Probabilistic analysis of global performances of diagnostic tests: interpreting the Lorenz curve-based summary measures.

Several indices based on the receiver operating characteristic curve (ROC curve) have previously been found to possess probabilistic interpretations. However, these interpretations are based on some unrealistic diagnostic scenarios. In this paper, the author presents a new approach using the Lorenz curve. The author found that the summary indices of the Lorenz curve, that is, the Pietra index and the Gini index, can be interpreted in several ways ('average change in post-test probability', 'per cent maximum prognostic information', and 'probability of correct diagnosis'). These interpretations have a close tie with real-world medical diagnosis, suggesting that these indices are proper measures of test characteristics.

[1]  Chuhsing Kate Hsiao,et al.  Alternative Summary Indices for the Receiver Operating Characteristic Curve , 1996, Epidemiology.

[2]  Richard J. Butler,et al.  Using incomplete moments to measure inequality , 1989 .

[3]  J A Swets,et al.  Measuring the accuracy of diagnostic systems. , 1988, Science.

[4]  J. Hilden.  The Area under the ROC Curve and Its Competitors , 1991, Medical decision making : an international journal of the Society for Medical Decision Making.

[5]  J. Knottnerus.  Application of Logistic Regression to the Analysis of Diagnostic Data , 1992, Medical decision making : an international journal of the Society for Medical Decision Making.

[6]  E Somoza,et al.  Evaluation and optimization of diagnostic tests using receiver operating characteristic analysis and information theory. , 1989, International journal of bio-medical computing.

[7]  B. Carroll,et al.  A specific laboratory test for the diagnosis of melancholia. Standardization, validation, and clinical utility. , 1981, Archives of general psychiatry.

[8]  W Zucchini,et al.  On the statistical analysis of ROC curves. , 1989, Statistics in medicine.

[9]  T. Koepsell,et al.  Measures of gain in certainty from a diagnostic test. , 1985, American journal of epidemiology.

[10]  E Somoza,et al.  Classifying Binormal Diagnostic Tests Using Separation - Asymmetry Diagrams with Constant-performance Curves , 1994, Medical decision making : an international journal of the Society for Medical Decision Making.

[11]  G. Samsa,et al.  Likelihood ratios with confidence: sample size estimation for diagnostic test studies. , 1991, Journal of clinical epidemiology.

[12]  G. Campbell,et al.  Advances in statistical methodology for the evaluation of diagnostic and laboratory tests. , 1994, Statistics in medicine.

[13]  J C Hershey,et al.  Knowing for the Sake of Knowing , 1990, Medical decision making : an international journal of the Society for Medical Decision Making.

[14]  W. C. Lee.  Analysis of seasonal data using the Lorenz curve and the associated Gini index. , 1996, International journal of epidemiology.

[15]  J. Hanley,et al.  The meaning and use of the area under a receiver operating characteristic (ROC) curve. , 1982, Radiology.

[16]  W. Youden,et al.  Index for rating diagnostic tests , 1950, Cancer.

[17]  Mitchell H. Gail,et al.  A family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data , 1989 .

[18]  W. Härdle.  Smoothing Techniques: With Implementation in S , 1991 .

[19]  W. C. Lee.  Characterizing exposure-disease association in human populations using the Lorenz curve and Gini index. , 1997, Statistics in medicine.

[20]  C. Begg,et al.  Advances in statistical methodology for diagnostic medicine in the 1980's. , 1991, Statistics in medicine.

[21]  Elisa T. Lee,et al.  Use of relative operating characteristic analysis in epidemiology. A method for dealing with subjective judgement. , 1981, American journal of epidemiology.

[22]  D. Kent,et al.  Using Treatment-tradeoff Preferences to Select Diagnostic Strategies , 1993, Medical decision making : an international journal of the Society for Medical Decision Making.

[23]  D B Matchar,et al.  Likelihood ratios for continuous test results--making the clinicians' job easier or harder? , 1993, Journal of clinical epidemiology.

[24]  S. W. Halpern,et al.  Application of Information Theory to Clinical Diagnostic Testing. The Electrocardiographic Stress Test , 1981, Circulation.

[25]  B. Gladen.  Matched-pair case-control studies when risk factors are correlated within the pairs. , 1996, International journal of epidemiology.

[26]  Henry S. Shryock,et al.  The Methods and Materials of Demography. , 1973 .

[27]  C. Metz.  Basic principles of ROC analysis. , 1978, Seminars in nuclear medicine.

[28]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .