Fast and Accurate Construction of Confidence Intervals for Heritability.

Estimation of heritability is fundamental in genetic studies. Recently, heritability estimation using linear mixed models (LMMs) has gained popularity because these estimates can be obtained from unrelated individuals collected in genome-wide association studies. Typically, heritability estimation under LMMs uses the restricted maximum likelihood (REML) approach. Existing methods for the construction of confidence intervals and estimators of SEs for REML rely on asymptotic properties. However, these assumptions are often violated because of the bounded parameter space, statistical dependencies, and limited sample size, leading to biased estimates and inflated or deflated confidence intervals. Here, we show that the estimation of confidence intervals by state-of-the-art methods is inaccurate, especially when the true heritability is relatively low or relatively high. We further show that these inaccuracies occur in datasets including thousands of individuals. Such biases are present, for example, in estimates of heritability of gene expression in the Genotype-Tissue Expression project and of lipid profiles in the Ludwigshafen Risk and Cardiovascular Health study. We also show that often the probability that the genetic component is estimated as 0 is high even when the true heritability is bounded away from 0, emphasizing the need for accurate confidence intervals. We propose a computationally efficient method, ALBI (accurate LMM-based heritability bootstrap confidence intervals), for estimating the distribution of the heritability estimator and for constructing accurate confidence intervals. Our method can be used as an add-on to existing methods for estimating heritability and variance components, such as GCTA, FaST-LMM, GEMMA, or EMMAX.

Exploiting population samples to enhance genome-wide association studies of disease.

It is widely acknowledged that genome-wide association studies (GWAS) of complex human disease fail to explain a large portion of heritability, primarily due to lack of statistical power-a problem that is exacerbated when seeking detection of interactions of multiple genomic loci. An untapped source of information that is already widely available, and that is expected to grow in coming years, is population samples. Such samples contain genetic marker data for additional individuals, but not their relevant phenotypes. In this article we develop a highly efficient testing framework based on a constrained maximum-likelihood estimate in a case-control-population setting. We leverage the available population data and optional modeling assumptions, such as Hardy-Weinberg equilibrium (HWE) in the population and linkage equilibrium (LE) between distal loci, to substantially improve power of association and interaction tests. We demonstrate, via simulation and application to actual GWAS data sets, that our approach is substantially more powerful and robust than standard testing approaches that ignore or make naive use of the population sample. We report several novel and credible pairwise interactions, in bipolar disorder, coronary artery disease, Crohn's disease, and rheumatoid arthritis.