title: Linear mixed model for heritability estimation that explicitly addresses environmental variation.
abstract: The linear mixed model (LMM) is now routinely used to estimate heritability. Unfortunately, as we demonstrate, LMM estimates of heritability can be inflated when using a standard model. To help reduce this inflation, we used a more general LMM with two random effects-one based on genomic variants and one based on easily measured spatial location as a proxy for environmental effects. We investigated this approach with simulated data and with data from a Uganda cohort of 4,778 individuals for 34 phenotypes including anthropometric indices, blood factors, glycemic control, blood pressure, lipid tests, and liver function tests. For the genomic random effect, we used identity-by-descent estimates from accurately phased genome-wide data. For the environmental random effect, we constructed a covariance matrix based on a Gaussian radial basis function. Across the simulated and Ugandan data, narrow-sense heritability estimates were lower using the more general model. Thus, our approach addresses, in part, the issue of "missing heritability" in the sense that much of the heritability previously thought to be missing was fictional. Software is available at https://github.com/MicrosoftGenomics/FaST-LMM.
authors.affiliation: Microsoft Research, Los Angeles, CA 90024; heckerma@microsoft.com.
authors.forename: David
authors.initials: D
authors.lastname: Heckerman
authors.affiliation: Wellcome Trust Sanger Institute, Hinxton CB10 1SA, United Kingdom; Department of Medicine, University of Cambridge, Cambridge CB2 0SP, United Kingdom;
authors.forename: Deepti
authors.initials: D
authors.lastname: Gurdasani
authors.affiliation: Microsoft Research, Redmond, WA 98052;
authors.forename: Carl
authors.initials: C
authors.lastname: Kadie
authors.affiliation: Wellcome Trust Sanger Institute, Hinxton CB10 1SA, United Kingdom; Department of Medicine, University of Cambridge, Cambridge CB2 0SP, United Kingdom;
authors.forename: Cristina
authors.initials: C
authors.lastname: Pomilla
authors.affiliation: Wellcome Trust Sanger Institute, Hinxton CB10 1SA, United Kingdom; Department of Medicine, University of Cambridge, Cambridge CB2 0SP, United Kingdom;
authors.forename: Tommy
authors.initials: T
authors.lastname: Carstensen
authors.affiliation: Wellcome Trust Sanger Institute, Hinxton CB10 1SA, United Kingdom;
authors.forename: Hilary
authors.initials: H
authors.lastname: Martin
authors.affiliation: Wellcome Trust Sanger Institute, Hinxton CB10 1SA, United Kingdom; Department of Medicine, University of Cambridge, Cambridge CB2 0SP, United Kingdom;
authors.forename: Kenneth
authors.initials: K
authors.lastname: Ekoru
authors.affiliation: MRC/UVRI Uganda Research Unit on AIDS, Uganda.
authors.forename: Rebecca N
authors.initials: RN
authors.lastname: Nsubuga
authors.affiliation: MRC/UVRI Uganda Research Unit on AIDS, Uganda.
authors.forename: Gerald
authors.initials: G
authors.lastname: Ssenyomo
authors.affiliation: MRC/UVRI Uganda Research Unit on AIDS, Uganda.
authors.forename: Anatoli
authors.initials: A
authors.lastname: Kamali
authors.affiliation: MRC/UVRI Uganda Research Unit on AIDS, Uganda.
authors.forename: Pontiano
authors.initials: P
authors.lastname: Kaleebu
authors.affiliation: Microsoft Research, Los Angeles, CA 90024;
authors.forename: Christian
authors.initials: C
authors.lastname: Widmer
authors.affiliation: Wellcome Trust Sanger Institute, Hinxton CB10 1SA, United Kingdom; Department of Medicine, University of Cambridge, Cambridge CB2 0SP, United Kingdom;
authors.forename: Manjinder S
authors.initials: MS
authors.lastname: Sandhu
mesh_terms: D004777:Environment; D006801:Humans; D040582:Inheritance Patterns; D016014:Linear Models; D008957:Models, Genetic; D010641:Phenotype
keywords: Gaussian radial basis function; environment; heritability estimation; linear mixed model; model misspecification