IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v103y2012i1p124-141.html
   My bibliography  Save this article

Nonparametric and semiparametric optimal transformations of markers

Author

Listed:
  • Chiang, Chin-Tsang
  • Chiu, Chih-Heng

Abstract

The receiver operating characteristic (ROC) curve of a likelihood-ratio function has been shown to be the highest among all transformations of continuous markers. For any sampling scheme with the same likelihoods, the induced conditional probability is derived to have the same ROC curve and is found to be more useful for inference purposes. To compromise the difficult task of high-dimensionality in fully nonparametric models and the risk of model misspecification in fully parametric ones, an appealing single-index model is also adopted in our optimization problem. Based on a nonparametric estimator of the area under the ROC curve (AUC), we develop its related inferences and provide some simple and easily checked conditions for the validity of asymptotic results. Since the optimal marker is estimated by using a semiparametric or nonparametric model, conventional theoretical approaches might be inappropriate to some circumstances. The applicability of our procedures are further demonstrated through extensive numerical experiments and data from the studies of Pima-Indian diabetes and liver disorders.

Suggested Citation

  • Chiang, Chin-Tsang & Chiu, Chih-Heng, 2012. "Nonparametric and semiparametric optimal transformations of markers," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 124-141, January.
    • Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:124-141
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X11001370
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    3. Gengsheng Qin & Xiao-Hua Zhou, 2006. "Empirical Likelihood Inference for the Area under the ROC Curve," Biometrics, The International Biometric Society, vol. 62(2), pages 613-622, June.
    4. Signorini, D.F. & Jones, M.C., 2004. "Kernel Estimators for Univariate Binary Regression," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 119-126, January.
    5. E. S. Venkatraman, 2000. "A Permutation Test to Compare Receiver Operating Characteristic Curves," Biometrics, The International Biometric Society, vol. 56(4), pages 1134-1138, December.
    6. Yingcun Xia, 2009. "Model checking in regression via dimension reduction," Biometrika, Biometrika Trust, vol. 96(1), pages 133-148.
    7. Sidi Maouloud, 2008. "Some uniform large deviation results in nonparametric function estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(2), pages 129-152.
    8. Shuangge Ma & Jian Huang, 2007. "Combining Multiple Markers for Classification Using ROC," Biometrics, The International Biometric Society, vol. 63(3), pages 751-757, September.
    9. Martin W. McIntosh & Margaret Sullivan Pepe, 2002. "Combining Several Screening Tests: Optimality of the Risk Score," Biometrics, The International Biometric Society, vol. 58(3), pages 657-664, September.
    10. Patrick J. Heagerty & Thomas Lumley & Margaret S. Pepe, 2000. "Time-Dependent ROC Curves for Censored Survival Data and a Diagnostic Marker," Biometrics, The International Biometric Society, vol. 56(2), pages 337-344, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lim, Alejandro & Chiang, Chin-Tsang & Teng, Jen-Chieh, 2021. "Estimating robot strengths with application to selection of alliance members in FIRST robotics competitions," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    2. Shao‐Hsuan Wang & Chin‐Tsang Chiang, 2020. "Concordance‐based estimation approaches for the optimal sufficient dimension reduction score," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 662-689, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Xiwei & Vexler, Albert & Markatou, Marianthi, 2015. "Empirical likelihood ratio confidence interval estimation of best linear combinations of biomarkers," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 186-198.
    2. Osamu Komori, 2011. "A boosting method for maximization of the area under the ROC curve," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 961-979, October.
    3. Zhang Zhiwei & Ma Shujie & Nie Lei & Soon Guoxing, 2017. "A Quantitative Concordance Measure for Comparing and Combining Treatment Selection Markers," The International Journal of Biostatistics, De Gruyter, vol. 13(1), pages 1-24, May.
    4. Yanqing Wang & Ying‐Qi Zhao & Yingye Zheng, 2020. "Learning‐based biomarker‐assisted rules for optimized clinical benefit under a risk constraint," Biometrics, The International Biometric Society, vol. 76(3), pages 853-862, September.
    5. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "Estimation and Inference Procedures for Semiparametric Distribution Models with Varying Linear-Index," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 396-424, June.
    6. Chin-Tsang Chiang & Shr-Yan Huang, 2009. "Estimation for the Optimal Combination of Markers without Modeling the Censoring Distribution," Biometrics, The International Biometric Society, vol. 65(1), pages 152-158, March.
    7. Jin, Hua & Lu, Ying, 2009. "Permutation test for non-inferiority of the linear to the optimal combination of multiple tests," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 664-669, March.
    8. Xin Huang & Gengsheng Qin & Yixin Fang, 2011. "Optimal Combinations of Diagnostic Tests Based on AUC," Biometrics, The International Biometric Society, vol. 67(2), pages 568-576, June.
    9. Carol Y. Lin & Lance A. Waller & Robert H. Lyles, 2012. "The likelihood approach for the comparison of medical diagnostic system with multiple binary tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1437-1454, December.
    10. Kajal Lahiri & Liu Yang, 2023. "Predicting binary outcomes based on the pair-copula construction," Empirical Economics, Springer, vol. 64(6), pages 3089-3119, June.
    11. Yuanjia Wang & Huaihou Chen & Runze Li & Naihua Duan & Roberto Lewis-Fernández, 2011. "Prediction-Based Structured Variable Selection through the Receiver Operating Characteristic Curves," Biometrics, The International Biometric Society, vol. 67(3), pages 896-905, September.
    12. Sonia Pérez-Fernández & Pablo Martínez-Camblor & Peter Filzmoser & Norberto Corral, 2021. "Visualizing the decision rules behind the ROC curves: understanding the classification process," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 135-161, March.
    13. Chiang, Chin-Tsang & Huang, Ming-Yueh & Bai, Ren-Hong, 2013. "Binary response models with M-phase case-control data," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 332-348.
    14. Yingye Zheng & Tianxi Cai & Ziding Feng, 2006. "Application of the Time-Dependent ROC Curves for Prognostic Accuracy with Multiple Biomarkers," Biometrics, The International Biometric Society, vol. 62(1), pages 279-287, March.
    15. Centorrino, Samuele & Florens, Jean-Pierre, 2021. "Nonparametric Instrumental Variable Estimation of Binary Response Models with Continuous Endogenous Regressors," Econometrics and Statistics, Elsevier, vol. 17(C), pages 35-63.
    16. Tianxi Cai & Thomas A Gerds & Yingye Zheng & Jinbo Chen, 2011. "Robust Prediction of t-Year Survival with Data from Multiple Studies," Biometrics, The International Biometric Society, vol. 67(2), pages 436-444, June.
    17. Samuele Centorrino & Jean-Pierre Florens, 2014. "Nonparametric Instrumental Variable Estimation of Binary Response Models," Department of Economics Working Papers 14-07, Stony Brook University, Department of Economics.
    18. Binbing Yu, 2009. "Approximating the risk score for disease diagnosis using MARS," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(7), pages 769-778.
    19. Qing Lu & Nancy Obuchowski & Sungho Won & Xiaofeng Zhu & Robert C. Elston, 2010. "Using the Optimal Robust Receiver Operating Characteristic (ROC) Curve for Predictive Genetic Tests," Biometrics, The International Biometric Society, vol. 66(2), pages 586-593, June.
    20. Mei-Cheng Wang & Shanshan Li, 2012. "Bivariate Marker Measurements and ROC Analysis," Biometrics, The International Biometric Society, vol. 68(4), pages 1207-1218, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:124-141. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.