An unbiased kinship estimation method

Accurate estimate of relatedness is important for genetic data analyses, such asheritability estimation and association mapping based on data collected fromgenome-wide association studies. Inaccurate relatedness estimates may lead tobiased heritability estimations and spurious associations. Individual-level genotypedata are often used to estimate kinship coefficient between individuals. Thecommonly used sample correlation-based genomic relationship matrix (scGRM)method estimates kinship coefficient by calculating the average samplecorrelation coefficient among all single nucleotide polymorphisms (SNPs), wherethe observed allele frequencies are used to calculate both the expectations andvariances of genotypes. Although this method is widely used, a substantialproportion of estimated kinship coefficients are negative, which are difficult tointerpret. In this paper, through mathematical derivation, we show that thereindeed exists bias in the estimated kinship coefficient using the scGRM methodwhen the observed allele frequencies are regarded as true frequencies. This leadsto negative bias for the average estimate of kinship among all individuals, whichexplains the estimated negative kinship coefficients. Based on this observation,we propose an unbiased estimation method, UKin, which can reduce kinshipestimation bias. We justify our improved method with rigorous mathematicalproof. We have conducted simulations as well as two real data analyses tocompare UKin with scGRM and another widely used kinship estimating method:KING. Our results demonstrate that both bias and root mean square error inkinship coefficient estimation could be reduced by using UKin. We furtherinvestigated the performance of UKin, scGRM and KING in calculating theSNP-based heritability, and show that UKin can improve estimation accuracy forheritability regardless of the scale of SNP panel.