Comments on the Logistic Function in ROC Analysis: Applications to Breast Cancer Detection

ROC analysis is rapidly becoming the method of choice for determining the performance of diagnostic imaging techniques. This discussion is intended to provide scientists working in diagnostic imaging with a more in-depth view of the detection task analysis than is currently available in the statistical methodology literature. The logistic function is defined and its utility is illustrated by analyzing two breast cancer detection modalities.

Die ROC-Analyse entwickelt sich schnell zur Methode der Wahl für die Bestimmung der Leistung von diagnostischen Bildtechniken. Diese Arbeit soll Wissenschaftlern, die sich mit der diagnostischen Bildverarbeitung beschäftigen, zu einem tiefergehenden Einblick in die Analyse der Entdeckungsaufgabe verhelfen, als er zur Zeit in der Literatur über die statistische Methodik verfügbar ist. Die logistische Funktion wird definiert und ihr Nutzen an Hand der Analyse von zwei Vorgehensweisen zur Entdeckung von Brustkrebs dargestellt.

Key-Words

ROC Analysis - Signal Detection - Diagnostic Imaging - Logistic Function - Breast Cancer Detection

Schlüssel-Wörter

ROC-Analyse - Zeichenentdeckung - diagnostische Bildverarbeitung - logistische Funktion - Entdeckung von Brustkrebs

• References

• 1 Abrahamson I. G, Levitt H. Statistical analysis of data from experiments in human signal detection. J. math. Psychol 1969; 6: 391.
• 2 Bock R. D, Jones L. V. The Measurement and Prediction of Judgment and Choice. San Francisco: Holden-Day; 1968
• 3 Dorfman D. D, Alf E. Maximum-likelihood estimation of parameters of signal-detection theory and determination of confidence intervals-rating method data. J. math. Psychol 1969; 6: 487.
• 4 Green D. M, Swets J. A. Signal Detection Theory and Psy- chophysics. New York: Krieger; 1974
• 5 Grey D, Morgan B. L. Some aspects of ROC curve-fitting: normal and logistic models. J. math. Psychol 1972; 9: 128.
• 6 Johnson N. L, Kotz S. Continuous Univariate Distributions. New York: John Wiley; 1970
• 7 Luce R. D. Thurstone’s discriminal processes fifty years later. Psychometrika 1977; 42: 461-489.
• 8 Lusted L. B. General problems in medical decision making with comments on ROC analysis. Semin. Nucl. Med 1978; 8: 299-306.
• 9 Metz C. E. Basic principles of ROC analysis. Semin. Nucl. Med 1978; 8: 283-298.
• 10 Ogilvie J. C, Greelman CD. Maximum-likelihood estimation of receiver operating characteristic curve parameters. J. math. Psychol 1968; 5: 377.
• 11 Rao C. R. Linear Statistical Inference and its Applications. New York: John Wiley; 1865
• 12 Swets J. A, Pickett R. M, Whitehead S. F, Getty D, Schnur J. A, Swets J. B, Freeman B. A. Assessment of diagnostic technologies. Science 1979; 205: 753-759.
• 13 Swets J. A, Pickett R. M. Evaluation of Diagnostic Devices in Clinical Medicine: a General Protocol. Bolt, Beranek and Newman, Inc.; Cambridge, Mass: 1979. Report 3819.
• 14 Swets J. A. ROC analysis applied to the evaluation of medical imaging techniques. Invest. Radiol 1979; 14: 109-121.
• 15 Thurstone L. L. Three psychophysical laws. Psychol. Rev 1927; 34: 424-432.
• 16 Thurstone L. L. A law of comparative judgment. Psychol. Rev 1927; 34: 273-286.
• 17 Thurstone L. L. Psychophysical analysis. Amer. J. Psychol 1927; 38: 368-389.