There are also some limitations of the current GPA model. Although extensions to three or more GWAS are straightforward in principle (from four-groups model to -groups model, ), the number of groups will increase exponentially as the number of GWAS increases. This makes many close to zero, resulting in poor parameter estimation (large variance) and thus reduced power. Currently, we suggest doing pairwise-GWAS analysis to explore the genetic relationship of different phenotypes. It is of great interest to develop statistical models to handle the multiple-GWAS case more effectively. Another limitation is that current GPA version can only handle binary annotation. Allowing more annotation structures (e.g., continuous annotation) in GPA is an important extension of current GPA model. We will investigate this issue in the future.
