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Statistical genetics' main objective is to investigate the heritability of complicated traits. The variance component approaches are favourable when estimating heritability using markers, compared to other previously proposed methods. The best suitable heritability estimator model is frequently ambiguous since data from genome-wide association studies, in which genetic architecture is frequently unknown, have a high degree of dimension. Initially primarily suggested for linkage research, the Haseman-Elston regression is a variance component technique. This study, however, provides a theoretical foundation for a modified HE that models linkage disequilibrium for a quantitative trait and can, thus, be used for GWAS. We applied the IBS-based HE regression to single-marker association studies (scenario I) and evaluated the variance component by employing multiple markers after substituting identical by descent scores with identity by state scores (scenario II). In scenario II, we go over the conditions under which the HE regression and the mixed linear model are similar; the difference between these two approaches is noticeable when an additive variance-covariance component is present. In a follow-up simulation analysis, we discovered that the IBS-based HE regression offered a more accurate heritability estimate than the mixed linear model when we used it to conduct case-control studies.
