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Journal of Statistical Theory and Practice

, Volume 7, Issue 2, pp 233–247 | Cite as

On the Use of Bayesian Model Averaging for Covariate Selection in Epidemiological Modeling

  • Melissa WhitneyEmail author
  • Louise Ryan
  • Jens Walkowiak
Article

Abstract

Bayesian model averaging (BMA) is a powerful technique to address model selection uncertainty and recent computational advances have led to a proliferation of usage. BMA methods are of particular interest in environmental health risk assessment because of the high degree of uncertainty that typically arises in that context. In this article, we review a variety of approaches to conducting BMA and compare four implementations in a setting where there are a number of potential predictors. We then use these four methods to calculate risk assessment measures that account for the uncertainty involved in modeling environmental exposures. These methods are used to reexamine data from a study conducted by Walkowiak et al. (2001) to investigate the effects of maternal polychlorinated biphenyl exposure on cognitive development in early childhood. This case study reveals that different strategies for implementing BMA can yield varying risk assessment results. We conclude with some practical recommendations.

Keywords

Benchmark dose Bayesian information criterion (BIC) Covariate selection Gibbs variable selection (GVS) Model selection Polychlorinated biphenyl (PCB) Reversible jump Markov-chain Monte Carlo (RJ MCMC) Model uncertainty 

