Mixture models in measurement error problems, with reference to epidemiological studies


Sylvia Richardson, Laurent Leblond, Isabelle Jaussent (INSERM, Paris) & Peter J. Green (Bristol)
This paper focuses on the question of the specification of the prior distribution of the unknown covariates in Bayesian measurement error problems. We propose a flexible semiparametric model for this distribution based on a mixture of normals with an unknown number of components. Using recent developments in MCMC methodology with variable dimension problems, implementation of this prior as part of a full Bayesian analysis of measurement error problems is described in classical set-ups encountered in epidemiological studies: logistic regression between unknown covariates and outcome, with normal or lognormal error model and a validation group. The performance of the Bayesian model is demonstrated in a simulation study that includes an assessment of the influence of misspecification of the prior distribution of the unknown covariates and a comparison with NPML methods. Finally, the methodology is illustrated on an epidemiological study of bone mass and hip fractures.
Some key words: Bayesian modelling Epidemiological studies, Finite mixture distributions, Heterogeneity, Logistic regression, Measurement error, MCMC algorithms, Sensitivity analysis, Reversible Jump algorithms.}
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