Objective Bayesian model selection for Cox regression

Statistics in Medicine

Volumn 35, Issue 29, 2016, Pages 5376-5390

  Held, Leonhard ^a   Gravestock, Isaac ^a   Sabanés Bové, Daniel ^b  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b F HOFFMANN LA ROCHE LTD   (Switzerland)

Author keywords

Bayes factor; clinical prediction; Cox model; g prior; model selection

Indexed keywords

ARTICLE; BAYES THEOREM; CALIBRATION; CARDIOVASCULAR DISEASE; COHORT ANALYSIS; INTERMETHOD COMPARISON; METHODOLOGY; PREDICTION; PRIMARY BILIARY CIRRHOSIS; PROCESS OPTIMIZATION; STATISTICAL MODEL; SURVIVAL; HUMAN; PROPORTIONAL HAZARDS MODEL;

BAYES THEOREM; COHORT STUDIES; HUMANS; LINEAR MODELS; PROPORTIONAL HAZARDS MODELS; RESEARCH DESIGN;

EID: 84984706616     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.7089     Document Type: Article

References (65)

1. Steyerberg E. Clinical Prediction Models. Springer: New York, 2009.
2. van Houwelingen HC, Putter H. Dynamic Prediction in Clinical Survival Analysis, Monographs on Statistics and Applied Probability, Vol. 123. Chapman and Hall/CRC: Boca Raton, 2012.
3. Berger JO, Pericchi LR. Objective Bayesian methods for model selection: introduction and comparison. In Model selection, IMS Lecture Notes, Lahiri P (ed.)., vol. 38. Institute of Mathematical Statistics: Beachwood, OH 2001; 135–207.
4. Barbieri MM, Berger JO. Optimal predictive model selection. Annals of Statistics 2004; 32(3):870–897.
5. Hoeting JA, Madigan D, Raftery AE, Volinsky CT. Bayesian model averaging: a tutorial. Statistical Science 1999; 14(4):382–417. With comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors.
6. Kass RE, Raftery AE. Bayes factors. Journal of the American Statistical Association 1995; 90(430):773–795.
7. Scott JG, Berger JO. Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem. Annals of Statistics 2010; 38(5):2587–2619.
8. O'Hagan A. Fractional Bayes factors for model comparison. Journal of the Royal Statistical Society. Series B (Methodological) 1995; 57(1):99–138.
9. Berger JO, Pericchi LR. The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association 1996; 91(433):109–122.
10. Bayarri MJ, Berger JO. The interplay of Bayesian and frequentist analysis. Statistical Science 2004; 19(1):58–80.
11. Copas JB. Regression, prediction and shrinkage. Journal of the Royal Statistical Society. Series B (Methodological) 1983; 45(3):311–354.
12. van Houwelingen JC, Le Cessie S. Predictive value of statistical models. Statistics in Medicine 1990; 9(11):1303–1325.
13. Copas JB. Using regression models for prediction: shrinkage and regression to the mean. Statistical Methods in Medical Research 1997; 6(2):167–183.
14. Liang F, Paulo R, Molina G, Clyde MA, Berger JO. Mixtures of g priors for Bayesian variable selection. Journal of the American Statistical Association 2008; 103(481):410–423.
15. Bayarri MJ, Berger JO, Forte A, García-Donato G. Criteria for Bayesian model choice with application to variable selection. Annals of Statistics 2012; 40(3):1550–1577.
16. George EI, Foster DP. Calibration and empirical Bayes variable selection. Biometrika 2000; 87(4):731–747.
17. Cui W, George EI. Empirical Bayes vs. fully Bayes variable selection. Journal of Statistical Planning and Inference 2008; 138(4):888–900.
18. Zellner A, Siow A. Posterior odds ratios for selected regression hypotheses. In Bayesian Statistics: Proceedings of the First International Meeting Held in Valencia, Bernardo JM, DeGroot MH, Lindley DV, Smith AFM (eds). University of Valencia Press: Valencia 1980; 585–603.
19. Sabanés Bové D, Held L. Hyper-g priors for generalized linear models. Bayesian Analysis 2011; 6(3):387–410.
20. Johnson VE. Bayes factors based on test statistics. Journal of the Royal Statistical Society. Series B (Methodological) 2005; 67(5):689–701.
21. Held L, Sabanés Bové D, Gravestock I. Approximate Bayesian model selection with the deviance statistic. Statistical Science 2015; 30:242–257.
22. Johnson VE. Properties of Bayes factors based on test statistics. Scandinavian Journal of Statistics 2008; 35(2):354–368.
23. Li Y, Clyde MA. Mixtures of g-priors in generalized linear models. Technical Report, 2015 Clemson University, USA. http://arxiv.org/abs/1503.06913.
24. Hu J, Johnson VE. Bayesian model selection using test statistics. Journal of the Royal Statistical Society. Series B (Methodological) 2009; 71(1):143–158.
25. Kass RE, Wasserman L. A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. Journal of the American Statistical Association 1995; 90(431):928–934.
26. Akaike H. Information measures and model selection. Bulletin of the International Statistical Institute 1983; 50:277–290.
27. Buckland ST, Burnham KP, Augustin NH. Model selection: an integral part of inference. Biometrics 1997; 53(2):603–618.
28. Volinsky CT, Madigan D, Raftery AE, Kronmal RA. Bayesian model averaging in proportional hazard models: assessing the risk of a stroke. Journal of the Royal Statistical Society. Series C (Applied Statistics) 1997; 46(4):433–448.
