Kinship estimation bias carries over to heritability estimation bias using variance components

Heritability is a fundamental parameter of diseases and other traits, quantifying the contribution of genetics to that trait. Kinship matrices are required for heritability estimation with variance components models. However, the most common "standard" kinship estimator employed by Genome-wide Complex Trait Analysis and other approaches, can be severely biased in structured populations. In this study, we characterize two heritability estimation biases in Genome-wide Complex Trait Analysis due to kinship estimation biases under population structure. For the standard ratio-of-means kinship estimator, we derive a closed-form expression for first heritability bias given by the mean kinship and the true heritability. The standard mean-of-ratios estimator, which is the most widely used in practice, exhibits both the bias shared with ratio-of-means and an additional, more severe bias caused by the upweighting of low-frequency variants. Using simulations with admixture and family structures, as well as simulated traits from 1,000 Genomes genotypes, we find that only Popkin-the only unbiased population kinship estimator-produces unbiased heritability estimates in structured settings. Pedigree-only estimates have upward heritability biases when there is population structure. Finally, we analyze three structured datasets with real phenotypes-the San Antonio Family Study, the Hispanic Community Health Study / Study of Latinos, and a multiethnic Nephrotic Syndrome cohort. The standard mean-of-ratios estimator can produce both downward and upward heritability biases depending on population structure and variant frequency spectrum, compared with the other two estimators. Overall, common kinship estimators result in heritability estimation biases when applied to structured populations, a challenge that Popkin successfully overcomes.