edgeR

edgeR's core innovation is its use of empirical Bayes shrinkage to estimate gene-specific dispersions. This approach borrows information across all genes to stabilize estimates, particularly for genes with low counts where variability is poorly estimated from data alone.

• Estimates a common dispersion across all genes
• Shrinks gene-wise dispersions toward a weighted likelihood empirical Bayes trend
• Dramatically improves power when biological replicates are limited
• Uses the quantile-adjusted conditional maximum likelihood (qCML) method for single-factor experiments

For simple two-group experimental designs, edgeR provides an exact test based on the negative binomial distribution. This test is analogous to Fisher's exact test but adapted for overdispersed count data.

• Computes exact p-values without asymptotic approximations
• Models the total count sum as an ancillary statistic
• Provides reliable Type I error control even at very small sample sizes
• Suitable for case-vs-control and treated-vs-untreated comparisons

For complex multi-factor experiments, edgeR offers a GLM-based approach that extends its methodology to arbitrary experimental designs. This framework supports additive and interaction models, continuous covariates, and blocking factors.

• Uses likelihood ratio tests or quasi-likelihood F-tests for hypothesis testing
• Handles batch effects and paired designs through the design matrix
• Supports time-course experiments and dose-response studies
• The quasi-likelihood (QL) pipeline adds an extra dispersion parameter to account for gene-specific variability beyond the negative binomial assumption

edgeR introduced the Trimmed Mean of M-values (TMM) normalization, which corrects for compositional biases in RNA-seq libraries. TMM assumes that the majority of genes are not differentially expressed and computes scaling factors accordingly.

• Trims genes with extreme log-fold changes (default 30%)
• Trims genes with extreme absolute expression (default 5%)
• Produces effective library sizes used as offsets in the model
• Robust to the presence of highly differentially expressed genes
• Outperforms simple total-count normalization when library composition varies

edgeR implements intelligent filtering strategies to increase detection power by removing genes that are unlikely to be differentially expressed before multiple testing correction.

• Filter by expression: Remove genes with consistently low counts across all samples
• Filter by count-per-million (CPM): Retain genes with a minimum CPM in a sufficient number of samples
• Reduces the multiple testing burden, increasing the number of discoveries
• Integrates with the Benjamini-Hochberg procedure for FDR control
• Provides functions like filterByExpr() for automated, data-driven filtering

The GLM framework in edgeR enables testing of interaction effects and complex contrasts, allowing researchers to answer nuanced biological questions beyond simple two-group comparisons.

• Test whether treatment effects differ between genotypes (interaction)
• Compare specific condition combinations using contrast matrices
• Perform ANOVA-like tests for multi-level factors
• Extract coefficients and their standard errors for downstream analysis
• Compatible with the limma package's makeContrasts() function for contrast specification

The foundational probability model underlying edgeR's statistical framework. RNA-seq count data exhibits overdispersion, where the variance exceeds the mean due to biological and technical variability. The negative binomial distribution models this by introducing a dispersion parameter that captures the extra-Poisson variation. edgeR estimates this gene-specific dispersion using a quantile-adjusted conditional maximum likelihood method, enabling accurate modeling of count variability.

The default normalization method implemented in edgeR to correct for differences in RNA composition between samples. TMM works by:

• Computing log-fold changes (M-values) and absolute expression levels (A-values) for each gene between a reference and test sample
• Trimming genes with extreme M-values (typically 30%) and extreme A-values (5%)
• Calculating a weighted mean of the remaining M-values to derive a scale factor This robust approach prevents highly differentially expressed genes from skewing normalization.

The original statistical test implemented in edgeR for simple two-group comparisons. Based on the negative binomial distribution, it computes an exact p-value by summing the probabilities of all possible outcomes with likelihoods less than or equal to the observed data under the null hypothesis. While computationally intensive, this test provides accurate p-values even for genes with very low counts, making it suitable for experiments with no biological replicates when a common dispersion is assumed.

The more flexible statistical engine in edgeR for complex experimental designs involving multiple factors, covariates, or time-series data. The GLM approach uses:

• A design matrix to encode the experimental structure
• Log-link function to relate the linear predictor to the expected count
• Likelihood ratio tests or quasi-likelihood F-tests to assess differential expression This framework handles batch effects, paired designs, and multi-group comparisons that the exact test cannot accommodate.

A standard diagnostic visualization for edgeR results that plots the log2 fold change on the x-axis against the -log10 adjusted p-value on the y-axis. This creates a characteristic 'volcano' shape where:

• Points in the upper corners represent genes with both large magnitude changes and high statistical significance
• Horizontal cutoff lines indicate the chosen FDR threshold (e.g., 0.05)
• Vertical cutoff lines mark the biological significance threshold (e.g., |log2FC| > 1) The plot enables rapid identification of top candidate biomarkers.