"Proper" Binormal ROC Curves: Theory and Maximum-Likelihood Estimation

Journal of Mathematical Psychology

Volumn 43, Issue 1, 1999, Pages 1-33

  Metz, Charles E ^a   Pan, Xiaochuan ^b  

^a UNIVERSITY OF CHICAGO MEDICAL CENTER   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002822137     PISSN: 00222496     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmps.1998.1218     Document Type: Article

References (30)

1. Birdsall, T. G. (1966). The theory of signal detectability: ROC curves and their character. Unpublished Ph.D. thesis, University of Michigan, Ann Arbor.
2. Brent, R. P. (1973). Algorithms for minimization without derivatives. Englewood Cliffs, NJ: Prentice-Hall.
3. Dennis, J. E., & More, J. J. (1977). Quasi-Newton methods, motivation and theory. SIAM Review, 19, 46-89.
4. Dorfman, D. D., & Alf, E. (1969). Maximum likelihood estimation of parameters of signal detection theory and determination of confidence intervals - Rating method data. Journal of Mathematical Psychology, 6, 487-496.
5. Dorfman, D. D. (1982). RSCORE II. In J. A. Swets & R. M. Pickett (Eds.), Evaluation of diagnostic systems: Methods from signal detection theory (pp. 208-232). New York: Academic Press.
6. Dorfman, D. D., & Berbaum, K. S. (1995). Degeneracy and discrete receiver operating characteristic rating data. Academic Radiology, 2, 907-915.
7. Egan, J. P. (1975). Signal detection theory and ROC analysis. New York: Academic Press.
8. Grey, D. R., & Morgan, B. J. T. (1972). Some aspects of ROC curve-fitting: Normal and logistic models. Journal of Mathematical Psychology, 9, 128-139.
9. Hanley, J. A., & McNeil, B. J. (1982). The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143, 29-36.
10. Hanley, J. A. (1988). The robustness of the binormal assumptions used in fitting ROC curves. Medical Decision Making, 8, 197-203.
11. International Commission on Radiation Units and Measurements. (1996). Medical imaging - The assessment of image quality (ICRU Report 54). Bethesda, MD: ICRU.
12. Kendall, M., & Stuart, A. (1979). The advanced theory of statistics (Vol. 2, Chap. 18). New York: MacMillan.
13. McClish, D. K. (1989). Analyzing a portion of the ROC curve. Medical Decision Making, 9, 190-195.
14. Metz, C. E. (1986a). ROC methodology in radiologic imaging. Investigative Radiology, 21, 720-733.
15. Metz, C. E. (1986b). Statistical analysis of ROC data in evaluating diagnostic performance. In D. Herbert & R. Myers (Eds.), Multiple regression analysis: Applications in the health sciences, pp. 365-384. New York: American Institute of Physics.
16. Metz, C. E. (1988). Current problems in ROC analysis. In W. W. Peppler & A. A. Alter (Eds.), Proceedings of the Chest Imaging Conference 1987 (pp. 315-316). Madison, WI: Department of Medical Physics, University of Wisconsin-Madison.
17. Metz, C. E. (1989). Some practical issues of experimental design and data analysis in radiological ROC studies. Investigative Radiology, 24, 243-245.
18. Metz, C. E., Herman, B. A., & Shen, J.-H. (1998). Maximum-likelihood estimation of ROC curves from continuously-distributed data, Statistics in Medicine, 17, 1033-1053.
19. Papoulis, A. (1994). Probability, random variables, and stochastic processes. New York: McGraw-Hill.
20. Polak, E. (1971). Computational methods in optimization. New York: Academic Press.
21. Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. (1989). Numerical recipes. Cambridge, UK: Cambridge Univ. Press.
22. Rao, C. R. (1970). Advanced statistical methods in biometric research. Darien, CT: Hafner.
23. Rockette, H. E., Obuchowski, N. A., & Gur, D. (1990). Nonparametric estimation of degenerate ROC data sets used for comparison of imaging systems. Investigations in Radiology, 25, 835-837.
24. Simpson, A. J., & Fitter, M. J. (1973). What is the best index of detectability? Psychology Bulletin, 80, 481-488.
25. Swets, J. A., Tanner, W. P., Jr., & Birdsall, T. G. (1961). Decision processes in perception. Psychology Reviews, 68, 301-340.
26. Swets, J. A. (1979). ROC analysis applied to the evaluation of medical imaging techniques. Investigative Radiology, 14, 109-121.
27. Swets, J. A., & Pickett, R. M. (1982). Evaluation of diagnostic systems: Methods from signal detection theory. New York: Academic Press.
28. Swets, J. A. (1983). Measuring the accuracy of diagnostic systems. Science, 240, 1285-1293.
29. Swets, J. A. (1986). Form of empirical ROCs in discrimination and diagnostic tasks: Implication for theory and measurement of performance. Psychological Bulletin, 99, 181-198.
30. Van Trees, H. L. (1968). Detection, estimation, and modulation theory (Part I). New York: Academic Press.