Flexible regression models for ROC and risk analysis, with or without a gold standard

Statistics in Medicine

Volumn 34, Issue 30, 2015, Pages 3997-4015

  Branscum, Adam J ^a   Johnson, Wesley O ^b   Hanson, Timothy E ^c   Baron, Andre T ^d  

^a OREGON STATE UNIVERSITY   (United States)

^b 5226 Donald Bren Hall   (United States)

^c UNIVERSITY OF SOUTH CAROLINA   (United States)

^d Loring Life Sciences   (United States)

Author keywords

Bayesian semiparametric; disease diagnosis; medical test evaluation; Polya tree

Indexed keywords

BIOLOGICAL MARKER; EPIDERMAL GROWTH FACTOR RECEPTOR; TUMOR MARKER;

AGED; ARTICLE; BAYES THEOREM; CASE CONTROL STUDY; CONTROLLED STUDY; HUMAN; LUNG CANCER; MAJOR CLINICAL STUDY; MALE; MATHEMATICAL COMPUTING; MEASUREMENT ACCURACY; RECEIVER OPERATING CHARACTERISTIC; RISK ASSESSMENT; SIMULATION; STANDARDIZATION; STATISTICAL MODEL; BIOSTATISTICS; BLOOD; COMPUTER SIMULATION; LUNG NEOPLASMS; REGRESSION ANALYSIS; STATISTICS AND NUMERICAL DATA;

BAYES THEOREM; BIOMARKERS, TUMOR; BIOSTATISTICS; COMPUTER SIMULATION; HUMANS; LUNG NEOPLASMS; MALE; MODELS, STATISTICAL; RECEPTOR, EPIDERMAL GROWTH FACTOR; REGRESSION ANALYSIS; RISK ASSESSMENT; ROC CURVE;

EID: 84956590424     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.6610     Document Type: Article

References (64)

