High heritability does not imply accurate prediction under the small additive effects hypothesis

TL;DR

This paper demonstrates that high heritability estimates do not necessarily lead to accurate predictions in genomic data, especially when the number of SNPs exceeds the sample size, using a machine learning approach.

Contribution

It introduces a predictive method for estimating genomic heritability with ridge regression and derives formulas linking prediction accuracy to sample size and SNP count.

Findings

High heritability does not guarantee prediction accuracy when p>n.

Ridge regression with GCV provides consistent heritability estimates.

Prediction accuracy depends on the ratio n/p, not just heritability.

Abstract

Genome-Wide Association Studies (GWAS) explain only a small fraction of heritability for most complex human phenotypes. Genomic heritability estimates the variance explained by the SNPs on the whole genome using mixed models and accounts for the many small contributions of SNPs in the explanation of a phenotype. This paper approaches heritability from a machine learning perspective, and examines the close link between mixed models and ridge regression. Our contribution is twofold. First, we propose estimating genomic heritability using a predictive approach via ridge regression and Generalized Cross Validation (GCV). We show that this is consistent with classical mixed model based estimation. Second, we derive simple formulae that express prediction accuracy as a function of the ratio n/p, where n is the population size and p the total number of SNPs. These formulae clearly show that a high heritability does not imply an accurate prediction when p>n. Both the estimation of heritability via GCV and the prediction accuracy formulae are validated using simulated data and real data from UK Biobank.