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Leveraging summary statistics to make inferences about complex phenotypes in large biobanks

As genetic sequencing becomes less expensive and data sets linking genetic data and medical records (e.g., Biobanks) become larger and more common, issues of data privacy and computational challenges become more necessary to address in order to realize the benefits of these datasets. One possibility for alleviating these issues is through the use of already-computed summary statistics (e.g., slopes and standard errors from a regression model of a phenotype on a genotype). If groups share summary statistics from their analyses of biobanks, many of the privacy issues and computational challenges concerning the access of these data could be bypassed. In this paper we explore the possibility of using summary statistics from simple linear models of phenotype on genotype in order to make inferences about more complex phenotypes (those that are derived from two or more simple phenotypes). We provide exact formulas for the slope, intercept, and standard error of the slope for linear regressions when combining phenotypes. Derived equations are validated via simulation and tested on a real data set exploring the genetics of fatty acids.