![[PDF]](/pb-assets/Icons/adobe-pdf-icon-1498649896243.png){kind=icon}
Abstract
Polytomous discrimination index is a novel and important diagnostic accuracy measure for multi-category classification. After reconstructing its probabilistic definition, we propose a nonparametric approach to the estimation of polytomous discrimination index based on an empirical sample of biomarker values. In this paper, we provide the finite-sample and asymptotic properties of the proposed estimators and such analytic results may facilitate the statistical inference. Simulation studies are performed to examine the performance of the nonparametric estimators. Two real data examples are analysed to illustrate our methodology.
References
| 1. | Hand, DJ, Till, RJ. A simple generalisation of the area under the ROC curve for multiple class classification problems. Mach Learn 2001; 45: 171–186. Google Scholar | ISI |
| 2. | Obuchowski, NA, Goske, MJ, Applegate, KE. Assessing physicians’ accuracy in diagnosing paediatric patients with acute abdominal pain: measuring accuracy for multiple diseases. Stat Med 2001; 20: 3261–3278. Google Scholar | Medline |
| 3. | Mossman, D . Three-way ROCs. Med Decis Making 1999; 19: 78–89. Google Scholar | SAGE Journals | ISI |
| 4. | Dreiseitl, S, Ohno-Machado, L, Binder, M. Comparing three-class diagnostic tests by three-way ROC analysis. Med Decis Making 2000; 20: 323–331. Google Scholar | SAGE Journals | ISI |
| 5. | Van Calster, B, Van Belle, V, Vergouwe, Y Extending the c-statistic to nominal polytomous outcomes: the polytomous discrimination index. Stat Med 2012; 31: 2610–2626. Google Scholar | Medline |
| 6. | Nakas, CT, Yiannoutsos, CT. Ordered multiple-class ROC analysis with continuous measurements. Stat Med 2004; 23: 3437–3449. Google Scholar | Medline | ISI |
| 7. | Li, J, Fine, JP. ROC analysis for multiple classes and multiple categories and its application in microarray studies. Biostatistics 2008; 9: 566–576. Google Scholar | Medline | ISI |
| 8. | Li, J, Jiang, B, Fine, JP. Multicategory reclassification statistics for assessing Improvements in diagnostic accuracy. Biostatistics 2013; 14: 382–394. Google Scholar | Medline |
| 9. | Vexler, A, Hutson, AD, Chen, X. Statistical testing strategies in the health sciences, London: Chapman & Hall/CRC Biostatistics Series, 2016. Google Scholar |
| 10. | Li, J, Zhou, XH, Fine, JP. A regression approach to ROC surfaces, with applications to Alzheimer’s disease. Sci China Math 2012; 55: 1583–1595. Google Scholar | Medline |
| 11. | Coombes, KR, Tsavachidis, S, Morris, JS Improved peak detection and quantification of mass spectrometry data acquired from surface-enhanced laser desorption and ionization by denoising spectra with the undecimated discrete wavelet transform. Proteomics 2005; 5: 4107–4117. Google Scholar | Medline | ISI |
| 12. | Ogdie, A, Li, J, Dai, L Identification of broadly applicable tissue biomarkers of synovitis with binary and multi-category receiver operating characteristic analysis. Biomarkers 2010; 15: 183–190. Google Scholar | Medline |
| 13. | Van Calster, B, Vergouwe, Y, Looman, CWN Assessing the discriminative ability of risk models for more than two outcome categories. Eur J Epidemiol 2012; 27: 761–770. Google Scholar | Medline |
| 14. | Van Hoorde, K, Van Huffel, S, Timmerman, D A spline-based tool to assess and visualize the calibration of multiclass risk predictions. J Biomed Informat 2015; 54: 283–293. Google Scholar | Medline |
| 15. | Inomata, H, Takei, M, Nakamura, H Epstein-Barr-virus-infected CD15 (Lewis X)-positive Hodgkin-lymphoma-like B cells in patients with rheumatoid arthritis. Open Rheumatol J 2009; 3: 41–47. Google Scholar | Medline |
| 16. | Novoselova, N, Beffa, CD, Wang, J HUM Calculator and HUM package for R: easy-to-use software tools for multicategory receiver operating characteristic analysis. Bioinformatics 2014; 30: 1635–1636. Google Scholar | Medline |
| 17. | Ohtsu, S, Yagi, H, Nakamura, M Enhanced neutrophilic granulopoiesis in rheumatoid arthritis. Involvement of neutrophils in disease progression. J Rheumatol 2000; 27: 1341–1351. Google Scholar | Medline |
| 18. | Ressom, HW, Varghese, RS, Drake, SK Peak selection from MALDI-TOF mass spectra using ant colony optimization. Bioinformatics 2007; 23: 619–626. Google Scholar | Medline | ISI |
| 19. | Ressom, HW, Varghese, RS, Goldman, L Analysis of MALDI-TOF mass spectrometry data for detection of glycan biomarkers. Pac Symp Biocomput 2008; 13: 216–227. Google Scholar |
| 20. | Van Calster, B, Van Belle, V, Vergouwe, Y Discrimination ability of prediction models for ordinal outcomes: relationships between existing measures and a new measure. Biometr J 2012; 54: 674–685. Google Scholar | Medline |
