Research Article

Data augmentation priors for Bayesian and semi-Bayes analyses of conditional-logistic and proportional-hazards regression

Corresponding Author

Sander Greenland

Department of Epidemiology, UCLA School of Public Health and Department of Statistics, UCLA College of Letters and Science, Los Angeles, CA 90095-1772, U.S.A.

Department of Epidemiology, UCLA School of Public Health, 22333 Swenson Drive, Topanga, CA 90290, U.S.A.Search for more papers by this author

Ronald Christensen,

Ronald Christensen

Department of Statistics, University of New Mexico, Albuquerque, NM 87131, U.S.A.

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Sander Greenland,

Corresponding Author

Sander Greenland

Department of Epidemiology, UCLA School of Public Health and Department of Statistics, UCLA College of Letters and Science, Los Angeles, CA 90095-1772, U.S.A.

Department of Epidemiology, UCLA School of Public Health, 22333 Swenson Drive, Topanga, CA 90290, U.S.A.Search for more papers by this author

Ronald Christensen,

Ronald Christensen

Department of Statistics, University of New Mexico, Albuquerque, NM 87131, U.S.A.

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First published: 10 August 2001

https://doi.org/10.1002/sim.902

Citations: 42

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Abstract

Data augmentation priors have a long history in Bayesian data analysis. Formulae for such priors have been derived for generalized linear models, but their accuracy depends on two approximation steps. This note presents a method for using offsets as well as scaling factors to improve the accuracy of the approximations in logistic regression. This method produces an exceptionally simple form of data augmentation that allows it to be used with any standard package for conditional-logistic or proportional-hazards regression to perform Bayesian and semi-Bayes analyses of matched and survival data. The method is illustrated with an analysis of a matched case-control study of diet and breast cancer. Copyright © 2001 John Wiley & Sons, Ltd.

REFERENCES

1 Good IJ. Good Thinking. University of Minnesota Press: Minneapolis, 1983; 9.
Google Scholar
2 Bedrick EJ, Christensen R, Johnson W. A new perspective on generalized linear models. Journal of the American Statistical Association 1996; 91: 1450–1460.
Web of Science® Google Scholar
3 Bedrick EJ, Christensen R, Johnson W. Bayesian binomial regression: predicting survival at a trauma center. American Statistician 1997; 51: 211–218.
10.2307/2684890
Web of Science® Google Scholar
4 Greenland S. Putting background information about relative risks into conjugate prior distributions. Biometrics 2001; 57 (in press).
10.1111/j.0006-341X.2001.00663.x
PubMed Web of Science® Google Scholar
5 Ursin G, Aragaki CC, Paganini-Hill A, Siemiatycki J, Thompson WD, Haile RW. Oral contraceptives and premenopausal bilateral breast cancer: a case-control study. Epidemiology 1992; 3: 414–419.
10.1097/00001648-199209000-00006
CAS PubMed Web of Science® Google Scholar
6 Witte JS, Greenland S, Haile RW, Bird CL. Hierarchical regression analysis applied to a study of multiple dietary exposures and breast cancer. Epidemiology 1994; 5: 612–621.
10.1097/00001648-199411000-00009
CAS PubMed Web of Science® Google Scholar
7 Greenland S. When should epidemiologic regressions use random coefficients? Biometrics 2000; 56: 915–921.
10.1111/j.0006-341X.2000.00915.x
CAS PubMed Web of Science® Google Scholar
8 Greenland S. A semi-Bayes approach to the analysis of correlated associations, with an application to an occupational cancer-mortality study. Statistics in Medicine 1992; 11: 219–230.
10.1002/sim.4780110208
CAS PubMed Web of Science® Google Scholar
9 Breslow NE, Day NE. Statistical Methods in Cancer Research. Vol. I. The Analysis of Case-Control Studies. IARC: Lyon, 1980.
Google Scholar
10 Cox DR, Hinkley DV. Theoretical Statistics. Chapman and Hall: New York, 1974.
10.1007/978-1-4899-2887-0
Google Scholar
11 Statacorp. Stata Statistical Software Release 5. Stata Press: College Station, TX, 1997.
Google Scholar
12 Prentice RL, Breslow NE. Retrospective studies and failure time models. Biometrika 1978; 65: 153–158.
10.1093/biomet/65.1.153
Web of Science® Google Scholar
13 Greenland S. Methods for epidemiologic analyses of multiple exposures: A review and comparative study of maximum-likelihood, preliminary-testing, and empirical-Bayes regression. Statistics in Medicine 1993; 12: 717–736.
10.1002/sim.4780120802
CAS PubMed Web of Science® Google Scholar
14 Greenland S. Second-stage least squares versus penalized quasi-likelihood for fitting hierarchical models in epidemiologic analyses. Statistics in Medicine 1997; 16: 515–526.
10.1002/(SICI)1097-0258(19970315)16:5<515::AID-SIM425>3.0.CO;2-V
CAS PubMed Web of Science® Google Scholar
15 Witte JS, Greenland S. Simulation study of hierarchical regression. Statistics in Medicine 1996; 15: 1161–1170.
10.1002/(SICI)1097-0258(19960615)15:11<1161::AID-SIM221>3.0.CO;2-7
CAS PubMed Web of Science® Google Scholar
16 Breslow NE, Leroux B, Platt R. Approximate hierarchical modelling of discrete data in epidemiologic research. Statistical Methods in Medical Research 1998; 7: 49–62.
10.1191/096228098675989345
CAS PubMed Google Scholar
17 Leonard T, Hsu JSJ. Bayesian Methods. Cambridge University Press: Cambridge, 1999.
Google Scholar
18 Gelman A, Carlin JB, Stern HA, Rubin DB. Bayesian Data Analysis. Chapman and Hall: New York, 1995.
10.1111/j.1574-6941.2001.tb00841.x
CAS PubMed Web of Science® Google Scholar
19 Carlin BP, Louis TA. Bayes and Empirical-Bayes Data Analysis. Chapman and Hall: New York, 1996.
Google Scholar
20 Greenland S. Probability logic and probabilistic induction. Epidemiology 1998; 9: 322–332.
10.1097/00001648-199805000-00018
CAS PubMed Web of Science® Google Scholar
21 Greenland S. Small-sample bias and corrections for conditional maximum-likelihood odds-ratio estimators. Biostatistics 2000; 1: 113–122.
10.1093/biostatistics/1.1.113
CAS PubMed Google Scholar
22 Rothman KJ. No adjustments for multiple comparisons are needed. Epidemiology 1990; 1: 43–46.
10.1097/00001648-199001000-00010
CAS PubMed Google Scholar
23 Savitz DA, Olshan AF. Multiple comparisons and related issues in the interpretation of epidemiologic data. American Journal of Epidemiology 1995; 142: 904–908.
10.1093/oxfordjournals.aje.a117737
CAS PubMed Web of Science® Google Scholar
24 Greenland S, Robins JM. Empirical-Bayes adjustments for multiple comparisons are sometimes useful. Epidemiology 1991; 1: 43–46.
Google Scholar
25 Poole C. Multiple comparisons? No problem!. Epidemiology 1991; 2: 241–243.
CAS PubMed Google Scholar

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Volume20, Issue16

30 August 2001

Pages 2421-2428

Data augmentation priors for Bayesian and semi-Bayes analyses of conditional-logistic and proportional-hazards regression

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Data augmentation priors for Bayesian and semi-Bayes analyses of conditional-logistic and proportional-hazards regression

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