Semiparametric regression modeling with mixtures of Berkson and classical error, with application to fallout from the Nevada test site

We construct Bayesian methods for semiparametric modeling of a monotonic regression function when the predictors arc 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 meastuement 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 theta 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 closes nearly double that of previous analyses but that also suggest much greater uncertainty in the relative risk.