Semiparametric regression modelling with mixtures of Berkson and classical error, with application to fallout from the Nevada Test Site

Summary. We construct Bayesian methods for semiparametric modeling of a monotonic regression func-tion 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 measure-ment 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