Bayesian semiparametric mixed effects models for meta‐analysis of the literature data : An application to cadmium toxicity studies

Abstract

We propose Bayesian semiparametric mixed effects models with measurement error to analyze the literature data collected from multiple studies in a meta‐analytic framework. We explore this methodology for risk assessment in cadmium toxicity studies, where the primary objective is to investigate dose‐response relationships between urinary cadmium concentrations and β2‐microglobulin. In the proposed model, a nonlinear association between exposure and response is described by a Gaussian process with shape restrictions, and study‐specific random effects are modeled to have either normal or unknown distributions with Dirichlet process mixture priors. In addition, nonparametric Bayesian measurement error models are incorporated to flexibly account for the uncertainty resulting from the usage of a surrogate measurement of a true exposure. We apply the proposed model to analyze cadmium toxicity data imposing shape constraints along with measurement errors and study‐specific random effects across varying characteristics, such as population gender, age, or ethnicity.