copy-number-copy-ratio-segmentation

name	copy-number-copy-ratio-segmentation
description	Normalize read-depth copy-ratio profiles and segment them into copy-number regions using circular binary segmentation (CBS, DNAcopy), hidden Markov models, HaarSeg, and fused-lasso methods. Covers GC-content, mappability, and replication-timing (wave-artifact) bias correction, panel-of-normals/PCA denoising, diploid-baseline centering, and algorithm selection by sequencing depth and event size. Use when choosing a segmentation algorithm, correcting depth bias, diagnosing oversegmentation or a mis-centered baseline, tuning CBS or HMM parameters, or understanding why a downstream CNV caller produced fragmented or shifted segments.
tool_type	mixed
primary_tool	DNAcopy

Version Compatibility

Reference examples tested with: R 4.3+ with DNAcopy 1.76+, Python 3.10+ with numpy 1.26+, pandas 2.2+; QDNAseq 1.38+ (optional, GC/mappability normalization).

Before using code patterns, verify installed versions match. If versions differ:

• R: packageVersion('DNAcopy') then ?segment to confirm arguments
• Python: pip show numpy pandas

If code throws an error, introspect the installed package and adapt the example. CBS lives in Bioconductor DNAcopy; HMM segmentation is provided by caller-specific backends (CNVkit uses pomegranate; HaarSeg has its own R/Python packages).

Copy-Ratio Segmentation

"Turn noisy per-bin depth into clean copy-number segments" -> Two stages, both error-prone. First, normalize the depth profile so the only remaining variation is copy number (not GC, mappability, or replication timing). Second, partition the normalized profile into segments of constant copy number. The segmentation algorithm choice has a predictable bias signature, and the diploid-baseline choice can invert every call.

• R: DNAcopy::segment (CBS, the reference implementation)
• Python: HMM via pomegranate; HaarSeg via haarseg
• The output feeds every CNV caller (cnvkit-analysis, gatk-cnv, allele-specific-copy-number)

Stage 1: Why Depth Is Biased Before It Is Copy Number

Raw read depth confounds copy number with three systematic biases:

Bias	Cause	Correction
GC content	PCR efficiency and probe hybridization vary with GC	Loess fit of depth vs GC (QDNAseq), or matched normal
Mappability	Multi-mapping reads under-counted in repetitive regions	Mappability track filter/weight; exclude low-mappability bins
Replication timing	Late-replicating DNA is under-represented — the "wave artifact"	Matched normal or PoN; GC correction alone does NOT remove it
Capture efficiency	Per-probe hybridization varies 10-100x (hybrid capture)	Panel of normals — the dominant bias for exomes/panels

The key postdoc-level point: GC correction alone is insufficient. The wave artifact in cancer WGS is driven by replication timing, a biological signal GC normalization cannot flatten. Only a matched normal or a panel of normals removes it. This is why a CNVkit flat reference (GC-only) produces systematic false focal calls and why GATK tangent normalization exists.

Stage 2: Segmentation Algorithm Taxonomy

Algorithm	Model	Strength	Fails when
CBS (circular binary segmentation)	Recursive t-statistic breakpoint test	High precision; excellent on small focal segments	Low depth (~3x): recall drops to ~42% (worse under over-dispersed counts); ~2 orders slower; fragments across assembly gaps
HMM	Hidden CN states, emission + transition	Depth-robust; high recall at low coverage	Less precise on small focal segments (~5 kb: ~76% precision vs CBS ~96%, Poisson model); EM finds only local optima
HaarSeg	Wavelet (Haar) multiscale edge detection	Very fast; good for shallow WGS	Less precise breakpoints than CBS; threshold-sensitive
Fused lasso (flasso)	L1-penalized piecewise-constant fit	Smooth; tunable sparsity	Penalty hard to set; can over-smooth focal events
ASPCF	Allele-specific piecewise-constant fit	Joint logR+BAF segmentation (ASCAT)	Needs BAF; see allele-specific-copy-number

Quantitative benchmark (Zhang et al 2024, Brief Bioinform): the cited precision/recall numbers (CBS ~42% recall at 3x; HMM ~81% recall at 3x; CBS ~96% precision vs HMM ~76% on 5 kb focal segments under a Poisson model) summarise that paper's reported direction of the trade-off. Verify the exact figures against the published tables before quoting them in print; the qualitative trade-off (depth-vs-event-size, CBS-vs-HMM) is robust across recent benchmarks but the precise percentages depend on the simulation model (Poisson vs over-dispersed negative-binomial). There is no universally correct choice.

Decision Tree

Scenario	Algorithm	Rationale
Panel / exome, adequate depth, focal events matter	CBS	Precise on small segments
Shallow WGS (< ~5x), broad events	HMM or HaarSeg	CBS recall degrades at low depth
Heterogeneous / impure tumor	HMM (e.g. CNVkit hmm-tumor)	Broader state transitions absorb noise
Germline, near-diploid	HMM with diploid-tight priors	Priors stabilize calls near CN=2
Allele-specific (need BAF)	ASPCF / FACETS joint CBS	See allele-specific-copy-number
Very large WGS, speed-critical	HaarSeg	Near-linear; CBS is ~100x slower

Bias Correction — GC Loess Normalization

Goal: Remove GC-content bias from a per-bin depth profile.

