Supplementary Material for: Joint Analysis for Integrating Two Related Studies of Different Data Types and Different Study Designs Using Hierarchical Modeling Approaches

<b><i>Background:</i></b> A chronic disease such as asthma is the result of a complex sequence of biological interactions involving multiple genes and pathways in response to a multitude of environmental exposures. However, methods to model jointly all factors are still evolving. Some of the current challenges include how to integrate knowledge from different data types and different disciplines, as well as how to utilize relevant external information such as gene annotation to identify novel disease genes and gene-environment inter-actions. <b><i>Methods:</i></b> Using a Bayesian hierarchical modeling framework, we developed two alternative methods for joint analysis of an epidemiologic study of a disease endpoint and an experimental study of intermediate phenotypes, while incorporating external information. <b><i>Results:</i></b> Our simulation studies demonstrated superior performance of the proposed hierarchical models compared to separate analysis with the standard single-level regression modeling approach. The combined analyses of the Southern California Children's Health Study and challenge study data suggest that these joint analytical methods detected more significant genetic main and gene-environment interaction effects than the conventional analysis. <b><i>Conclusion:</i></b> The proposed prior framework is very flexible and can be generalized for an integrative analysis of diverse sources of relevant biological data.