Linear mixed models (LMM) are widely used to estimate narrow sense heritability explained by tagged single-nucleotide polymorphisms (SNPs). However, those estimates are valid only if large sample sizes are used. We propose a Bayesian covariance component model (BCCM) that takes into account the genetic correlation among phenotypes and genetic correlation among individuals. The use of the BCCM allows us to circumvent issues related to small sample sizes, including overfitting and boundary estimates. Using expression of genes in breast cancer pathway, obtained from the Multiple Tissue Human Expression Resource (MuTHER) project, we demonstrate a significant improvement in the accuracy of SNP-based heritability estimates over univariate and likelihood-based methods. According to the BCCM, except CHURC1 (h2 = 0.27, credible interval = (0.2, 0.36)), all tested genes have trivial heritability estimates, thus explaining why recent progress in their eQTL identification has been limited.
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