Dissecting effects of complex mixtures: who's afraid of informative priors?

Epidemiologic studies commonly investigate multiple correlated exposures, which are difficult to analyze appropriately. Hierarchical modeling provides a promising approach for analyzing such data by adding a higher-level structure or prior model for the exposure effects. This prior model can incorporate additional information on similarities among the correlated exposures and can be parametric, semiparametric, or nonparametric. We discuss the implications of applying these models and argue for their expanded use in epidemiology. While a prior model adds assumptions to the conventional (first-stage) model, all statistical methods (including conventional methods) make strong intrinsic assumptions about the processes that generated the data. One should thus balance prior modeling assumptions against assumptions of validity, and use sensitivity analyses to understand their implications. In doing so - and by directly incorporating into our analyses information from other studies or allied fields - we can improve our ability to distinguish true causes of disease from noise and bias.