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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