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Bootstrap estimated true and false positive rates and ROC curve

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  • Adler, Werner
  • Lausen, Berthold

Abstract

Diagnostic studies and new biomarkers are assessed by the estimated true and false positive rates of the classification rule. One diagnostic rule is considered for high-dimensional predictor data. Cross-validation and the leave-one-out bootstrap are discussed to estimate true and false positive rates of classifiers by the machine learning methods Adaboost, Bagging, Random Forest, (penalized) logistic regression and support vector machines. The .632+ bootstrap estimation of the misclassification error has been previously proposed to adjust the overfitting of the apparent error. This idea is generalized to the estimation of true and false positive rates. Tree-based simulation models with 8 and 50 binary non-informative variables are analysed to examine the properties of the estimators. Finally, a bootstrap estimation of receiver operating characteristic (ROC) curves is suggested and a .632+ bootstrap estimation of ROC curves is discussed. This approach is applied to high-dimensional gene expression data of leukemia and predictors of image data for glaucoma diagnosis.

Suggested Citation

  • Adler, Werner & Lausen, Berthold, 2009. "Bootstrap estimated true and false positive rates and ROC curve," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 718-729, January.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:3:p:718-729
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    References listed on IDEAS

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    1. Chen, Zhelun & O’Neill, Zheng & Wen, Jin & Pradhan, Ojas & Yang, Tao & Lu, Xing & Lin, Guanjing & Miyata, Shohei & Lee, Seungjae & Shen, Chou & Chiosa, Roberto & Piscitelli, Marco Savino & Capozzoli, , 2023. "A review of data-driven fault detection and diagnostics for building HVAC systems," Applied Energy, Elsevier, vol. 339(C).
    2. Mogensen, Ulla B. & Ishwaran, Hemant & Gerds, Thomas A., 2012. "Evaluating Random Forests for Survival Analysis Using Prediction Error Curves," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i11).
    3. Foucher Yohann & Danger Richard, 2012. "Time Dependent ROC Curves for the Estimation of True Prognostic Capacity of Microarray Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(6), pages 1-22, November.
    4. 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.
    5. Mikulec Artur & Misztal Małgorzata, 2018. "Does the Type of Business Activity and the Enterprise Location Affect a Firm’S Survival? Results of an Analysis for Natural Persons Conducting Economic Activity in the Łódzkie Voivodship," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 22(3), pages 23-40, September.
    6. Adler, Werner & Brenning, Alexander & Potapov, Sergej & Schmid, Matthias & Lausen, Berthold, 2011. "Ensemble classification of paired data," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1933-1941, May.

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