Dispersion Estimation Negative Binomial

dispersion-estimation-negative-binomial

Summary

Estimate gene-wise dispersion parameters for negative binomial generalized linear models in RNA-seq count data using DESeq2. This is a foundational step in differential expression analysis that accounts for the mean-variance relationship inherent in RNA-seq data.

When to use

You have raw RNA-seq count data (from HTSeq, featureCounts, Salmon, or similar quantification tools) organized in a count matrix with samples as columns and genes as rows, and you need to test for differential expression between conditions using a negative binomial model. Dispersion estimation is mandatory before statistical inference on fold changes or p-values.

When NOT to use

• Your data are already normalized (e.g., log2-transformed, FPKM, or TPM values); DESeq2 requires raw integer counts.
• You have fewer than ~3 biological replicates per condition; dispersion sharing across genes relies on sufficient sample size to fit a robust trend.
• Your experimental design is purely observational with no clear grouping variable; the design formula requires at least one categorical factor.

Inputs

• count matrix (genes × samples, integer counts)
• sample metadata (colData with condition/factor assignments)
• design formula (e.g., ~condition or ~batch+condition)

Outputs

• DESeqDataSet with estimated gene-wise dispersions (accessible via dispersions() function)
• fitted mean-dispersion trend curve
• per-gene negative binomial GLM coefficients and standard errors

How to apply

Construct a DESeqDataSet object from your count matrix using a design formula that specifies the experimental factors (e.g., ~cell+dex for cell type and treatment effects). Call the DESeq() function, which internally estimates gene-wise dispersions in three stages: (1) compute a per-gene maximum-likelihood estimate, (2) fit a smooth curve (mean-dispersion trend) across all genes to share information, and (3) use the fitted curve as a prior to shrink individual gene estimates toward the trend. The degree of shrinkage is data-driven and stronger for genes with high variance or low counts. This moderated dispersion estimate improves statistical power by borrowing strength across genes while protecting against overfitting.

Related tools

• DESeq2 (Core package that implements dispersion estimation via moderated maximum-likelihood and empirical Bayes shrinkage toward a fitted trend) — https://github.com/thelovelab/DESeq2
• edgeR (Alternative package for negative binomial dispersion estimation (not discussed in this article but a common competitor))

Examples

library(DESeq2); library(airway); data(airway); dds <- DESeqDataSet(airway, design = ~cell+dex); dds <- DESeq(dds); head(dispersions(dds))

Evaluation signals

• Dispersion values should be positive and typically range from 0.01 to 10 for well-behaved RNA-seq data; very large dispersions (>100) suggest outliers or model misspecification.
• The fitted dispersion trend should be smooth and monotonically decreasing as a function of mean normalized count (higher-abundance genes have lower relative variance).
• Genes with similar mean expression should have similar shrunk dispersions due to the trend curve, whereas the per-gene ML estimates may be highly variable.
• Comparison of dispersions before and after shrinkage: shrunk values should be less extreme and more stable than raw ML estimates, especially for low-count genes.
• Post-estimation p-value distributions should be approximately uniform under the null (no differential expression); heavy right-skew suggests under-estimated dispersions.

Limitations

• Dispersion estimation assumes negative binomial distribution; violations (e.g., zero-inflation, spatial correlation in sequencing artifacts) are not modeled.
• The smooth trend is fit using all genes; if a large fraction are truly differentially expressed, the trend may be biased upward.
• Very small sample sizes (<3 replicates per group) lead to unstable trend estimates and poor shrinkage; the article does not formally specify a minimum.
• Outlier samples or genes with extreme counts can distort the trend; pre-filtering of very low-count genes is recommended but not automatic.

Evidence

• [other] The package DESeq2 provides methods to test for differential expression by use of negative binomial generalized linear models: "The package DESeq2 provides methods to test for differential expression by use of negative binomial generalized linear models"
• [other] Run DESeq() to estimate dispersions and fit negative binomial generalized linear models for each gene: "Run DESeq() to estimate dispersions and fit negative binomial generalized linear models for each gene"
• [other] Construct DESeqDataSet from count matrix with design formula: "dds <- DESeqDataSetFromMatrix(countData = cts, colData = coldata, design= ~ batch + condition)"
• [other] the results function automatically performs independent filtering based on the mean of normalized counts for each gene: "the results function automatically performs independent filtering based on the mean of normalized counts for each gene"