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Performance and estimation of the true error rate of classification rules built with additional information. An application to a cancer trial

Author

Listed:
  • Conde David

    (Departamento de Estadística e I.O.,Universidad de Valladolid, 47011 Valladolid, Spain)

  • Salvador Bonifacio

    (Departamento de Estadística e I.O.,Universidad de Valladolid, 47011 Valladolid, Spain)

  • Rueda Cristina

    (Departamento de Estadística e I.O.,Universidad de Valladolid, 47011 Valladolid, Spain)

  • Fernández Miguel A.

    (Departamento de Estadística e I.O.,Universidad de Valladolid, 47011 Valladolid, Spain)

Abstract

Classification rules that incorporate additional information usually present in discrimination problems are receiving certain attention during the last years as they perform better than the usual rules. Fernández, M. A., C. Rueda and B. Salvador (2006): “Incorporating additional information to normal linear discriminant rules,” J. Am. Stat. Assoc., 101, 569–577, proved that these rules have lower total misclassification probability than the usual Fisher’s rule. In this paper we consider two issues; on the one hand, we compare these rules with those based on shrinkage estimators of the mean proposed by Tong, T., L. Chen and H. Zhao (2012): “Improved mean estimation and its application to diagonal discriminant analysis,” Bioinformatics, 28(4): 531–537. with regard to four criteria: total misclassification probability, area under ROC curve, well-calibratedness and refinement; on the other hand, we consider the estimation of the true error rate, which is a very interesting parameter in applications. We prove results on the apparent error rate of the rules that expose the need of new estimators of their true error rate. We propose four such new estimators. Two of them are defined incorporating the additional information into the leave-one-out-bootstrap. The other two are the corresponding cross-validation after bootstrap versions. We compare these estimators with the usual ones in a simulation study and in a cancer trial application, showing the good behavior of the rules that incorporate additional information and of the new leave-one-out bootstrap estimators of their true error rate.

Suggested Citation

  • Conde David & Salvador Bonifacio & Rueda Cristina & Fernández Miguel A., 2013. "Performance and estimation of the true error rate of classification rules built with additional information. An application to a cancer trial," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(5), pages 583-602, October.
    • Handle: RePEc:bpj:sagmbi:v:12:y:2013:i:5:p:583-602:n:3
    DOI: 10.1515/sagmb-2012-0037
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    References listed on IDEAS

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    1. Oh, Man-Suk & Shin, Dong Wan, 2011. "A unified Bayesian inference on treatment means with order constraints," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 924-934, January.
    2. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    3. Margaret Sullivan Pepe & Tianxi Cai & Gary Longton, 2006. "Combining Predictors for Classification Using the Area under the Receiver Operating Characteristic Curve," Biometrics, The International Biometric Society, vol. 62(1), pages 221-229, March.
    4. Fernandez, Miguel A. & Rueda, Cristina & Salvador, Bonifacio, 2006. "Incorporating Additional Information to Normal Linear Discriminant Rules," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 569-577, June.
    5. Lee, Jae Won & Lee, Jung Bok & Park, Mira & Song, Seuck Heun, 2005. "An extensive comparison of recent classification tools applied to microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 869-885, April.
    6. Lin Dan & Shkedy Ziv & Yekutieli Dani & Burzykowski Tomasz & Göhlmann Hinrich W.H. & De Bondt An & Perera Tim & Geerts Tamara & Bijnens Luc, 2007. "Testing for Trends in Dose-Response Microarray Experiments: A Comparison of Several Testing Procedures, Multiplicity and Resampling-Based Inference," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-28, October.
    7. Rosa A. Schiavo & David J. Hand, 2000. "Ten More Years of Error Rate Research," International Statistical Review, International Statistical Institute, vol. 68(3), pages 295-310, December.
    8. Salvador, B. & Fernandez, M.A. & Martin, I. & Rueda, C., 2008. "Robustness of classification rules that incorporate additional information," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2489-2495, January.
    9. Margaret Pepe & Holly Janes & Gary Longton & Wendy Leisenring & Polly Newcomb, 2004. "Limitations of the Odds Ratio in Gauging the Performance of a Diagnostic or Prognostic Marker," UW Biostatistics Working Paper Series 1035, Berkeley Electronic Press.
    10. Kim, Ji-Hyun, 2009. "Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3735-3745, September.
    11. Graf Alexandra C. & Bauer Peter, 2009. "Model Selection Based on FDR-Thresholding Optimizing the Area under the ROC-Curve," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-22, June.
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