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

Sylvia Richardson, Laurent Leblond, Isabelle Jaussent and Peter J. Green

Journal of the Royal Statistical Society Series A, 2002, vol. 165, issue 3, 549-566

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.

Date: 2002
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