Bayesian multivariate hierarchical transformation models for ROC analysis

Statistics in Medicine

Volumn 25, Issue 3, 2006, Pages 459-479

  O'Malley, A James ^a   Zou, Kelly H ^a,b  

^a HARVARD MEDICAL SCHOOL   (United States)

^b BRIGHAM AND WOMEN S HOSPITAL   (United States)

Author keywords

Bayesian methods; Box Cox transformation; Hierarchical models; Multivariate analysis; Receiver operating characteristic (ROC) curve

Indexed keywords

PROSTATE SPECIFIC ANTIGEN;

ARTICLE; BAYES THEOREM; CLINICAL TRIAL; CLUSTER ANALYSIS; DIAGNOSTIC ACCURACY; DIAGNOSTIC TEST; HUMAN; MULTIVARIATE ANALYSIS; OUTCOMES RESEARCH; PARAMETRIC TEST; PROSTATE CANCER; PROSTATECTOMY; RECEIVER OPERATING CHARACTERISTIC; SCORING SYSTEM; STATISTICAL DISTRIBUTION; STATISTICAL MODEL;

BAYES THEOREM; BIOPSY; CLUSTER ANALYSIS; HUMANS; MALE; MODELS, STATISTICAL; MULTICENTER STUDIES; MULTIVARIATE ANALYSIS; PROSPECTIVE STUDIES; PROSTATE-SPECIFIC ANTIGEN; PROSTATECTOMY; PROSTATIC NEOPLASMS; ROC CURVE;

EID: 31744443393     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.2187     Document Type: Article

References (36)

1. Campbell G. Advances in statistical methodology for the evaluation of diagnostic and laboratory tests. Statistics in Medicine 1994; 13:499-508.
2. Metz CE, Herman BA, Shen JH. Maximum likelihood estimation of receiver operating characteristic (ROC) curves from continuously-distributed data. Statistics in Medicine 1998; 17:1033-1053.
3. Pepe MS. An interpretation for the ROC curve and inference using GLM procedures. Biometrics 2000; 56: 352-359.
4. Cai T, Pepe MS. Semiparametric receiver operating characteristic analysis to evaluate biomarkers for disease. Journal of the American Statistical Association 2002; 97:1099-1107.
5. Zhou XH, McClish DK, Obuchowski NA. Statistical Methods in Diagnostic Medicine. Wiley: New York, 2002.
6. O'Malley AJ, Zou KH, Fielding JR, Tempany CMC. Bayesian regression methodology for estimating a receiver operating characteristic curve with two radiologic applications: prostate biopsy and spiral CT of ureteral stones. Academic Radiology 2001; 8:713-725.
7. Ishwaran H, Gatsonis CA. A general class of hierarchical ordinal regression models with applications to correlated ROC analysis. The Canadian Journal of Statistics 2000; 28:731-750.
8. Gatsonis CA. Random-effects models for diagnostic accuracy data. Academic Radiology 1995; (2nd Suppl.): S12-S21.
9. Hellmich M, Abrams KR, Jones DR, Lambert PC. A Bayesian approach to a general regression model for ROC curves. Medical Decision Making 1998; 18:436-443.
10. Slate EH, Turnbull BW. Statistical models for longitudinal biomarkers of disease onset. Statistics in Medicine 2000; 19:617-637.
11. Heagerty PJ, Lumley T, Pepe MS. Time-dependent ROC curves for censored survival data and a diagnostic marker. Biometrics 2000; 56:337-344.
12. Etzioni R, Pepe M, Longton G, Hu C, Goodman G. Incorporating the time dimension in receiver operating characteristic curves: a case study of prostate cancer. Medical Decision Making 1999; 19:242-251.
13. Tu W, Zhou X-H. A Wald test comparing medical costs based on log-normal distributions with zero valued costs. Statistics in Medicine 1999; 18:2749-2761.
14. Oberg A, Davidian M. Estimating data transformations in nonlinear mixed effects models. Biometrics 2000; 56:65-72.
15. Faraggi D, Reiser B. Estimation of the area under the ROC curve. Statistics in Medicine 2002; 21:3093-3106.
16. Hsieh F, Turnbull BW. Nonparametric and semiparametric estimation of the receiver operating characteristic curve. The Annals of Statistics 1996; 24:25-40.
17. Zou KH, Hall WJ. Two transformation models for estimating an ROC curve derived from continuous data. Journal of Applied Statistics 2000; 27:621-631.
18. Wieand S, Gail MH, James BR, James KL. A family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data. Biometrika 1989; 76:585-592.
19. Zou KH, Hall WJ, Shapiro DE. Smooth non-parametric receiver operating characteristic (ROC) curves for continuous diagnostic tests. Statistics in Medicine 1997; 16:2143-2156.
20. Cole TJ. The LMS method for constructing normalized growth standards. European Journal of Clinical Nutrition 1990; 44:45-60.
21. Kao T, McCabe GP. Optimal sample allocation for normal discrimination and logistic regression under stratified sampling. Journal of the American Statistical Association 1991; 86:432-436.
22. Box GEP, Cox DR. An analysis of transformations. Journal of the Royal Statistical Society, Series B 1964; 26:211-246.
23. Spiegelhalter DJ, Thomas A, Best NG. WinBUGS Version 1.2. MRC Biostatistics Unit: Cambridge, U.K., 1999.
24. Best N, Cowles MK, Vines K. Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output. MRC Biostatistics Unit: Cambridge, U.K., 1995.
25. Tempany CMC, Zhou X-H, Zerhouni EA, Rifkin MD, Quint LE, Piccoli CW, Ellis JH, McNeil BJ. Staging of prostate cancer: results of radiology diagnostic oncology group project comparison of three MR imaging techniques. Radiology 1994; 192:47-54.
26. D'Amico AV, Whittington R, Malkowicz SB, Schultz D, Blank K, Broderick GA, Tomaszewski JE, Renshaw AA, Kaplan I, Beard CJ, Wein A. Biochemical outcome after radical prostatectomy, external beam radiation therapy, or interstitial radiation therapy for clinically localized prostate cancer. Journal of the American Medical Association 1998; 280:969-974.
27. Hanley JA, McNeil BJ. The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 1982; 143:29-36.
28. Su JQ, Liu JS. Linear combinations of multiple diagnostic markers. Journal of the American Statistical Association 1993; 88:1350-1355.
29. Marshall RJ. The predictive value of simple rules for combining two diagnostic tests. Biometrics 1989; 45: 1213-1222.
30. Berger JO. Statistical Decision Theory and Bayesian Analysis (2nd edn). Springer: New York, 1985.
31. Rubin DB. Multiple Imputation for Nonresponse in Surveys. Wiley: Chichester, New York, 1987.
32. Mood AM, Graybill FA, Boes DC. Introduction to the Theory of Statistics (3rd edn). McGraw-Hill: Singapore, 1974; 76.
33. Draper D. Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society, Series B 1995; 57:45-97.
34. Raftery AE. Bayesian model selection in social research (with discussion). In Sociological Methodology, Marsden PV (ed.). Blackwells Publishers: Cambridge, MA, 1995; 111-195.
35. Hoeting JA, Madigan D, Raftery AE, Volinsky CT. Bayesian model averaging: a tutorial. Statistical Science 1999; 14:382-401.
36. O'Malley AJ, Zou KH. Bayesian hierarchical transformation models for receiver operating characteristic curve analysis. ASA Proceedings of the Health Policy Statistics Section 2002; 2541-2550.