  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.
