Why does GCTA work?

This paper, by two of my collaborators, examines the validity of a recently introduced technique called GCTA (Genome-wide Complex Trait Analysis). GCTA allows an estimation of heritability due to common SNPs using relatively small sample sizes (e.g., a few thousand genotype-phenotype pairs). The new method is independent of, but delivers results consistent with, "classical" methods such as twin and adoption studies. To oversimplify, it examines pairs of unrelated individuals and computes the correlation between pairwise phenotype similarity and genotype similarity (relatedness). It has been applied to height, intelligence, and many medical and psychiatric conditions.

When the original GCTA paper (Common SNPs explain a large proportion of the heritability for human height) appeared in Nature Genetics it stimulated quite a lot of attention. But I was always uncertain of the theoretical justification for the technique -- what are the necessary conditions for it to work? What are conservative error estimates for the derived heritability? My impression, from talking to some of the authors, is that they had a mainly empirical view of these questions. The paper below elaborates significantly on the theory behind GCTA.

Conditions for the validity of SNP-based heritability estimation

James J Lee, Carson C Chow
doi: 10.1101/003160

ABSTRACT

The heritability of a trait ($h^2$) is the proportion of its population variance caused by genetic differences, and estimates of this parameter are important for interpreting the results of genome-wide association studies (GWAS). In recent years, researchers have adopted a novel method for estimating a lower bound on heritability directly from GWAS data that uses realized genetic similarities between nominally unrelated individuals. The quantity estimated by this method is purported to be the contribution to heritability that could in principle be recovered from association studies employing the given panel of SNPs ($h^2_\textrm{SNP}$). Thus far the validity of this approach has mostly been tested empirically. Here, we provide a mathematical explication and show that the method should remain a robust means of obtaining $h^2_\textrm{SNP}$ under circumstances wider than those under which it has so far been derived.