Estimating Variance Explained by all DNA Loci in a Genome-Wide Meta-Analysis

Twin and family studies have routinely observed that many psychological traits and disorders are at least moderately heritable (Turkheimer & Gottesman, 1991). Genome-wide studies of single nucleotide polymorphisms (SNPs), however, have had only limited success in finding specific variants associated with psychological outcomes explaining the estimated level of heritability. In response, it has been variously hypothesized that genome-wide studies may lack statistical power to identify the small effects of individual SNPs, that heritability may be a result of other forms of genetic variation, or that twin studies may over-estimate the degree of heritability for common psychological traits (Bohacek, Gapp, Saab, & Mansuy, 2013; Maher, 2008; Park et al., 2010; Zuk, Hechter, Sunyaev, & Lander, 2012). To help investigate these hypotheses, So, Li, and Sham (2011) and others have proposed methods to estimate the proportion of heritability that can be jointly attributed to all SNPs even when there is insufficient power to identify effects for individual variants. The current dissertation expands upon the method of So, Li, and Sham (2011) to provide more flexible and accurate estimates of the proportion of variance in psychological traits that can be explained by observed SNPs. Specifically, it is shown that valid estimates of the proportion of variance explained can be obtained using the results of genome-wide meta-analysis, leveraging the larger sample sizes in meta-analysis to achieve much greater precision in estimating the joint effect of all SNPs. In addition, Monte Carlo p-values are developed to provide hypothesis testing of the estimate of variance explained that accounts for bias and skewness in the null distribution of estimates. Formulas are also derived to allow estimation in genome-wide studies that include covariates with either dichotomous or continuous traits. Simulation studies verify the validity of these procedures, and clearly demonstrate strong statistical power to identify the relative influence of SNPs with small effects that are unlikely to be detected in conventional genome-wide studies. Finally, the developed methods are applied to a genome-wide meta-analysis of self-rated health. Implications of the results for identifying heterogeneity in meta-analyses are discussed, and guidelines are suggested for the minimum sample sizes necessary to estimate the total SNP effect.