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

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The paper focuses on a Bayesian treatment of measurement error problems and on the question of the specification of the prior distribution of the unknown covariates. It presents a flexible semiparametric model for this distribution based on a mixture of normal distributions with an unknown number of components. Implementation of this prior model as part of a full Bayesian analysis of measurement error problems is described in classical set-ups that are encountered in epidemiological studies: logistic regression between unknown covariates and outcome, with a normal or log-normal error model and a validation group. The feasibility of this combined model is tested and its performance 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 the semiparametric maximum likelihood method of Roeder, Carroll and Lindsay. Finally, the methodology is illustrated on a data set on coronary heart disease and cholesterol levels in blood.

Keywords: Bayesian modelling; Epidemiological studies; Errors in variables; Finite mixture distributions; Heterogeneity; Logistic regression; Markov chain Monte Carlo algorithms; Misspecification

Document Type: Research Article


Affiliations: 1: Imperial College School of Medicine, London, UK 2: Institut National de la Santé et de la Recherche Médicale, Villejuif, France 3: University of Bristol, UK

Publication date: 2002-10-01

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