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Nonparametric estimation of the threshold at an operating point on the ROC curve

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  • Yousef, Waleed A.
  • Kundu, Subrata
  • Wagner, Robert F.

Abstract

In the problem of binary classification (or medical diagnosis), the classification rule (or diagnostic test) produces a continuous decision variable which is compared to a critical value (or threshold). Test values above (or below) that threshold are called positive (or negative) for disease. The two types of errors associated with every threshold value are Type I (false positive) and Type II (false negative) errors. The Receiver Operating Curve (ROC) describes the relationship between probabilities of these two types of errors. The inverse problem is considered; i.e., given the ROC curve (or its estimate) of a particular classification rule, one is interested in finding the value of the threshold [xi] that leads to a specific operating point on that curve. A nonparametric method for estimating the threshold is proposed. Asymptotic distribution is derived for the proposed estimator. Results from simulated data and real-world data are presented for finite sample size. Finding a particular threshold value is crucial in medical diagnoses, among other fields, where a medical test is used to classify a patient as "diseased" or "nondiseased" based on comparing the test result to a particular threshold value. When the ROC is estimated, an operating point is obtained by fixing probability of one type of error, and obtaining the other one from the estimated curve. Threshold estimation can then be viewed as a quantile estimation for one distribution but with the utilization of the second one.

Suggested Citation

  • Yousef, Waleed A. & Kundu, Subrata & Wagner, Robert F., 2009. "Nonparametric estimation of the threshold at an operating point on the ROC curve," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4370-4383, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4370-4383
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    References listed on IDEAS

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    1. Margaret Sullivan Pepe, 2000. "An Interpretation for the ROC Curve and Inference Using GLM Procedures," Biometrics, The International Biometric Society, vol. 56(2), pages 352-359, June.
    2. Lloyd, Chris J. & Yong, Zhou, 1999. "Kernel estimators of the ROC curve are better than empirical," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 221-228, September.
    3. Jing Qin, 2003. "Using logistic regression procedures for estimating receiver operating characteristic curves," Biometrika, Biometrika Trust, vol. 90(3), pages 585-596, September.
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    1. Yousef, Waleed A., 2013. "Assessing classifiers in terms of the partial area under the ROC curve," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 51-70.
    2. Coolen-Maturi, Tahani & Elkhafifi, Faiza F. & Coolen, Frank P.A., 2014. "Three-group ROC analysis: A nonparametric predictive approach," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 69-81.

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