Estimation of genetic heritabilities of human traits in case-control studies.

It is of great interest to detect missing heritability for human complex traits. Additive genetic effects (ADD), maternal genetic effects (MGE), and parent-of-origin effects (POE) play important roles in genetic mechanisms. Methods have been developed in the literature to analyze heritabilities due to ADD, POE, and MGE separately but not simultaneously. In this paper, a new model termed APM is proposed based on mother-child duos genetic data, which orthogonally decomposes heritabilities due to ADD, POE, and MGE. This orthogonal decomposition is biologically interpretable since it ideally characterizes independent contributions due to the three effects. We focus on case-control data that are widely adopted in genetics studies and develop a novel method R-PCGC by adjusting estimation biases due to sampling bias in case-control studies and imposing nonnegative constraints on the heritability estimates. Large sample properties such as consistency and asymptotic normality are established for R-PCGC. The desired properties of R-PCGC (i.e., asymptotic unbiasedness and nonnegativity) are confirmed through simulations. Finally, R-PCGC regression is applied to a case-control study of preterm births from the Danish National Birth Cohort (DNBC).