Premium
Mixture models in measurement error problems, with reference to epidemiological studies
Author(s) -
Richardson Sylvia,
Leblond Laurent,
Jaussent Isabelle,
Green Peter J.
Publication year - 2002
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/1467-985x.00252
Subject(s) - covariate , statistics , bayesian probability , logistic regression , mathematics , econometrics , data set , observational error , bayesian linear regression , computer science , bayesian inference
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.