Estimation of multiple correlated effects on a disease outcome when the data are nested: a hierarchical Bayesian approach

The paper deals with the analysis of multiple exposures on the occurrence of a disease. We consider observational case-control data in a multilevel setting, with subjects nested in clusters. A hierarchical Bayesian model is proposed to tackle the within-cluster dependence and the correlation among the exposures, simultaneously. To do that, we assign prior distributions on the crucial parameters by exploiting additional information at different levels, as well as reasonable assumptions and previous knowledge. The model is applied to a multi-centric study aiming to investigate the association of dietary exposures with the colon-rectum cancer. Compared with results obtained with conventional regressions, our hierarchical Bayesian model yields great gains in terms of more consistent and less biased estimates