Bayesian methods for highly correlated exposure data

Studies that include individuals with multiple highly correlated exposures are common in epidemiology. Because standard maximum likelihood techniques often fail to converge in such instances, hierarchical regression methods have seen increasing use. Bayesian hierarchical regression places prior distributions on exposure-specific regression coefficients to stabilize estimation and incorporate prior knowledge, if available. A common parametric approach in epidemiology is to treat the prior mean and variance as fixed constants. An alternative parametric approach is to place distributions on the prior mean and variance to allow the data to help inform their values. As a more flexible semiparametric option, one can place an unknown distribution on the coefficients that simultaneously clusters exposures into groups using a Dirichlet process prior. We also present a semiparametric model with a variable-selection prior to allow clustering of coefficients at 0. We compare these 4 hierarchical regression methods and demonstrate their application in an example estimating the association of herbicides with retinal degeneration among wives of pesticide applicators.