Linear Mixed-Effect Models Through the Lens of Hardy–Weinberg Disequilibrium

For genetic association studies with related individuals, the linear mixed-effect model is the most commonly used method. In this report, we show that contrary to the popular belief, this standard method can be sensitive to departure from Hardy–Weinberg equilibrium (i.e., Hardy–Weinberg disequilibrium) at the causal SNPs in two ways. First, when the trait heritability is treated as a nuisance parameter, although the association test has correct type I error control, the resulting heritability estimate can be biased, often upward, in the presence of Hardy–Weinberg disequilibrium. Second, if the true heritability is used in the linear mixed-effect model, then the corresponding association test can be biased in the presence of Hardy–Weinberg disequilibrium. We provide some analytical insights along with supporting empirical results from simulation and application studies.