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Semiparametric Regression Modeling with Mixtures of Berkson and Classical Error, with Application to Fallout from the Nevada Test Site

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Summary.

We construct Bayesian methods for semiparametric modeling of a monotonic regression function when the predictors are measured with classical error, Berkson error, or a mixture of the two. Such methods require a distribution for the unobserved (latent) predictor, a distribution we also model semi-parametrically. Such combinations of semiparametric methods for the dose-response as well as the latent variable distribution have not been considered in the measurement error literature for any form of measurement error. In addition, our methods represent a new approach to those problems where the measurement error combines Berkson and classical components. While the methods are general, we develop them around a specific application, namely, the study of thyroid disease in relation to radiation fallout from the Nevada test site. We use this data to illustrate our methods, which suggest a point estimate (posterior mean) of relative risk at high doses nearly double that of previous analyses but that also suggest much greater uncertainty in the relative risk.
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Keywords: Bayes; Berkson error; Classical error; Dose–response; Latent variables; Likelihood; Measurement error; Pólya trees; Radiation epidemiology; Semiparametric; Thyroid cancer

Document Type: Research Article

Affiliations: 1: Department of Statistics, Texas A&M University, College Station, Texas 77843–3143, U.S.A. 2: SENES Oak Ridge, Center for Risk Analysis, 102 Donner Drive, Oak Ridge, Tennessee 37830, U.S.A.

Publication date: 01 March 2002

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