Poisson Statistical Enrichment Testing

poisson-statistical-enrichment-testing

Summary

Applies Poisson statistics to identify genomic regions where ChIP-Seq signal significantly exceeds local background noise, computing q-value scores at single-base-pair resolution to rank peaks by statistical confidence. This is a critical intermediate step in narrow peak calling that converts pileup coverage and local bias estimates into statistical significance measures.

When to use

After extending ChIP sample reads to their predicted fragment length and constructing local lambda bias tracks (incorporating d-scaled, 1 kb, 10 kb, and genome-wide backgrounds). Apply this skill when you have aligned, deduplicated ChIP and control bedGraph pileup tracks and need to identify enriched regions by computing base-pair-level q-values before calling peak boundaries.

When NOT to use

• Input ChIP or control files have not been deduplicated — run macs3 filterdup first
• Fragment length d has not been predicted or estimated — run macs3 predictd on ChIP data
• Local bias track has not been constructed or normalized to account for multiple scales (d, slocal, llocal, genome-wide)

Inputs

• ChIP pileup bedGraph (coverage extended by predicted fragment length d)
• local lambda bedGraph (maximum bias track scaled by ChIP/control ratio)

Outputs

• q-value bedGraph track (one q-value score per base pair)

How to apply

Use macs3 bdgcmp with the -m qpois mode to compare the ChIP pileup coverage track against the scaled local lambda track (representing the expected background signal). This generates a q-value score for each genomic base pair using the Poisson model: q-values are computed as -log10(p-value) where the p-value reflects the probability of observing the ChIP count given the lambda (background) expectation. The local lambda is pre-computed by taking the maximum bias across d/2, 1 kb slocal, 10 kb llocal windows, and genome-wide backgrounds, then scaled by the ChIP-to-control sequencing depth ratio (e.g., 0.99858 in the CTCF example). The resulting bedGraph contains q-value scores suitable for thresholding (e.g., -log10(0.05) ≈ 1.301) in subsequent peak calling.

Related tools

• macs3 bdgcmp (Compares ChIP pileup against local lambda using Poisson model (-m qpois) to generate base-pair-level q-value scores) — https://github.com/macs3-project/MACS
• macs3 pileup (Pre-processing step to generate ChIP coverage track extended by fragment length d) — https://github.com/macs3-project/MACS
• macs3 bdgopt (Pre-processing step to normalize and scale local bias components and construct final lambda track) — https://github.com/macs3-project/MACS

Examples

macs3 bdgcmp -t ChIP_pileup.bedGraph -c local_lambda.bedGraph -m qpois -o qvalue.bedGraph

Evaluation signals

• Output bedGraph contains exactly one q-value score per genomic position; no missing or NaN values in regions of interest
• Q-value distribution shows expected shape: low values (high enrichment) at peak summits, increasing values away from peaks
• Q-value range is compatible with downstream peak calling threshold (e.g., -log10(0.05) ≈ 1.301); verify cutoff is within observed q-value range
• Peaks called from q-value track using macs3 bdgpeakcall match published reference narrowPeak set for the same dataset (e.g., CTCF ENCODE peaks)
• Peaks with high q-values (strong enrichment) overlap known ChIP-binding motifs or published peak annotations; low q-value peaks fail validation

Limitations

• Poisson model assumes read counts follow Poisson distribution; violations (overdispersion) can occur with low-complexity regions or repetitive sequences
• Local lambda computation depends on accurate fragment length prediction (d); errors in d propagate to q-value scoring
• Q-values are sensitive to sequencing depth and the magnitude of the ChIP-to-control scaling ratio; imbalanced library sizes can inflate false positives or negatives
• The method requires deduplicated input; high duplicate rates artificially reduce signal and inflate q-value thresholds

Evidence

• [methods] Compare ChIP and local lambda to get the scores in pvalue or qvalue: "To identify enriched regions and predict peaks, the ChIP signals and local lambda stored in the BEDGRAPH file must be compared using a statistical model"
• [methods] using the bdgcmp module, which outputs a score for each base pair in the genome: "using the bdgcmp module, which outputs a score for each base pair in the genome"
• [methods] Compare ChIP pileup against local lambda using macs3 bdgcmp with -m qpois to generate q-value scores for each base pair.: "Compare ChIP pileup against local lambda using macs3 bdgcmp with -m qpois to generate q-value scores for each base pair."
• [methods] Scale combined background by ChIP-to-control ratio (0.99858) using macs3 bdgopt multiply to create local lambda track.: "Scale combined background by ChIP-to-control ratio (0.99858) using macs3 bdgopt multiply to create local lambda track."
• [methods] By default, the MACS3 callpeak function calculates local bias by considering the maximum bias from the surrounding 1kb, 10kb, the fragment length d, and the whole genome background: "By default, the MACS3 callpeak function calculates local bias by considering the maximum bias from the surrounding 1kb, 10kb, the fragment length d, and the whole genome background"