Bayesian hierarchical estimation of dose response curves

In many applications, there is interest in estimating a collection of related functions. For example, in epidemiology these functions may correspond to dose-response curves for an environmental exposure at different lag times. A typical approach to analyzing such data is to use splines to allow for flexible estimation of dose response curves. However, in lagged data extremely high correlation makes such approaches very unreliable (or impossible). Our focus is on estimating the dose-response effects of chrysotile asbestos exposure during multiple previous times on current mortality. Data come from an occupational cohort study of textile workers in South Carolina. We focus on hierarchical Bayesian methods for incorporating dependence between related dose response curves through an appropriate prior. We propose general classes of priors that induce flexible dependence in random functions. Efficient algorithms are developed for posterior inference. The methods are illustrated using simulations, and an application to the occupational cohort study examining the health effects of asbestos exposure.