Accurate and Efficient Estimation of Local Heritability using Summary Statistics and LD Matrix

Abstract

Existing SNP-heritability estimation methods that leverage GWAS summary statistics produce estimators that are less efficient than the restricted maximum likelihood (REML) estimator using individual-level data under linear mixed models (LMMs). Improving statistical efficiency, i.e., increasing the precision and reducing the variance of a heritability estimator, is particularly important for regional analyses, as local genetic variances tend to be small. We introduce a new estimator for local heritability, "HEELS", which attains comparable statistical efficiency as REML (i.e. relative efficiency greater than 92%) but only requires summary-level statistics -- Z-scores from marginal association tests and the empirical LD. HEELS significantly improves the statistical efficiency of the existing summary-statistics-based heritability estimators, such as GRE and LDSC, by reducing the variance of the heritability estimator by more than 3-fold and 7-fold, for GRE and LDSC respectively. Moreover, HEELS remains statistically unbiased and efficient under model mis-specification. We also introduce a unified framework to evaluate and compare the performance of different LD approximations. We propose representing the empirical LD as the sum of a low-rank matrix and a banded matrix. This approximation not only reduces the storage cost and thus improves the portability of the LD matrix, but also increases the computational efficiency of the HEELS estimation. We demonstrate the statistical efficiency of HEELS and the advantages of our proposed LD approximation strategies both in simulations and through empirical analyses of the UK Biobank data.