In RNA-seq differential expression analysis, investigators aim to detect those genes with changes in expression level across conditions, despite technical and biological variability in the observations. A common task is to accurately estimate the effect size, often in terms of a logarithmic fold change (LFC).
When the read counts are low or highly variable, the maximum likelihood estimates for the LFCs has high variance, leading to large estimates not representative of true differences, and poor ranking of genes by effect size. One approach is to introduce filtering thresholds and pseudocounts to exclude or moderate estimated LFCs. Filtering may result in a loss of genes from the analysis with true differences in expression, while pseudocounts provide a limited solution that must be adapted per dataset.
Researchers from the University of North Carolina-Chapel Hill propose the use of a heavy-tailed Cauchy prior distribution for effect sizes, which avoids the use of filter thresholds or pseudocounts. The proposed method, Approximate Posterior Estimation for GLM, apeglm, has lower bias than previously proposed shrinkage estimators, while still reducing variance for those genes with little information for statistical inference.
Effects of estimating A when counts are very low
On the x-axis is the true value of A across simulations, and on the y-axis is the estimate ˆ A using the method implemented in apeglm . The boxes denote the result of 10 iterations, and the blue dot denotes the true value A . In the Methods, the estimated standard errors are treated as known in order to estimate the scale of a Normal distribution from which the true LFCs may have originated. We simulated n=5 vs 5 Poisson counts, with a baseline rate λ either set to 1, 5, or 10. We then simulated a LFC between the two groups, and 1,000 such “genes” were simulated. The LFC was drawn from a Normal distribution with mean 0 and variance A , with A ∈ [0 . 25 , 0 . 5 , 0 . 75 , 1]. Our estimate ˆ A using the formula proposed by Efron and Morris  assuming known variances had negative bias for λ = 1 (although it roughly tracks the trend), but performed well for λ = 5 or λ = 10, where it only slightly underestimated A .
Availability: The apeglm package is available as an R/Bioconductor package at https://bioconductor.org/packages/apeglm, and the methods can be called from within the DESeq2 software.
Zhu A, Ibrahim JG, Love MI. (2018) Heavy-tailed prior distributions for sequence count data: removing the noise and preserving large differences. Bioinformatics [Epub ahead of print]. [abstract]