Computationally efficient, exact, covariate-adjusted genetic principal component analysis by leveraging individual marker summary statistics from large biobanks

The popularization of biobanks provides an unprecedented amount of genetic and phenotypic information that can be used to research the relationship between genetics and human health. Despite the opportunities these datasets provide, they also pose many problems associated with computational time and costs, data size and transfer, and privacy and security. The publishing of summary statistics from these biobanks, and the use of them in a variety of downstream statistical analyses, alleviates many of these logistical problems. However, major questions remain about how to use summary statistics in all but the simplest downstream applications. Here, we present a novel approach to utilize basic summary statistics (estimates from single marker regressions on single phenotypes) to evaluate more complex phenotypes using multivariate methods. In particular, we present a covariate-adjusted method for conducting principal component analysis (PCA) utilizing only biobank summary statistics. We validate exact formulas for this method, as well as provide a framework of estimation when specific summary statistics are not available, through simulation. We apply our method to a real data set of fatty acid and genomic data.