Abstract
In recent years, a number of literatures published large-scale genome-wide association studies (GWASs) for human diseases or traits while adjusting for other heritable covariate. However, it is known that these GWASs are biased, which may lead to biased genetic estimates or even false positives. In this study, we provide a method called "BTOB" which extends the biased GWAS to bivariate GWAS by integrating the summary association statistics from the biased GWAS and the GWAS for the adjusted heritable covariate. We employ the proposed BTOB method to analyze the summary association statistics from the large scale meta-GWASs for waist-to-hip ratio (WHR) and body mass index (BMI), and show that the proposed approach can help identify more susceptible genes compared with the corresponding univariate GWASs. Theoretical results and simulations also confirm the validity and efficiency of the proposed BTOB method.