A random-sum Wilcoxon statistic and its application to analysis of ROC and LROC data

Journal of Statistical Planning and Inference

Volumn 141, Issue 1, 2011, Pages 335-344

  Tang, Liansheng Larry ^a   Balakrishnan, N ^b  

^a Krasnow Institute for Advanced Study   (United States)

^b MCMASTER UNIVERSITY   (Canada)

Author keywords

Diagnostic accuracy; Distribution free comparison; Random sum statistic; Tomography study

Indexed keywords

EID: 77956282726     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2010.06.011     Document Type: Article

References (20)

1. Chakraborty D., Winter L. Free-response methodology: alternate analysis and a new observer-performance experiment. Radiology 1990, 174(3):873-881. URL: 〈http://radiology.rsnajnls.org/cgi/content/abstract/174/3/873.
2. Chakraborty D.P. Maximum likelihood analysis of free-response receiver operating characteristic (fROC) data. Medical Physics 1989, 16(4):561-568. URL: 〈http://link.aip.org/link/?MPH/16/561/1.
3. Gnedenko B.V., Korolev V.Y. Random Summation: Limit Theorems and Applications 1996, CRC Press.
4. Goddard M.J., Hinberg I. Receiver operator characteristic (ROC) curves and non-normal data: an empirical study. Statistics in Medicine 1990, 9:325-337.
5. Guiasu S. On the asymptotic distribution of the sequences of random variables with random indices. The Annals of Mathematical Statistics 1971, 42(6):2018-2028. URL: 〈http://www.jstor.org/stable/2240129.
6. Hanley J., McNeil B. The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 1982, 143:29-36.
7. Kallergi M., Lucier B.J., Berman C.G., Hersh M.R., Kim J.J., Szabunio M.S., Clark R.A. High-performance wavelet compression for mammography: localization response operating characteristic evaluation. Radiology 2006, 238(1):62-73. URL: 〈http://radiology.rsnajnls.org/cgi/content/abstract/238/1/62.
8. Lehmann E.L. Nonparametrics: Statistical Methods Based on Ranks 1998, Holden-Day, San Francisco.
9. Lloyd C.J. Using smoothed receiver operating characteristic curves to summarize and compare diagnostic systems. Journal of the American Statistical Association 1998, 93:1356-1364.
10. Perkins N.J., Schisterman E.F., Vexler A. Receiver operating characteristic curve inference from a sample with a limit of detection. American Journal of Epidemiology 2007, 165(3):325-333.
11. Robbins H. The asymptotic distribution of the sum of a random number of random variables. Bulletin of the American Mathematical Society 1948, 54(12):1151-1161.
12. Robbins H. On the asymptotic distribution of the sum of a random number of random variables. Proceedings of the National Academy of Sciences of the United States of America 1948, 34(4):162-163. URL: 〈http://www.pnas.org/content/34/4/162.short.
13. Schisterman E., Reiser B., Faraggi D. ROC analysis for markers with mass at zero. Statistics in Medicine 2006, 25(4):623-638.
14. Schisterman E., Rotnitzky A. Estimation of the mean of a k-sample u-statistic with missing outcomes and auxiliaries. Biometrika 2001, 88(3):713-725. URL: 〈http://www.jstor.org/stable/2673441.
15. Seltzer S., Swensson R., Nawfel R., Lentini J., Kazda I., Judy P. Visualization and detection-localization on computed tomographic images. Investigative Radiology 1991, 26(4):285-294.
16. Starr S.J., Metz C.E., Lusted L.B., Goodenough D.J. Visual detection and localization of radiographic images. Radiology 1975, 116:533-538.
17. Swensson R.G. Unified measurement of observer performance in detecting and localizing target objects on images. Medical Physics 1996, 23:1709-1725.
18. Szasz D. Limit theorems for the distributions of the sums of a random number of random variables. The Annals of Mathematical Statistics 1972, 43(6):1902-1913. URL: 〈http://www.jstor.org/stable/2240201.
19. Vexler A., Liu A., Eliseeva E., Schisterman E.F. Maximum likelihood ratio tests for comparing the discriminatory ability of biomarkers subject to limit of detection. Biometrics 2008, 64(3):895-903.
20. Zhou X.H., McClish D.K., Obuchowski N. Statistical Methods in Diagnostic Medicine 2002, John Wiley & Sons, New York.