  The study of expression Quantitative Trait Loci (eQTL) is an important
problem in genomics and biomedicine. While detection (testing) of eQTL
associations has been widely studied, less work has been devoted to the
estimation of eQTL effect size. To reduce false positives, detection methods
frequently rely on linear modeling of rank-based normalized or log-transformed
gene expression data. Unfortunately, these approaches do not correspond to the
simplest model of eQTL action, and thus yield estimates of eQTL association
that can be uninterpretable and inaccurate. In this paper we propose a new,
log-of-linear model for eQTL action, termed ACME, that captures allelic
contributions to cis-acting eQTLs in an additive fashion, yielding effect size
estimates that correspond to a biologically coherent model of cis-eQTLs. We
describe a non-linear least-squares algorithm to fit the model by maximum
likelihood, and obtain corresponding $p$-values. We perform careful
investigation of the model using a combination of simulated data and data from
the Genotype Tissue Expression (GTEx) project. Our results reveal little
evidence for dominance effects, a parsimonious result that accords with a
simple biological model for allele-specific expression and supports use of the
ACME model. We show that Type-I error is well-controlled under our approach in
a realistic setting, so that rank-based normalizations are unnecessary.
Furthermore, we show that such normalizations can be detrimental to power and
estimation accuracy under the proposed model. We then provide summaries of ACME
effect sizes for whole-genome cis-eQTLs in the GTEx data.
