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Quadratic Optimization to Identify Highly Heritable Quantitative Traits from Complex Disease Features

Identifying genetic variation underlying a complex disease is important. Many complex diseases have heterogeneous phenotypes and are products of a variety of genetic and environmental factors acting in concert. Deriving highly heritable quantitative traits of a complex disease can improve the identification of genetic risk of the disease. The most sophisticated methods so far perform unsupervised cluster analysis on phenotypic features; and then a quantitative trait is derived based on each resultant cluster. Heritability is estimated to assess the validity of the derived quantitative traits. However, none of these methods explicitly maximize the heritability of the derived traits. We propose a quadratic optimization approach that directly utilizes heritability as an objective during the derivation of quantitative traits of a disease. This method maximizes an objective function that is formulated by decomposing the traditional maximum likelihood method for estimating heritability of a quantitative trait. We demonstrate the effectiveness of the proposed method in finding a trait with high heritability on synthetic data. We also apply our algorithm to identify highly heritable traits of complex human behavior disorders, such as opioid use disorder and cocaine use disorders. Our approach outperforms standard cluster analysis methods to identify highly heritable traits of opioid use and cocaine use.