We conducted comprehensive simulation studies to evaluate GPA performance. The p-values for non-risk SNPs can be simulated easily from a uniform distribution . For risk-SNPs, we can simulate their p-values via different approaches. The most favorable simulation for our GPA model is to simulate them from the Beta distribution. To examine the robustness of our GPA model, we adopted an alternative simulation scheme under the framework of the linear mixed model and liability threshold model that has gained increasing interest recently (e.g., [9], [13]). The detailed procedures will be described later. But we emphasize that there is substantial discrepancy between the generative model used in simulation and the GPA model. The primary purpose of our simulation study is to investigate whether the GPA model can robustly improve the power to detect risk SNPs by integrating multiple GWAS data sets and annotation data despite this discrepancy.
