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An Exponential Model Used for optimal Threshold selection on ROC Curues

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  • William L. England

Abstract

A two-parameter exponential equation for modeling a receiver operating characteristic (ROC) curve is presented, where the area under the curve is a simple function of one of the parameters. The model makes no distributional assumptions about the underlying normal and abnormal patient populations or about the shape of the resulting ROC curves. In a computer simulation of 75 ROC curves, the model provides a fit equivalent to the maximum likelihood estimate method commonly used for ROC curve fitting. Similar results are obtained using the model to fit ROC curve data from the literature. The model's equation calculates the true-positive ratio as a function of the false-positive ratio, and has a first derivative that is useful for finding the optimal decision threshold for a diagnostic testing procedure. In particular, the model is useful in a computer program for finding jointly optimal thresholds for multiple sequential tests. Key words: receiver operating characteristic (ROC) curve; decision theory; optimization; computer simulation. (Med Decis Making 8:120-131, 1988)

Suggested Citation

  • William L. England, 1988. "An Exponential Model Used for optimal Threshold selection on ROC Curues," Medical Decision Making, , vol. 8(2), pages 120-131, June.
    • Handle: RePEc:sae:medema:v:8:y:1988:i:2:p:120-131
    DOI: 10.1177/0272989X8800800208
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    References listed on IDEAS

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    1. James E. Goin & David F. Preston & Joe H. Gallagher & Audrey V. Wegst, 1983. "Comparison of Five Digital Scintigraphic Display Modes," Medical Decision Making, , vol. 3(2), pages 215-227, June.
    2. Peter Schönemann & Ledyard Tucker, 1967. "A maximum likelihood solution for the method of successive intervals allowing for unequal stimulus dispersions," Psychometrika, Springer;The Psychometric Society, vol. 32(4), pages 403-417, December.
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