Using summary statistics to evaluate the genetic architecture of multiplicative combinations of initially analyzed phenotypes with a flexible choice of covariates

While the promise of electronic medical record and biobank data is large, major questions remain about patient privacy, computational hurdles, and data access. One promising area of recent development is pre-computing non-individually identifiable summary statistics to be made publicly available for exploration and downstream analysis. In this manuscript we demonstrate how to utilize pre-computed linear association statistics between individual genetic variants and phenotypes to infer genetic relationships between products of phenotypes (e.g., ratios; logical combinations of binary phenotypes using and and or) with customized covariate choices. We propose a method to approximate covariate adjusted linear models for products and logical combinations of phenotypes using only pre-computed summary statistics. We evaluate our methods accuracy through several simulation studies and an application modeling various fatty acid ratios using data from the Framingham Heart Study. These studies show consistent ability to recapitulate analysis results performed on individual level data including maintenance of the Type I error rate, power, and effect size estimates. An implementation of this proposed method is available in the publicly available R package pcsstools.