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.