29. Newcombe P, Raza Ali H, Blows F, Provenzano E, Pharoah P, Caldas C, Richardson S. Weibull regression with Bayesian variable selection to identify prognostic tumour markers of breast cancer survival. Statistical Methods in Medical Research 2014. DOI: 10.1177/0962280214548748 [Epub ahead of print].
30. Volinsky CT, Raftery AE. Bayesian information criterion for censored survival models. Biometrics 2000; 56(1):256–262.
31. Aitkin M, Clayton D. The fitting of exponential, weibull and extreme value distributions to complex censored survival data using GLIM. Journal of the Royal Statistical Society. Series C (Applied Statistics) 1980; 29(2):156–163.
32. Holford TR. The analysis of rates and of survivorship using log-linear models. Biometrics 1980; 36(2):299–305.
33. Sabanés Bové D, Held L. Comment on Cai and Betensky (2003), on the Poisson approximation for hazard regression. Biometrics 2013; 69:795.
34. Cox DR. Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological) 1972; 34(2):187–220.
35. Cox DR. Partial likelihood. Biometrika 1975; 62(2):269–276.
36. Clayton D, Hills M. Statistical Models in Epidemiology. Oxford University Press: Oxford, 1993.
37. Collett D. Modelling Survival Data in Medical Research 3rd edn. Chapman & Hall/CRC: Boca Raton, 2014.
38. Murphy SA, van der Vaart AW. On profile likelihood. Journal of the American Statistical Association 2000; 95(450):449–465.
39. Davidson RR, Lever WE. The limiting distribution of the likelihood ratio statistic under a class of local alternatives. Sankhya: The Indian Journal of Statistics, Series A 1970; 32(2):209–224.
40. Banerjee M. Likelihood ratio tests under local alternatives in regular semiparametric models. Statistica Sinica 2005; 15(3):635–644.
41. Begun JM, Hall WJ, Huang WM, Wellner JA. Information and asymptotic efficiency in parametric-nonparametric models. The Annals of Statistics 1983; 11(2):432–452.
42. van Houwelingen JC. Validation, calibration, revision and combination of prognostic survival models. Statistics in Medicine 2000; 19(24):3401–3415.
43. Therneau TM, Grambsch PM. Modeling Survival Data: Extending the Cox Model. Springer: New York, 2000.
44. Leng C, Zhang HH. Model selection in nonparametric hazard regression. Journal of Nonparametric Statistics 2006 2007; 18(7-8):417–429.
45. Lin Y, Zhang HH. Component selection and smoothing in multivariate nonparametric regression. The Annals of Statistics 2006; 34(5):2272–2297.
46. Lin CY, Halabi S. On model specification and selection of the Cox proportional hazards model. Statistics in Medicine 2013; 32(26):4609–4623.
47. Geisser S. On prior distributions for binary trials. The American Statistician 1984; 38(4):244–247.
48. Sabanés Bové D, Held L. Bayesian fractional polynomials. Statistics and Computing 2011; 21(3):309–324.
49. Box G. EP, Tidwell PW. Transformation of the independent variables. Technometrics 1962; 4(4):531–550.
50. Royston P, Altman DG. Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling. Journal of the Royal Statistical Society. Series C (Applied Statistics) 1994; 43(3):429–467.
51. Gerds TA, Cai T, Schumacher M. The performance of risk prediction models. Biometrical Journal 2008; 50(4):457–479.
52. Graf E, Schmoor C, Sauerbrei W, Schumacher M. Assessment and comparison of prognostic classification schemes for survival data. Statistics in Medicine 1999; 18:2529–2545.
53. Gerds TA, Schumacher M. Consistent estimation of the expected Brier score in general survival models with right-censored event times. Biometrical Journal 2006; 48(6):1029–1040.
54. Tibshirani R. The Lasso method for variable selection in the Cox model. Statistics in Medicine 1997; 16(4):385–395.
55. Yuan M, Lin Y. Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society. Series B. Statistical Methodology 2006; 68(1):49–67.
56. van Houwelingen JC. Dynamic prediction by landmarking in event history analysis. Scandinavian Journal of Statistics 2007; 34:70–85.
57. Sabanés Bové D, Held L, Kauermann G. Mixtures of g-priors for generalised additive model selection with penalised splines. Journal of Computational and Graphical Statistics 2015; 24:394–415.
58. Cohen A. Dummy variables in stepwise regression. The American Statistician 1991; 45(5):226–228.
59. Tibshirani R. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B 1996; 58(1):267–288.
60. Zou H, Hastie T. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society. Series B. Statistical Methodology 2005; 67(2):301–320.
61. Meier L, van de Geer S, Bühlmann P. The group Lasso for logistic regression. Journal of the Royal Statistical Society. Series B (Methodological) 2008; 70:53–71.
62. 1 penalized estimation in the Cox proportional hazards model. Biometrical Journal 2010; 52(1):70–84.
63. Zhang HH, Lu W. Adaptive Lasso for Cox's proportional hazards model. Biometrika 2007; 94(3):691–703.
64. Wang H, Leng C. A note on adaptive group Lasso. Computational Statistics & Data Analysis 2008; 52(12):5277–5286.
65. Heinze G, Schemper M. A solution to the problem of monotone likelihood in Cox regression. Biometrics 2001; 57(1):114–119.