Approximate Bayesian logistic regression via penalized likelihood by data augmentation

Stata Journal

Volumn 15, Issue 3, 2015, Pages 712-736

  Discacciati, Andrea ^a   Orsini, Nicola ^a   Greenland, Sander ^b  

^a KAROLINSKA INSTITUTE   (Sweden)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bayesian methods; Data augmentation; Logistic models; Penalized likelihood estimation; penlogit; st0400

Indexed keywords

EID: 85000991995     PISSN: 1536867X     EISSN: 15368734     Source Type: Journal    
DOI: 10.1177/1536867x1501500306     Document Type: Article

References (30)

1. Bedrick, E. J., R. Christensen, and W. Johnson. 1996. A new perspective on priors for generalized linear models. Journal of the American Statistical Association 91: 1450-1460.
2. Brown, B. W., F. M. Spears, and L. B. Levy. 2002. The log F: A distribution for all seasons. Computational Statistics 17: 47-58.
3. Cole, S. R., H. Chu, and S. Greenland. 2014. Maximum likelihood, profile likelihood, and penalized likelihood: A primer. American Journal of Epidemiology 179: 252-260.
4. Cole, S. R., H. Chu, S. Greenland, G. Hamra, and D. B. Richardson. 2012. Bayesian posterior distributions without Markov chains. American Journal of Epidemiology 175: 368-375.
5. Coveney, J. 2008. firthlogit: Stata module to calculate bias reduction in logistic regression. Statistical Software Components S456948, Department of Economics, Boston College. http://econpapers.repec.org/software/bocbocode/s456948.htm.
6. Cox, D. R. 1975. Partial likelihood. Biometrika 62: 269-276.
7. Efron, B. 2012. Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction. New York, NY: Cambridge University Press.
8. Firth, D. 1993. Bias reduction of maximum likelihood estimates. Biometrika 80: 27-38.
9. Greenland, S. 1989. Modeling and variable selection in epidemiologic analysis. American Journal of Public Health 79: 340-349.
10. Greenland, S. 2000. When should epidemiologic regressions use random coefficients? Biometrics 56: 915-921.
11. Greenland, S. 2001. Putting background information about relative risks into conjugate prior distributions. Biometrics 57: 663-670.
12. Greenland, S. 2003. Generalized conjugate priors for Bayesian analysis of risk and survival regressions. Biometrics 59: 92-99.
13. Greenland, S. 2006. Bayesian perspectives for epidemiological research: I. Foundations and basic methods. International Journal of Epidemiology 35: 765-775.
14. Greenland, S. 2007a. Prior data for non-normal priors. Statistics in Medicine 26: 3578-3590.
15. Greenland, S. 2007b. Bayesian perspectives for epidemiological research: II. Regression analysis. International Journal of Epidemiology 36: 195-202.
16. Greenland, S. 2008. Invited commentary: Variable selection versus shrinkage in the control of multiple confounders (with discussion). American Journal of Epidemiology 167: 523-531.
17. Greenland, S. 2009. Relaxation penalties and priors for plausible modeling of nonidentified bias sources. Statistical Science 24: 195-210.
18. Greenland, S., and R. Christensen. 2001. Data augmentation priors for Bayesian and semi-Bayes analyses of conditional-logistic and proportional-hazards regression. Statistics in Medicine 20: 2421-2428.
19. Hastie, T., R. J. Tibshirani, and J. Friedman. 2009. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd ed. New York: Springer.
20. Heinze, G., and M. Schemper. 2002. A solution to the problem of separation in logistic regression. Statistics in Medicine 21: 2409-2419.
21. Higgins, J. P. T., and D. J. Spiegelhalter. 2002. Being sceptical about meta-analyses: A Bayesian perspective on magnesium trials in myocardial infarction. International Journal of Epidemiology 31: 96-104.
22. Jones, M. C. 2004. Families of distributions arising from distributions of order statistics. TEST 13: 1-43.
23. Landaw, E. W., P. F. Sampson, and J. D. Toporek. 1982. Advanced nonlinear regression in BMDP. In Proceedings of the Statistical Computing Section, 228-233. Washington, DC: American Statistical Association.
24. Le Cessie, S., and J. C. van Houwelingen. 1992. Ridge estimators in logistic regression. Journal of the Royal Statistical Society, Series C 41: 191-201.
25. Maldonado, G., and S. Greenland. 1993. Simulation study of confounder-selection strategies. American Journal of Epidemiology 138: 923-936.
26. Neutra, R. R., S. E. Fienberg, S. Greenland, and E. A. Friedman. 1978. Effect of fetal monitoring on neonatal death rates. New England Journal of Medicine 299: 324-326.
27. Royston, P. 2007. Profile likelihood for estimation and confidence intervals. Stata Journal 7: 376-387.
28. Steyerberg, E. W. 2008. Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating. New York: Springer.
29. Sullivan, S. G., and S. Greenland. 2013. Bayesian regression in SAS software. International Journal of Epidemiology 42: 308-317. With Erratum, International Journal of Epidemiology 43: 1667-1668.
30. Sullivan, S. G., and S. Greenland. 2014. Re: Sullivan S. G., Greenland S. Bayesian regression in SAS software. Int J Epidemiol 2013; 42: 308-17. International Journal of Epidemiology 43: 974.