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A Bayesian approach to case-control studies with errors in the covariates Vallée, Marc

Abstract

It is not uncommon to be faced with imprecise exposure measurements when dealing with case-control data. In cancer case-control studies, for instance, smoking histories may be unreliable. The usual methods of analysis involve logistic regression with different correction factors. The approach we adopt involves Bayesian fitting of a retrospective discriminant analysis model. The parameters of interest are the regression coefficients in the prospective logodds ratio for disease. Under a standard non-informative prior, the posterior means of these parameters are infinite. Posterior medians, however, perform reasonably relative to other estimators that adjust for covariate imprecision. For models with only continuous exposures, the Bayesian inference can be implemented with exact posterior simulation. The presence of binary covariates requires some elements of a covariance matrix to be fixed. We develop a general approach for sampling such a constrained covariance matrix. The Bayesian inference in this context now demands the use of a Gibbs sampling algorithm.

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