A Bias Correction Method for Substructure Estimation with Small Reference Sample Sizes

Reference data are important for accurate estimation of population substructure, yet sufficiently large reference samples are often unavailable for some populations. This limitation is especially important for methods that estimate population substructure from genetic summary data using reference allele frequencies derived from reference samples, such as Summix2. Here, we systematically evaluated how reference sample size for five continental reference groups [African (AFR), East Asian (EAS), European (EUR), Indigenous American (IAM), and South Asian (SAS)] affects Summix2 substructure estimates in simulated Latino-like, African American-like, and Peruvian-like populations, as well as real African American genetic data. We show that small reference sample sizes introduce systematic bias in substructure proportion estimates. We identified a sample size threshold of 150 individuals per reference group for accurate estimates with a mean estimation error below 0.05. We also developed two bias corrections: a simple inverse sample size correction and a flexible power-law correction. The power-law correction provided the greatest reduction in mean estimation error when all reference groups had small reference sample sizes, whereas the simple inverse sample size correction performed better when a single reference group had a small reference sample size. These findings provide practical guidance and bias adjustments for reliable population substructure estimation from genetic summary data, particularly when reference populations have small sample sizes.