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Bayesian Methods in Epidemiology

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Handbook of Epidemiology

Abstract

This chapter gives a self-contained introduction to the Bayesian approach to statistical inference. Standard epidemiological problems such as diagnostic tests, the analysis of prevalence, case-control, and cohort data will serve as examples. More advanced topics, such as empirical Bayes methods and Markov chain Monte Carlo techniques, are also covered.

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Notes

  1. 1.

    Odds ω = π ∕ (1 − π) can be back-transformed to probabilities π using π = ω ∕ (1 + ω).

  2. 2.

    Probability statements for continuous random variables X can be obtained through integration of the density function, for example, \(\mathrm{Pr}(a \leq X \leq b) =\int _{ a}^{b}\mathrm{p}(x)dx\).

  3. 3.

    The mathematical symbol ∝ stands for “is proportional to.”

  4. 4.

    The mathematical symbol ∼ stands for “is distributed as.”

References

  • Altham PME (1969) Exact Bayesian analysis of a 2 ×2 contingency table and Fisher’s “exact” significance test. J R Stat Soc B 31:261–269

    Google Scholar 

  • Bayarri MJ, Berger JO (2004) The interplay of Bayesian and frequentist analysis. Stat Sci 19(1):58–80

    Article  Google Scholar 

  • Bayes T (1763) An essay towards solving a problem in the doctrine of chances. Philos Trans R Soc 53:370–418

    Google Scholar 

  • Berger JO, Sellke T (1987) Testing a point null hypothesis: irreconcilability of P values and evidence (with discussion). J Am Stat Assoc 82:112–139

    Google Scholar 

  • Bernardo JM, Smith AFM (1994) Bayesian theory. Wiley, Chichester

    Book  Google Scholar 

  • Besag J, York J, Mollié A (1991) Bayesian image restoration, with two applications in spatial statistics (with discussion). Ann Inst Stat Math 43:1–59

    Article  Google Scholar 

  • Boice JD, Monson RR (1977) Breast cancer in women after repeated fluroscopic examinations of the chest. J Natl Cancer Inst 59:823–832

    PubMed  Google Scholar 

  • Box GEP (1980) Sampling and Bayes’ inference in scientific modelling and robustness (with discussion). J R Stat Soc A 143:383–430

    Article  Google Scholar 

  • Breslow NE (1996) Statistics in epidemiology: the case-control study. In: Armitage P, David HA (eds) Advances in biometry. Wiley, New York, pp 287–318

    Google Scholar 

  • Clayton D, Hills M (1993) Statistical models in epidemiology. Oxford University Press, Oxford

    Google Scholar 

  • Clayton D, Kaldor J (1987) Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics 43:671–681

    Article  CAS  PubMed  Google Scholar 

  • Cornfield J (1951) A method of estimating comparative rates from clinical data. Applications to cancer of the lung, breast, and cervix. J Natl Cancer Inst 11:1269–1275

    CAS  PubMed  Google Scholar 

  • Cornfield J (1966) Sequential trials, sequential analysis and the likelihood principle. Am Stat 20:18–23

    Google Scholar 

  • Cornfield J (1976) Recent methodological contributions to clinical trials. Am J Epidemiol 104:408–421

    CAS  PubMed  Google Scholar 

  • Cox DR (2005) Principles of statistical inference. Cambridge University Press, Cambridge

    Google Scholar 

  • Davison AC (2003) Statistical models. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Edwards W, Lindman H, Savage LJ (1963) Bayesian statistical inference in psychological research. Psychol Rev 70:193–242

    Article  Google Scholar 

  • Fisher RA (1934) Statistical methods for research workers, 3rd edn. Oliver and Boyd, Edinburgh

    Google Scholar 

  • Goodman SN (1999a) Towards evidence-based medical statistics. 1: the P value fallacy. Ann Int Med 130:995–1004

    Article  CAS  PubMed  Google Scholar 

  • Goodman SN (1999b) Towards evidence-based medical statistics. 2: the Bayes factor. Ann Int Med 130:1005–1013

    Article  CAS  PubMed  Google Scholar 

  • Goodman SN (2005) Introduction to Bayesian methods I: measuring the strength of evidence. Clin Trials 2:282–290

