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Despite important advances from Genome Wide Association Studies (GWAS), for most complex human traits and diseases, a sizable proportion of genetic variance remains unexplained and prediction accuracy (PA) is usually low. Evidence suggests that PA can be improved using Whole-Genome Regression (WGR) models where phenotypes are regressed on hundreds of thousands of variants simultaneously. The Genomic Best Linear Unbiased Prediction (G-BLUP, a ridge-regression type method) is a commonly used WGR method and has shown good predictive performance when applied to plant and animal breeding populations. However, breeding and human populations differ greatly in a number of factors that can affect the predictive performance of G-BLUP. Using theory, simulations, and real data analysis, we study the performance of G-BLUP when applied to data from related and unrelated human subjects. Under perfect linkage disequilibrium (LD) between markers and QTL, the prediction R-squared (R 2 ) of G-BLUP reaches trait-heritability, asymptotically. However, under imperfect LD between markers and QTL, prediction R 2  based on G-BLUP has a much lower upper bound. We show that the minimum decrease in prediction accuracy caused by imperfect LD between markers and QTL is given by (1− b ) 2 , where  b  is the regression of marker-derived genomic relationships on those realized at causal loci. For pairs of related individuals, due to within-family disequilibrium, the patterns of realized genomic similarity are similar across the genome; therefore  b  is close to one inducing small decrease in R 2 . However, with distantly related individuals  b  reaches very low values imposing a very low upper bound on prediction R 2 . Our simulations suggest that for the analysis of data from unrelated individuals, the asymptotic upper bound on R 2  may be of the order of 20% of the trait heritability. We show how PA can be enhanced with use of variable selection or differential shrinkage of estimates of marker effects.

Prediction of Complex Human Traits Using the Genomic Best Linear Unbiased Predictor