1. Erkanli A, Sung M, Costello EJ, Angold A. Bayesian semi-parametric ROC analysis. Statistics in Medicine 2006; 25:3905–3928.
2. Wang C, Turnbull BW, Gröhn YT, Nielsen SS. Nonparametric estimation of ROC curves based on Bayesian models when the true disease state is unknown. Journal of Agricultural, Biological, and Environmental Statistics 2007; 12:128–146.
3. Fosgate GT, Scott HM, Jordan ER. Development of a method for Bayesian nonparametric ROC analysis with application to an ELISA for Johne's disease in dairy cattle. Preventive Veterinary Medicine 2007; 81:178–193.
4. Branscum AJ, Johnson WO, Hanson TE, Gardner IA. Bayesian semiparametric ROC curve estimation and disease diagnosis. Statistics in Medicine 2008; 27:2474–2496.
5. Hanson TE, Kottas A, Branscum AJ. Modelling stochastic order in the analysis of ROC data: Bayesian non-parametric approaches. Applied Statistics 2008; 57:207–225.
6. Hanson TE, Branscum AJ, Gardner IA. Multivariate mixtures of Polya trees for modelling ROC data. Statistical Modelling 2008; 8:81–96.
7. Gu J, Ghosal S, Roy A. Bayesian bootstrap estimation of ROC curve. Statistics in Medicine 2008; 27:5407–5420.
8. Inácio V, Turkman AA, Nakas CT, Alonzo TA. Nonparametric Bayesian estimation of the three-way receiver operating characteristic surface. Biometrical Journal 2011; 53:1011–1024.
9. Ladouceur L, Rahme E, Belisle P, Scott AN, Schwartzman K, Joseph L. Modeling continuous diagnostic test data using approximate Dirichlet process distributions. Statistics in Medicine 2011; 30:2648–2662.
10. Hung H, Chiang C-T. Nonparametric methodology for the time-dependent partial area under the ROC curve. Journal of Statistical Planning and Inference 2011; 141:3829–3838.
11. Colak E, Mutlu F, Bal C, Oner S, Ozdamar K, Gok B, Cavusoglu Y. Comparison of semiparametric, parametric, and nonparametric ROC analysis for continuous diagnostic tests using a simulation study and acute coronary syndrome data. Computational and Mathematical Methods in Medicine 2012; 2012:Article ID 698320, 7 pages. DOI: 10.1155/2012/698320.
12. Hanfang Y, Zhao Y. Smoothed empirical likelihood for ROC curves with censored data. Journal of Multivariate Analysis 2012; 109:254–263.
13. Inácio de Carvalho V, Jara A, Hanson TE, de Carvalho M. Bayesian nonparametric ROC regression modeling. Bayesian Analysis 2013; 8:623–646.
14. Martinez-Camblora P, Carleos C, Corral N. General nonparametric ROC curve comparison. Journal of the Korean Statistical Society 2013; 43:71–81.
15. Broemeling LD. Bayesian Biostatistics and Diagnostic Medicine. Chapman & Hall: Boca Raton, FL, 2007.
16. Collins J, Huynh M. Estimation of diagnostic test accuracy without full verification: a review of latent class methods. Statistics in Medicine 2014; 33:4141–4169.
17. Gastwirth JL, Johnson WO. Quality control for screening tests: applications to HIV and drug use detection. Journal of the American Statistical Association 1994; 89:972–981.
18. Johnson WO, Gastwirth JL. Dual group screening. Journal of Statistical Planning and Inference 2000; 83:449–473.
19. Baron AT, Lafky JM, Boardman CH, Balasubramaniam S, Suman VJ, Podratz KC, Maihle NJ. Serum sErbB1 and epidermal growth factor levels as tumor biomarkers in women with stage III or IV epithelial ovarian cancer. Cancer Epidemiology Biomarkers and Prevention 1999; 8:129–137.
20. Baron AT, Boardman CH, Lafky JM, Rademaker A, Liu D, Fishman DA, Podratz KC, Maihle NJ. Soluble epidermal growth factor receptor (sEGFR) [corrected] and cancer antigen 125 (CA125) as screening and diagnostic tests for epithelial ovarian cancer. Cancer Epidemiology Biomarkers and Prevention 2005; 14:306–318.
21. Albert PS, Dodd LE. A cautionary note on the robustness of latent class models for estimating diagnostic error without a gold standard. Biometrics 2004; 60:427–435.
22. Jones G, Johnson WO, Hanson TE, Christensen R. Identifiability of models for multiple diagnostic testing in the absence of a gold standard. Biometrics 2010; 66:855–863.
23. Box GEP. Science and statistics. Journal of the American Statistical Association 1976; 71:791–799.
24. Pepe MS. The Statistical Evaluation of Medical Tests for Classification and Prediction, Oxford Statistical Science Series. Oxford University Press, 2003.
25. Krzanowski WJ, Hand DJ. ROC Curves for Continuous Data. Chapman & Hall: Boca Raton, FL, 2009.
26. Henkelman RM, Kay I, Bronskill MJ. Receiver operating characteristic (ROC) without truth. Medical Decision Making 1990; 10:24–29.
27. Beiden SV, Campbell G, Meier K, Wagner RF. On the problem of ROC analysis without truth: the EM algorithm and the information matrix. In Medical Imaging 2000: Image Perception and Performance, Krupinski EA (ed.) SPIE Digital Library: San Diego, CA, 2000; 126–134.
28. Kupinski MA, Hoppin JW, Clarkson E, Barrett HH, Kastis GA. Estimation in medical imaging without a gold standard. Academic Radiology 2002; 9:290–297.
29. Choi YK, Johnson WO, Collins MT, Gardner IA. Bayesian estimation of ROC curves in the absence of a gold standard. Journal of Agricultural, Biological, and Environmental Statistics 2006; 11:210–229.
30. Choi YK, Johnson WO, Thurmond MC. Diagnosis using predictive probabilities without cut-offs. Statistics in Medicine 2006; 25:699–717.
