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, and is particularly challenging when sets of both unrelated individuals and closely related family members are included. 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 two main novel strategies: (i) matrix substitution based on decomposition of a target family-orthogonalized covariance matrix, and (ii) using family-averaged data to obtain loadings. We illustrate the performance via simulations, including resampling from 1000 Genomes Project data, and analysis of a cystic fibrosis dataset. The matrix substitution approach has similar performance to the current standard, but is simple and uses only a genotype covariance matrix, while the family-average method shows superior performance. Our approaches are accompanied by novel ancillary approaches that provide considerable insight, including individual-specific eigenvalue scree plots.