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While the individuals chosen for a genome-wide association study (GWAS) maynot be closely related to each other, there can be distant (cryptic)relationships that confound the evidence of disease association. These crypticrelationships violate the GWAS assumption regarding the independence of thesubjects' genomes, and failure to account for these relationships results inboth false positives and false negatives.  This paper presents a method to correct for these cryptic relationships. Weaccurately detect distant relationships using an expectation maximization (EM)algorithm for finding the identity coefficients from genotype data with knowprior knowledge of relationships. From the identity coefficients we compute thekinship coefficients and employ a kinship-corrected association test.  We assess the accuracy of our EM kinship estimation algorithm. We show thaton genomes simulated from a Wright-Fisher pedigree, our method convergesquickly and requires only a relatively small number of sites to be accurate. Wealso demonstrate that our kinship coefficient estimates outperformstate-of-the-art covariance-based approaches and PLINK's kinship estimate.  To assess the kinship-corrected association test, we simulated individualsfrom deep pedigrees and drew one site to recessively determine the diseasestatus. We applied our EM algorithm to estimate the kinship coefficients andran a kinship-adjusted association test. Our approach compares favorably withthe state-of-the-art and far out-performs a na\"ive association test.  We advocate use of our method to detect cryptic relationships and forcorrecting association tests. Not only is our model easy to interpret due tothe use of identity states as latent variables, but also inference providesstate-of-the-art accuracy.

Correcting for Cryptic Relatedness in Genome-Wide Association Studies