A non-linear regression method for estimation of gene-environment heritability.

MOTIVATION: Gene-environment (GxE) interactions are one of the least studied aspects of the genetic architecture of human traits and diseases. The environment of an individual is inherently high dimensional, evolves through time and can be expensive and time consuming to measure. The UK Biobank study, with all 500 000 participants having undergone an extensive baseline questionnaire, represents a unique opportunity to assess GxE heritability for many traits and diseases in a well powered setting. RESULTS: We have developed a randomized Haseman-Elston non-linear regression method applicable when many environmental variables have been measured on each individual. The method (GPLEMMA) simultaneously estimates a linear environmental score (ES) and its GxE heritability. We compare the method via simulation to a whole-genome regression approach (LEMMA) for estimating GxE heritability. We show that GPLEMMA is more computationally efficient than LEMMA on large datasets, and produces results highly correlated with those from LEMMA when applied to simulated data and real data from the UK Biobank. AVAILABILITY AND IMPLEMENTATION: Software implementing the GPLEMMA method is available from https://jmarchini.org/gplemma/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Inferring Gene-by-Environment Interactions with a Bayesian Whole-Genome Regression Model.

The contribution of gene-by-environment (GxE) interactions for many human traits and diseases is poorly characterized. We propose a Bayesian whole-genome regression model for joint modeling of main genetic effects and GxE interactions in large-scale datasets, such as the UK Biobank, where many environmental variables have been measured. The method is called LEMMA (Linear Environment Mixed Model Analysis) and estimates a linear combination of environmental variables, called an environmental score (ES), that interacts with genetic markers throughout the genome. The ES provides a readily interpretable way to examine the combined effect of many environmental variables. The ES can be used both to estimate the proportion of phenotypic variance attributable to GxE effects and to test for GxE effects at genetic variants across the genome. GxE effects can induce heteroskedasticity in quantitative traits, and LEMMA accounts for this by using robust standard error estimates when testing for GxE effects. When applied to body mass index, systolic blood pressure, diastolic blood pressure, and pulse pressure in the UK Biobank, we estimate that 9.3%, 3.9%, 1.6%, and 12.5%, respectively, of phenotypic variance is explained by GxE interactions and that low-frequency variants explain most of this variance. We also identify three loci that interact with the estimated environmental scores (-log10p>7.3).