Mixture models in measurement error problems, with reference to epidemiological studies |
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Authors: | Sylvia Richardson Laurent Leblond Isabelle Jaussent Peter J Green |
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Institution: | Imperial College School of Medicine, London, UK; Institut National de la Santéet de la Recherche Médicale, Villejuif, France;and University of Bristol, UK |
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Abstract: | Summary. 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. |
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Keywords: | Bayesian modelling Epidemiological studies Errors in variables Finite mixture distributions Heterogeneity Logistic regression Markov chain Monte Carlo algorithms Misspecification |
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