Differential Expression Testing

Differential expression testing operates by attempting to reject the null hypothesis—the assumption that the mean expression of a gene is identical between two groups. In single-cell experiments, this test is performed independently for 20,000+ genes, creating a severe multiple testing problem. Without correction, a p-value threshold of 0.05 would yield ~1,000 false positives per experiment purely by chance.

• Family-Wise Error Rate (FWER) control via Bonferroni correction is often too conservative for exploratory genomics.
• False Discovery Rate (FDR) control, typically using the Benjamini-Hochberg procedure, is the standard approach, accepting a controlled proportion of false positives among all discoveries.

Single-cell expression data is fundamentally count-based and exhibits overdispersion—the variance exceeds the mean, violating Poisson assumptions. Standard models include:

• Negative Binomial (NB) distribution: The workhorse of bulk RNA-seq, modeling counts with a dispersion parameter. Used by DESeq2 and edgeR.
• Zero-Inflated Negative Binomial (ZINB): Extends NB to explicitly model dropout events—zeros caused by technical failure to capture transcripts rather than true absence. Used by MAST and scDD.
• Wilcoxon Rank-Sum test: A non-parametric alternative that makes no distributional assumptions, widely used in single-cell tools like Seurat for its computational speed and robustness to outliers.

A critical statistical pitfall is treating individual cells as independent replicates, a form of pseudoreplication that inflates statistical power and produces spuriously significant results. Cells from the same donor or sample are not independent observations.

• True biological replicates are the independent experimental units (e.g., different patients, animals, or cultures).
• Pseudobulk aggregation sums counts across cells within each sample to create one observation per gene per replicate, then applies bulk RNA-seq tools like DESeq2 or edgeR.
• Mixed-effects models (e.g., muscat, dream) incorporate sample identity as a random effect, modeling within-sample correlation while retaining single-cell resolution.

In high-dimensional single-cell data, statistical significance (p-value) and biological significance (effect size) often diverge. With thousands of cells, even trivially small expression differences can achieve extreme statistical significance.

• Log2 Fold Change (log2FC) quantifies the magnitude of expression difference between groups. A gene with log2FC of 0.1 may be statistically significant but biologically irrelevant.
• Minimum effect size thresholds (e.g., |log2FC| > 0.5 or 1.0) are commonly applied to filter results.
• Percentage of cells expressing the gene in each group (% detected) provides orthogonal evidence that a difference reflects a population-level shift rather than a handful of outlier cells.

Batch effects—systematic technical variation from different experimental runs, sequencing lanes, or sample processing dates—can confound differential expression results if they correlate with the condition of interest. A gene may appear differentially expressed due to batch artifacts rather than biology.

• Diagnostic checks: Principal component analysis colored by batch and condition can reveal confounding before testing.
• Blocking strategies: Including batch as a covariate in the statistical model (e.g., ~ batch + condition in DESeq2) adjusts for additive batch effects.
• Data integration methods like Harmony or scVI remove batch effects prior to testing but must be applied cautiously to avoid removing true biological signal.

Differential expression in single-cell data faces unique statistical challenges absent in bulk RNA-seq:

• Sparsity: Typical scRNA-seq datasets have >90% zeros, driven by both biological absence and technical dropouts, challenging distributional assumptions.
• Zero inflation: The excess of zeros beyond what standard count distributions predict requires specialized models or data imputation.
• Dynamic expression: In trajectory or pseudotime analyses, differential expression is not between discrete groups but along a continuous path, requiring methods like tradeSeq or monocle3's graph-autocorrelation tests.
• Subject-specific variability: In human studies, inter-individual variation often dominates the signal, requiring careful modeling of donor effects.