Estimation of Interpretable eQTL Effect Sizes Using a Log of Linear Model

Expression Quantitative Trait Loci (eQTL) detection is the task of identifying regulatory relationships between genes and genomic loci. Often, this is performed through a multiple testing procedure, where individual tests are based on regression p-values for gene-SNP pairs. Due to the non-Normality of residuals when raw gene expression data is used, normalizing transformations are usually applied to gene expression as a technique for controlling false discoveries. In this paper, however, we show that the most common transformations are uninterpretable in terms of biological eQTL action, or statistically unjustified with respect to real data. We propose a new model called ACME which respects biological understanding of eQTLs and is corroborated by a real data set provided by the Genotype Tissue Expression (GTEx) consortium. We derive a non-linear least-squares algorithm to fit the model and compute p-values. We argue that the use of the ACME model facilitates accurate and interpretable effect size estimation and p-value computation for the individual gene-SNP pairs relevant to current eQTL studies, and provide careful simulation analyses to ensure that Type-I error is controlled in the absence of the harsher normalizing transformations that ACME avoids. Finally, we provide some basic exploratory downstream analyses incorporating ACME-estimated effect sizes to show the model's potential.