31. Hall P, Zhou X-H. Nonparametric estimation of component distributions in a multivariate mixture. Annals of Statistics 2003; 31:201–224.
32. Zhou X-H, Castelluccio P, Zhou C. Nonparametric estimation of ROC curves in the absence of a gold standard. Biometrics 2005; 61:600–609.
33. Albert PS. Random effects modeling approaches for estimating ROC curves from repeated ordinal tests without a gold standard. Biometrics 2007; 63:593–602.
34. Wang C, Turnbull BW, Gröhn YT, Nielsen SS. Estimating receiver operating characteristic curves with covariates when there is no perfect reference test for diagnosis of Johne's disease. Journal of Dairy Science 2006; 89:3038–3046.
35. Wang C, Turnbull BW, Nielsen SS, Gröhn YT. Bayesian analysis of longitudinal Johne's disease diagnostic data without a gold standard test. Journal of Dairy Science 2006; 94:2320–2328.
36. Norris M, Johnson WO, Gardner IA. Modeling bivariate longitudinal diagnostic outcome data in the absence of a gold standard. Statistics and Its Interface 2009; 2:171–185.
37. Branscum AJ, Johnson WJ, Baron AT. Robust medical test evaluation using flexible Bayesian semiparametric regression models. Epidemiology Research International 2013; 2013:Article ID 131232.
38. Rodriguez A, Martinez JC. Bayesian semiparametric estimation of covariate-dependent ROC curves. Biostatistics 2014; 2:353–369.
39. Pepe MS. Three approaches to regression analysis of receiver operating characteristic curves for continuous test results. Biometrics 1998; 54:124–135.
40. Rodríguez-Álvarez MX, Tahoces PG, Cadarso-Suárez C, Lado MJ. Comparative study of ROC regression techniques – applications for the computer-aided diagnostic system in breast cancer detection. Computational Statistics and Data Analysis 2011; 55:888–902.
41. Magder LS, Hughes JP. Logistic regression when the outcome is measured with uncertainty. American Journal of Epidemiology 1997; 146:195–203.
42. McInturff P, Johnson WO, Gardner IA, Cowling DW. Bayesian modeling of risk based on outcomes that are subject to error. Statistics in Medicine 2004; 23:1095–1107.
43. Ferguson TS. Prior distributions on spaces of probability measures. Annals of Statistics 1974; 2:615–629.
44. Lavine M. Some aspects of Polya tree distributions for statistical modeling. Annals of Statistics 1992; 20:1222–1235.
45. Lavine M. More aspects of Polya tree distributions for statistical modeling. Annals of Statistics 1994; 22:1161–1176.
46. Hanson TE, Johnson WO. Modeling regression error with a mixture of Polya trees. Journal of the American Statistical Association 2002; 97:1020–1033.
47. Hanson TE. Inferences for mixtures of finite Polya trees. Journal of the American Statistical Association 2006; 101:1548–1565.
48. Christensen R, Johnson W, Branscum A, Hanson TE. Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians. CRC Press: Boca Raton, FL, 2010.
49. Christensen R, Hanson T, Jara A. Parametric nonparametric statistics: an introduction to mixtures of finite Polya trees. The American Statistician 2008; 62:296–306.
50. Jiang W, Tanner MA. On the identifiability of mixtures-of-experts. Neural Networks 1999; 12:197–220.
51. Faraggi D. Adjusting receiver operating characteristic curves and related indices for covariates. The Statistician 2003; 52:179–192.
52. Bedrick EJ, Christensen R, Johnson WO. A new perspective on priors for generalized linear models. Journal of the American Statistical Association 1996; 91:1450–1460.
53. Zhang B, Chen Z, Albert PS. Estimating diagnostic accuracy of raters without a gold standard by exploiting a group of experts. Biometrics 2012; 68:1294–1302.
54. Hanson TE, Branscum AJ, Johnson WJ. Informative g-priors for logistic regression. Bayesian Analysis 2014; 9:597–612.
55. Gelman A, Jakulin A, Pittau MG, Su Y-S. A weakly informative default prior distribution for logistic and other regression models. Annals of Applied Statistics 2008; 2:1360–1383.
56. Geisser S, Eddy W. A predictive approach to model selection. Journal of the American Statistical Association 1979; 74:153–60.
57. Park T, Casella G. The Bayesian lasso. Journal of the American Statistical Association 2008; 103:681–686.
58. Huang A, Xu S, Cai X. Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC Genetics 2013; 14:5.
59. Thurmond MC, Johnson WO, Muñoz-Zanzi C, Su CL, Hietala S. Probability diagnostic assignment for serologic measures, with application to Neospora caninum infection. American Journal of Veterinary Research 2002; 63:318–325.
60. Walker SG, Mallick BK. Hierarchical generalized linear models and frailty models with Bayesian nonparametric mixing. Journal of the Royal Statistical Society, Series B 1997; 59:845–860.
61. Branscum AJ, Hanson TE. Bayesian nonparametric meta-analysis using Polya tree mixture models. Biometrics 2008; 64:825–833.
62. Jara A, Hanson TE, Lesaffre E. Robustifying generalized linear mixed models using a new class of mixtures of multivariate Polya trees. Journal of Computational and Graphical Statistics 2009; 18:838–860.
63. San Martin E, Jara A, Rolin J-M, Mouchart M. On the Bayesian nonparametric generalization of IRT-type models. Psychometrika 2011; 76:385–409.
64. Gonzalez-Manteiga W, Pardo-Fernandez JC, Van Keilegom I. ROC curves in non-parametric location-scale regression models. Scandinavian Journal of Statistics 2011; 38:169–184.