HEDE: Heritability estimation in high dimensions by ensembling debiased estimators in genome-wide association studies

Abstract

Estimating heritability using a large number of SNPs in Genome-Wide Association Studies (GWAS) is of substantial interest. Various approaches have emerged over the years, broadly categorized as either random effects or fixed effects heritability methods. These methods are sensitive to their assumptions on the underlying signal structure. We propose a robust fixed effect-based ensemble approach to estimate heritability or the signal-to-noise ratio in high-dimensional linear models where the sample size and dimension grow proportionally. Our method ensembles post-processed versions of the debiased lasso and debiased ridge estimators, and incorporates a data-driven strategy for hyperparameter selection that significantly boosts estimation performance. We establish rigorous consistency guarantees that hold despite adaptive tuning. Extensive simulations demonstrate our method’s superiority over state-of-the-art methods across various signal structures and genetic architectures, ranging from sparse to relatively dense and from evenly to unevenly distributed signals. Furthermore, we discuss advantages of fixed effects heritability estimation compared to random effects estimation. Our theoretical guarantees hold for realistic distributions observed in genetic studies, where genotypes typically take on discrete values and are often well modeled by sub-Gaussian random variables. We establish our theoretical results by deriving uniform bounds, built upon the convex Gaussian min-max theorem, and leveraging universality results. Finally, we showcase the efficacy of our approach in estimating height and BMI heritability using the GWAS data from the UK Biobank.