Estimation in mixed effects model with errors in variables

Estimating the overall fraction of phenotypic variance attributed to high-dimensional predictors measured with error

In prospective genomic studies (e.g., DNA methylation, metagenomics, and transcriptomics), it is crucial to estimate the overall fraction of phenotypic variance (OFPV) attributed to the high-dimensional genomic variables, a concept similar to heritability analyses in genome-wide association studies (GWAS). Unlike genetic variants in GWAS, these genomic variables are typically measured with error due to technical limitation and temporal instability. While the existing methods developed for GWAS can be used, ignoring measurement error may severely underestimate OFPV and mislead the design of future studies. Assuming that measurement error variances are distributed similarly between causal and noncausal variables, we show that the asymptotic attenuation factor equals to the average intraclass correlation coefficients of all genomic variables, which can be estimated based on a pilot study with repeated measurements. We illustrate the method by estimating the contribution of microbiome taxa to body mass index and multiple allergy traits in the American Gut Project. Finally, we show that measurement error does not cause meaningful bias when estimating the correlation of effect sizes for two traits.