AMS Classification

62P 

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References

  1. Bailer, A. J., R. B. Noble, and M. W. Wheeler. 2005. Model uncertainty and risk estimation for experimental studies of quantal responses. Risk Anal., 25, 291–299.CrossRefGoogle Scholar
  2. Budtz-Jorgensen, E., N. Keiding, and P. Grandjean. 2001. Benchmark Dose calculations from epidemiological data. Biometrics, 57, 698–706.MathSciNetCrossRefGoogle Scholar
  3. Caldwell, B. M., and R. H. Bradley. 1985. Home observation for measurement of the environment. New York, NY, Dorsey.Google Scholar
  4. Carlin, B. P., and S. Chib 1995. Bayesian model choice via Markov chain Monte Carlo methods. J. R. Stat. Soc. Ser. B, 57, 473–484.zbMATHGoogle Scholar
  5. Clyde, M. 1999. Discussion of Bayesian model averaging: A tutorial by Hoeting JA, Madigan D, Raftery AE, Volinksy CT. Stat. Sci., 14, 382–417.MathSciNetCrossRefGoogle Scholar
  6. Clyde, M. 2000. Model uncertainty and health effects studies for particulate matter. Environmetrics, 11, 745–763.CrossRefGoogle Scholar
  7. Clyde, M. 2003. Model averaging. In Subjective and objective Bayesian statistics, (ed. J. Press, 320–333. New York, NY, John Wiley and Sons.Google Scholar
  8. Clyde, M., and E. I. George. 2004. Model uncertainty. Stat. Sci., 19, 81–94.MathSciNetCrossRefGoogle Scholar
  9. Crump, K. S. 1984. A new method for determining allowable daily intakes. Fundam. Appl. Toxicol., 4, 854–871.CrossRefGoogle Scholar
  10. Crump, K. S. 1995. Calculation of benchmark doses from continuous data. Risk Anal., 15, 79–89.CrossRefGoogle Scholar
  11. Dellaportas, P., J. Forster, and I. Ntzoufras. 2002. Bayesian model and variable selection using MCMC. Stat. and Computing, 12, 27–36.MathSciNetCrossRefGoogle Scholar
  12. Draper, D. (1995). Assessment and propagation of model uncertainty. J. R. Stat. Soc., Ser. B, 57, 45–97.MathSciNetzbMATHGoogle Scholar
  13. Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin. 2004. Bayesian data analysis, 2nd ed. Boca Raton, FL, Chapman and Hall/CRC.zbMATHGoogle Scholar
  14. George, E. I., and R. E. McCulloch. 1993. Gibbs variable selection via Gibbs sampling. J. Am. Stat. Assoc., 88, 881–889.CrossRefGoogle Scholar
  15. Green, P. J. 1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711–732.MathSciNetCrossRefGoogle Scholar
  16. Hoeting, J. A., D. Madigan, A. E. Raftery, and C. T. Volinsky. 1999. Bayesian model averaging: A tutorial. Stat. Sci., 14, 382–117.MathSciNetCrossRefGoogle Scholar
  17. Hoeting, J., A. E. Raftery, and D. Madigan. 1996. A method for simultaneous variable selection and outlier identification in linear regression. Comput. Stat. Data Anal., 22, 251–270.CrossRefGoogle Scholar
  18. Jacobson, J. L. and S. W. Jacobson. 1996. Intellectual impairment in children exposed to polychlorinated biphenyls in utero. N. Engl. J. Medi., 335, 783–789.CrossRefGoogle Scholar
  19. Kass, R., and A. Raftery. 1995. Bayes factors. J. Am. Stat. Assoc., 90, 773–795.MathSciNetCrossRefGoogle Scholar
  20. Longnecker, M. P., M. S. Wolff, B. C. Gladen, J. W. Brock, P. Grandjean, J. L. Jacobson, S. A. Korrick, W. J. Rogan, N. Weisglas-Kuperus, I. Hertz-Picciotto, P. Ayotte, P. Stewart, G. Winneke, M. J. Charles, S. W. Jacobson, E. Dewailly, E. R. Boersma, L. M. Altshul, B. Heinzow, J. J. Pagano, and A. A. Jensen. 2003. Comparison of polychlorinated biphenyl levels across studies of human neurodevelopment. Environ. Health Perspect., 111, 65–70.CrossRefGoogle Scholar
  21. Lunn, D. J., A. Thomas, N. Best, and D. Spiegelhalter. 2000. WinBUGS—A Bayesian modeling framework: Concepts, structure and extensibility. Stat. and Comput., 10, 325–337.CrossRefGoogle Scholar
  22. Morales, K. H., J. G. Ibrahim, C. Chen, and L. M. Ryan. 2006. Bayesian model averaging with applications to benchmark dose estimation for arsenic in drinking water. J. Am. Stat. Assoc., 101, 9–17.MathSciNetCrossRefGoogle Scholar
  23. Ntzoufras, I. 2002. Gibbs variable selection using BUGS. J. Stat. Software, 7, 1–19.CrossRefGoogle Scholar
  24. Raftery, A. E. 1995. Bayesian model selection in social research. Sociol. Methodol., 25, 111–163.CrossRefGoogle Scholar
  25. Raftery, A. E., D. Madigan, and J. Hoeting. 1997. Bayesian model averaging for linear regression models. J. Am. Stat. Assoc., 92, 179–191.MathSciNetCrossRefGoogle Scholar
  26. Ribas-Fitó, N., M. Sala, M. Kogevinas, and J. Sunyer. 2001. Polychlorinated biphenyls (PCBs) and neurological development in children: A systematic review. J. Epidemiol. Commun. Health, 55, 537–546.CrossRefGoogle Scholar
  27. Schwarz, G. 1978. Estimating the dimension of a model. Ann. Stat., 6, 461–464.MathSciNetCrossRefGoogle Scholar
  28. Vreugdenhil, H. J. I. 2003. Neurodevelopmental effects of prenatal exposure to environmental levels of PCBs and dioxins in children at school age. Rotterdam, The Netherlands, Optima Grafische Communicatie.Google Scholar
  29. Walkowiak, J., J. A. Wiener, A. Fastabend, B. Heinzow, U. Kramer, E. Schmidt, H. J. Steingrueber, S. Wundram, and G. Winneke. 2001. Environmental exposure to polychlorinated biphenyls and quality of the home environment: Effects on psychodevelopment in early childhood. Lancet, 358, 1602–1607.CrossRefGoogle Scholar
  30. Wasserman, L. 2000. Bayesian model selection and model averaging. J. Math. Psychol., 44, 92–107.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  1. 1.Harvard School of Public HealthBostonUSA
  2. 2.University of Technology Sydney and Commonwealth Scientific and Industrial Research OrganizationSydneyAustralia
  3. 3.Heinrich-Heine-UniversitaetDusseldorfGermany

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