Pervasive Downward Bias in Estimates of Liability-Scale Heritability in Genome-wide Association Study Meta-analysis: A Simple Solution

Background: Single nucleotide polymorphism–based heritability is a fundamental quantity in the genetic analysis of complex traits. For case-control phenotypes, for which the continuous distribution of risk in the population is unobserved, observed-scale heritability estimates must be transformed to the more interpretable liability scale. This article describes how the field standard approach incorrectly performs the liability correction in that it does not appropriately account for variation in the proportion of cases across the cohorts comprising the meta-analysis. We propose a simple solution that incorporates cohort-specific ascertainment using the summation of effective sample sizes across cohorts. This solution is applied at the stage of single nucleotide polymorphism–based heritability estimation and does not require generating updated meta-analytic genome-wide association study summary statistics. Methods: We began by performing a series of simulations to examine the ability of the standard approach and our proposed approach to recapture liability-scale heritability in the population. We went on to examine the differences in estimates obtained from these 2 approaches for real data for 12 major case-control genome-wide association studies of psychiatric and neurologic traits. Results: We found that the field standard approach for performing the liability conversion can downwardly bias estimates by as much as approximately 50% in simulation and approximately 30% in real data. Conclusions: Prior estimates of liability-scale heritability for genome-wide association study meta-analysis may be drastically underestimated. To this end, we strongly recommend using our proposed approach of using the sum of effective sample sizes across contributing cohorts to obtain unbiased estimates