistics 1951; 22(1): 79–86. http://www.jstor.org/stable/2236703
Cover, T., and Thomas, J. Elements of Information Theory. John Wiley and Sons; 1991.
Burnham, K. P., and Anderson, D. R. Model selection and multi model inference: a practical information-theoretic approach. Springer New York; 2002.
Dumonceaux, R., and Antle, C. E. Discrimination between the log-normal and the weibull distributions. Technometrics 1973; 15(4): 923–926.
Kundu, D., and Manglick, A. Discriminating between the Weibull and Log Normal distributions. Naval Research Logistics 2004; 51: 893–905.
Pascual, F. G. Maximum likelihood estimation under misspecified Log Normal and Weibull distributions. Communications in Statistics - Simulation and Computations 2005; 34(3): 503–524.
Volkau, I., Prakash, B., Anand, K.N.A., et. al. Extraction of the midsagittal plane from morphological neuro images using the Kullback-Leibler’s measure. Medical Image Analysis 2006; 10: 863–874.
Cabella, B.C.T., Sturzbecher, M.J., Tedeschi, W., et. al. A numerical study of the Kullback-Leibler distance in functional magnetic resonance imaging. Braz. J. Phys. 2008; 38: 20–25. http://dx.doi.org/10.1590/S0103-97332008000100005
Hughes, G., and Bhattacharya, B. Symmetry Properties of Bi-Normal and Bi-Gamma Receiver Operating Characteristic Curves. Entropy 2013; 15(4): 1342–1356.
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