Correcting statistical bias in correlation-based kinship estimators

Accurate estimate of relatedness is important for genetic data analyses, such as association mapping and heritability estimation based on data collected from genome-wide association studies. Inaccurate relatedness estimates may lead to spurious associations and biased heritability estimations. 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 the bias. We justify our improved method with rigorous mathematical proof. We have conducted simulations as well as two real data analyses to demonstrate that both bias and root mean square error in kinship coefficient estimation can be reduced by using UKin. Further simulations indicate that the power in association mapping can also be improved by using our unbiased kinship estimates to adjust for cryptic relatedness. Author summaryInference of relatedness plays an important role in genetic data analysis. Many methods have been proposed to estimate kinship coefficients, including the commonly used genomic relationship matrix method. However, a substantial proportion of the kinship coefficients estimated by this method are negative, which is difficult to interpret. In this paper, through mathematical derivation, we show that there indeed exists a negative bias in this approach. To correct for this bias, we propose a new kinship coefficient estimation method, UKin, which is unbiased without requiring extra genetic information nor added computational complexity. The better performance of UKin in reducing bias and root mean squared error is demonstrated through theory, simulations and analysis of data from the young-onset breast cancer and familial intracranial aneurysm studies.