Bayesian models for multiple outcomes nested in domains

We consider the problem of estimating the effect of exposure on multiple continuous outcomes, when the outcomes are measured on different scales and are nested within multiple outcome classes, or "domains." Our Bayesian model extends the linear mixed models approach to allow the exposure effect to differ across domains and across outcomes within domains. Our model can be parameterized to allow shrinkage of the effects within the different levels of nesting, or to allow fixed domain-specific effects with no shrinkage. Our model also allows covariate effects to differ across outcomes and domains. Our methodology is applied to data on prenatal methylmercury exposure and multiple outcomes in four domains measured at 9 years of age on children enrolled in the Seychelles Child Development Study. We use three different priors and found that our main conclusions were not sensitive to the choice of prior. Simulation studies examine the model performance under alternative scenarios. Our results demonstrate that a sizeable increase in power is possible.