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.
Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 6997801, Israel.
Regev
R
Schweiger
Department of Statistics, Tel Aviv University, Tel Aviv 6997801, Israel.
Shachar
S
Kaufman
Zora Biosciences, 02150 Espoo, Finland; School of Medicine, University of Tampere, 33014 Tampere, Finland; Finnish Clinical Biobank Tampere, University Hospital of Tampere, 33521 Tampere, Finland.
Reijo
R
Laaksonen
Fifth Department of Medicine (Nephrology, Hypertensiology, Endocrinology, Diabetology, Rheumatology), Medical Faculty Mannheim, Heidelberg University, Mannheim 68167, Germany.
Marcus E
ME
Kleber
Fifth Department of Medicine (Nephrology, Hypertensiology, Endocrinology, Diabetology, Rheumatology), Medical Faculty Mannheim, Heidelberg University, Mannheim 68167, Germany; Clinical Institute of Medical and Chemical Laboratory Diagnostics, Medical University of Graz, Graz 8036, Austria; Synlab Academy, Synlab Services GmbH, Mannheim 68165, Germany.
Winfried
W
März
Department of Computer Science, University of California, Los Angeles, Los Angeles, CA 90095, USA; Department of Human Genetics, University of California, Los Angeles, Los Angeles, CA 90095, USA.
Eleazar
E
Eskin
Department of Statistics, Tel Aviv University, Tel Aviv 6997801, Israel.
Saharon
S
Rosset
Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 6997801, Israel; Molecular Microbiology and Biotechnology Department, Tel Aviv University, Tel Aviv 6997801, Israel; International Computer Science Institute, 1947 Center Street, Berkeley, CA 94704, USA. Electronic address: heran@post.tau.ac.il.
Eran
E
Halperin
D002318:Cardiovascular Diseases / Q000235:genetics*; D003198:Computer Simulation; D016001:Confidence Intervals; D059647:Gene-Environment Interaction; D055106:Genome-Wide Association Study; D005838:Genotype; D006801:Humans; D008957:Models, Genetic; D015233:Models, Statistical; D020412:Multifactorial Inheritance / Q000235:genetics*; D020641:Polymorphism, Single Nucleotide / Q000235:genetics*; D019655:Quantitative Trait, Heritable