    Article  PubMed  Google Scholar 

  • Greenland S (2006) Bayesian perspectives for epidemiological research: I. foundations and basic models. Int J Epidemiol 35:765–775

    Article  PubMed  Google Scholar 

  • Greenland S (2007) Bayesian perspectives for epidemiological research: I. regression analysis. Int J Epidemiol 36:195–202

    Article  PubMed  Google Scholar 

  • Greenland S (2008) Introduction to Bayesian statistics. In: Rothman KJ, Greenland S, Lash TL (eds) Modern epidemiology, 3rd edn. LWW, Philadelphia, pp 328–344

    Google Scholar 

  • Greenland S, Rothman KJ (2008) Introduction to categorical statistics. In: Rothman KJ, Greenland S, Lash TL (eds) Modern epidemiology, 3rd edn. LWW, Philadelphia, pp 238–257

    Google Scholar 

  • Howard JV (1998) The 2 ×2 table: a discussion from the Bayesian viewpoint. Stat Sci 4:351–367

    Google Scholar 

  • Liebermeister C (1877) Über Wahrscheinlichkeitsrechnung in Anwendung auf therapeutische Statistik. Sammlung klinischer Vorträge (Innere Medicin No. 31–64) 110:935–962

    Google Scholar 

  • Mossman D, Berger JO (2001) Intervals for posttest probabilities: a comparison of 5 methods. Med Decis Making 21:498–507

    Article  CAS  PubMed  Google Scholar 

  • Nurminen M, Mutanen P (1987) Exact Bayesian analysis of two proportions. Scand J Stat 14: 67–77

    Google Scholar 

  • O’Hagan A, Buck CE, Daneshkhah A, Eiser JR, Garthwaite PH, Jenkinson DJ, Oakley JE, Rakow T (2006) Uncertain judgements; eliciting experts’ probabilities. Wiley, Chichester

    Book  Google Scholar 

  • Pawitan Y (2001) In all likelihood: statistical modelling and inference using likelihood. Oxford University Press, New York

    Google Scholar 

  • Rothman KJ (2002) Epidemiology; an introduction. Oxford University Press, New York

    Google Scholar 

  • Rue H, Held L (2005) Gaussian Markov random fields: theory and applications. Chapman and Hall, Boca Raton

    Book  Google Scholar 

  • Savitz DA, Wachtel H, Barnes FA, John EM, Tvrdik JG (1988) Case-control study of childhood cancer and exposure to 60-Hz magnetic fields. Am J Epidemiol 128:21–38

    CAS  PubMed  Google Scholar 

  • Sellke T, Bayarri MJ, Berger JO (2001) Calibration of p values for testing precise null hypotheses. Am Stat 55:62–71

    Article  Google Scholar 

  • Seneta E (1994) Carl Liebermeister’s hypergeometric tails. Hist Math 21:453–462

    Article  Google Scholar 

  • Seneta E, Phipps MC (2001) On the comparison of two observed frequencies. Biom J 43:23–43

    Article  Google Scholar 

  • Spiegelhalter DJ, Abrams KR, Myles JP (2004) Bayesian approaches to clinical trials and health-care evaluation. Wiley, New York

    Google Scholar 

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Authors and Affiliations

    Authors
    1. Leonhard Held
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    Editor information

    Editors and Affiliations

    1. Department of Epidemiological Methods and Etiologic Research, Leibniz Institute for Prevention Research and Epidemiology – BIPS, Bremen, Germany

      Wolfgang Ahrens

    2. Department of Biometry and Data Management, Leibniz Institute for Prevention Research and Epidemiology – BIPS, Bremen, Germany

      Iris Pigeot

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    © 2014 Springer Science+Business Media New York

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    Held, L. (2014). Bayesian Methods in Epidemiology. In: Ahrens, W., Pigeot, I. (eds) Handbook of Epidemiology. Springer, New York, NY. https://doi.org/10.1007/978-0-387-09834-0_57

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    • DOI: https://doi.org/10.1007/978-0-387-09834-0_57

    • Publisher Name: Springer, New York, NY

    • Print ISBN: 978-0-387-09833-3

    • Online ISBN: 978-0-387-09834-0

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