An unbiased kinship estimation method for genetic data analysis

Accurate estimate of relatedness is important for genetic data analyses, such as heritability estimation and association mapping based on data collected from genome-wide association studies. Inaccurate relatedness estimates may lead to biased heritability estimations and spurious associations. Individual-level genotype data are often used to estimate kinship coefficient between individuals. The commonly used sample correlation-based genomic relationship matrix (scGRM) method estimates kinship coefficient by calculating the average sample correlation coefficient among all single nucleotide polymorphisms (SNPs), where the observed allele frequencies are used to calculate both the expectations and variances of genotypes. Although this method is widely used, a substantial proportion of estimated kinship coefficients are negative, which are difficult to interpret. In this paper, through mathematical derivation, we show that there indeed exists bias in the estimated kinship coefficient using the scGRM method when the observed allele frequencies are regarded as true frequencies. This leads to negative bias for the average estimate of kinship among all individuals, which explains the estimated negative kinship coefficients. Based on this observation, we propose an unbiased estimation method, UKin, which can reduce kinship estimation bias. We justify our improved method with rigorous mathematical proof. We have conducted simulations as well as two real data analyses to compare UKin with scGRM and three other kinship estimating methods: rGRM, tsGRM, and KING. Our results demonstrate that both bias and root mean square error in kinship coefficient estimation could be reduced by using UKin. We further investigated the performance of UKin, KING, and three GRM-based methods in calculating the SNP-based heritability, and show that UKin can improve estimation accuracy for heritability regardless of the scale of SNP panel.