Computation of ancestry scores with mixed families and unrelated   individuals
  The issue of robustness to family relationships in computing genotype ancestry scores such as eigenvector projections has received increased attention in genetic association, as the scores are widely used to control spurious association. We use a motivational example from the North American Cystic Fibrosis (CF) Consortium genetic association study with 3444 individuals and 898 family members to illustrate the challenge of computing ancestry scores when sets of both unrelated individuals and closely-related family members are included. We propose novel methods to obtain ancestry scores and demonstrate that the proposed methods outperform existing methods. The current standard is to compute loadings (left singular vectors) using unrelated individuals and to compute projected scores for remaining family members. However, projected ancestry scores from this approach suffer from shrinkage toward zero. We consider in turn alternate strategies: (i) within-family data orthogonalization, (ii) matrix substitution based on decomposition of a target family-orthogonalized covariance matrix, (iii) covariance-preserving whitening, retaining covariances between unrelated pairs while orthogonalizing family members, and (iv) using family-averaged data to obtain loadings. Except for within-family orthogonalization, our proposed approaches offer similar performance and are superior to the standard approaches. We illustrate the performance via simulation and analysis of the CF dataset. 
Yi-Hui Zhou, J.S. Marron, Fred Wright
stat.ME