Genome-wide association studies (GWAS) have been extremely successfully in identifying genetic variants associated with complex traits and diseases in humans [1]. In GWAS, hundreds of thousands or millions of SNPs are tested one by one for statistical evidence of association with a trait, and to avoid false positive discoveries due to the very large number of statistical tests being conducted, usually a very stringent p-value threshold, e.g. 5×10−8, is used to report a significant finding. Therefore, if there are many genes each with a small effect affecting the trait, most of these genetic variants will fail to pass the stringent threshold and remain undetected. This is one of the explanations of the ‘missing heritability’ question, that genetic variants identified from GWAS so far explain a fraction of the heritability for complex traits [2]. We proposed a method, which is able to estimate the total amount of variance explained by all SNPs together without testing the SNPs individually for a quantitative trait [3], and subsequently extended it to the estimation of missing heritability for binary disease data from ascertained case-control studies
