  One of the major developments in recent years in the search for missing
heritability of human phenotypes is the adoption of linear mixed-effects models
(LMMs) to estimate heritability due to genetic variants which are not
significantly associated with the phenotype. A variant of the LMM approach has
been adapted to case-control studies and applied to many major diseases by Lee
et al. (2011), successfully accounting for a considerable portion of the
missing heritability. For example, for Crohn's disease their estimated
heritability was 22% compared to 50-60% from family studies. In this letter we
propose to estimate heritability of disease directly by regression of phenotype
similarities on genotype correlations, corrected to account for ascertainment.
We refer to this method as genetic correlation regression (GCR). Using GCR we
estimate the heritability of Crohn's disease at 34% using the same data. We
demonstrate through extensive simulation that our method yields unbiased
heritability estimates, which are consistently higher than LMM estimates.
Moreover, we develop a heuristic correction to LMM estimates, which can be
applied to published LMM results. Applying our heuristic correction increases
the estimated heritability of multiple sclerosis from 30% to 52.6%.
