Supplementary Material for: Modifiers and Subtype-Specific Analyses in Whole-Genome Association Studies: A Likelihood Framework

<i>Objective:</i> We propose new statistical methods for analyzing genetic case/control association data in which cases can be further classified into subtypes, for example, based on clinical features. The primary utility of our work is the ability to distinguish between subtype-specific and modifier effects of genetic variants within a single testing framework. <i>Methods:</i> A range of disease/subtype causal models are defined for genetic variants involving subtype-specific and modifier effects. We present a log-linear modeling framework enabling comparison between these causal models and selection of the best-fit model. <i>Results:</i> We evaluate and compare the analytic power and model selection performance of the proposed work with standard two-group-based association tests. Simulation studies demonstrate that our approach has similar or greater power than the traditional approach over a range of causal models. We also report empirical findings about the impact of misspecification of subtype frequency during model selection, and extend the application of the proposed work to the cross-disorder association studies of multiple diseases. <i>Conclusion:</i> Whether a variant is a disease risk factor, is subtype specific, or modifies disease features has important consequences for the interpretation and follow-up of genetic associations. Our framework provides a simple, systematic way to evaluate and describe associations involving such subtype-specific or modifier effects.