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Equivalence of prospective and retrospective models in the Bayesian analysis of case-control studies

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  • Shaun R. Seaman

Abstract

The natural likelihood to use for a case-control study is a 'retrospective' likelihood, i.e. a likelihood based on the probability of exposure given disease status. Prentice & Pyke (1979) showed that, when a logistic regression form is assumed for the probability of disease given exposure, the maximum likelihood estimators and asymptotic covariance matrix of the log odds ratios obtained from the retrospective likelihood are the same as those obtained from the 'prospective' likelihood, i.e. that based on probability of disease given exposure. We prove a similar result for the posterior distribution of the log odds ratios in a Bayesian analysis. This means that the Bayesian analysis of case-control studies may be done using a relatively simple model, the logistic regression model, which treats data as though generated prospectively and which does not involve nuisance parameters for the exposure distribution. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Shaun R. Seaman, 2004. "Equivalence of prospective and retrospective models in the Bayesian analysis of case-control studies," Biometrika, Biometrika Trust, vol. 91(1), pages 15-25, March.
  • Handle: RePEc:oup:biomet:v:91:y:2004:i:1:p:15-25
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    Cited by:

    1. Shi Li & Bhramar Mukherjee & Stuart Batterman & Malay Ghosh, 2013. "Bayesian Analysis of Time-Series Data under Case-Crossover Designs: Posterior Equivalence and Inference," Biometrics, The International Biometric Society, vol. 69(4), pages 925-936, December.
    2. Mukherjee, Bhramar & Liu, Ivy, 2009. "A note on bias due to fitting prospective multivariate generalized linear models to categorical outcomes ignoring retrospective sampling schemes," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 459-472, March.
    3. Dhiman Bhadra & Michael J. Daniels & Sungduk Kim & Malay Ghosh & Bhramar Mukherjee, 2012. "A Bayesian Semiparametric Approach for Incorporating Longitudinal Information on Exposure History for Inference in Case–Control Studies," Biometrics, The International Biometric Society, vol. 68(2), pages 361-370, June.

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