Approach: Fit a loess curve of depth versus GC content, divide each bin by its fitted value, log2-transform. This corrects GC but not replication timing — use a normal for that.

import numpy as np
import pandas as pd
from statsmodels.nonparametric.smoothers_lowess import lowess

def gc_correct(bins):
    '''GC-correct a per-bin depth profile. bins: columns chrom, start, depth, gc.
    Returns log2 copy ratio relative to the GC-corrected genome median.'''
    df = bins[(bins['depth'] > 0) & bins['gc'].between(0.3, 0.7)].copy()
    fitted = lowess(df['depth'], df['gc'], frac=0.3, return_sorted=False)
    df['corrected'] = df['depth'] / fitted
    df['log2'] = np.log2(df['corrected'] / df['corrected'].median())
    return df

For exomes and panels, a panel of normals (per-bin median of normals, or PCA denoising) is preferred over GC-only correction because it also removes capture and replication-timing bias.

Segmentation — CBS with DNAcopy

Goal: Segment a normalized log2 profile into copy-number regions.

Approach: Build a CNA object, smooth single-bin outliers, run CBS, then merge adjacent segments whose means differ by less than a noise-scaled threshold (sdundo).

library(DNAcopy)

# bins: data frame with chrom, maploc (bin midpoint), log2
cna <- CNA(genomdat = bins$log2, chrom = bins$chrom, maploc = bins$maploc,
           data.type = 'logratio', sampleid = 'tumor')
cna <- smooth.CNA(cna)                          # damp single-bin outliers

# alpha = breakpoint significance; undo.splits='sdundo' merges segments whose means
# are within undo.SD noise standard deviations -- the main guard against oversegmentation.
seg <- segment(cna, alpha = 0.01, undo.splits = 'sdundo', undo.SD = 2,
               verbose = 1)
write.table(seg$output, 'tumor.segments.tsv', sep = '\t',
            quote =  row.names  

Failure Modes

Oversegmentation / hyperfragmentation

Trigger: CBS alpha too liberal, undo.SD too small, or a noisy (high-MAD) profile; FACETS cval too low.

Mechanism: The breakpoint test fires on noise; the profile shatters into many tiny segments that do not correspond to real copy-number changes.

Symptom: Hundreds of short segments; segment count scales with noise, not biology; downstream integer CN incoherent with per-bin medians.

Fix: Raise alpha toward 0.01 or stricter, increase undo.SD (e.g. 2-3), or denoise the input first (better PoN, drop low-coverage bins). Three signatures (Steele 2022) had to be discarded as oversegmentation artifacts — fragmentation propagates into every downstream analysis, including copy-number signatures.

The diploid-baseline centering trap

Trigger: Centering the log2 profile on its median or mode in a hyper-aneuploid or whole-genome-doubled genome.

Mechanism: Centering assumes the commonest log2 value is diploid. In a WGD genome the commonest state is tetraploid; centering on it shifts the whole profile so true diploid regions read as deletions and amplifications read as neutral.

Symptom: Genome-wide gain or loss inconsistent with biology; segmentation is fine but every call has the wrong sign.

Fix: Do not depth-center aneuploid genomes. Anchor the diploid baseline with BAF/SNV data via an allele-specific caller, which estimates absolute ploidy. GISTIC and most callers require a correctly centered seg file as input.

CBS recall degrades at low depth

Trigger: CBS on shallow data (< ~5x WGS, or low-coverage bins).

Mechanism: The two-sample t-statistic loses power when per-bin variance swamps the mean difference; CBS misses real breakpoints (recall ~42% at 3x under a Poisson model, worse under over-dispersed counts), while the segments it does call stay fairly precise.

Symptom: Real events absent from the segmentation; recall poor on a genome with known CNVs.

Fix: Use HMM (depth-robust, ~81% recall at 3x) or HaarSeg for shallow data; or increase bin size to raise per-bin counts before segmenting.

CBS fragments across assembly gaps

Trigger: CBS run over a profile with centromere/telomere gaps not handled as chromosome breaks.

Mechanism: CBS treats gapped data as independent subsets; spurious breakpoints appear at gap edges.

Symptom: Segment boundaries clustered at centromeres; tiny artifactual segments flanking gaps.

Fix: Segment per chromosome arm, or supply gap-aware chromosome coordinates so CBS does not bridge gaps.

HMM EM converges to a local optimum

Trigger: HMM with poor initial parameters or too few iterations.

Mechanism: Baum-Welch EM is not globally optimal; emission/transition parameters can settle in a local optimum, mis-assigning states.

Symptom: Reruns give different state assignments; CN states inconsistent with the visible profile.

Fix: Use informative priors (diploid-centered for germline, broader for tumor), run multiple initializations, and sanity-check state means against the per-bin distribution.

Reconciliation: When Segmentations Disagree

Pattern	Likely cause	Action
CBS shatters where HMM gives clean broad segments	Low depth — CBS over-fits noise	Trust HMM; CBS needs more depth
HMM misses a focal event CBS finds	HMM window resolution too coarse	Trust CBS for focal; HMM blurs small events
Both agree on arms, differ on focal boundaries	Different breakpoint resolution	Arm calls are robust; treat focal boundaries as approximate
Segmentation differs run-to-run	HMM local optima, or unfixed random seed	Fix seeds; use multiple HMM initializations

Operational rule: Match the algorithm to depth and event size — CBS for adequate-depth focal work, HMM/HaarSeg for shallow or broad. Confirm the diploid baseline against an allele-specific ploidy estimate before any sign-dependent interpretation. Report arm-level segments with confidence; treat focal boundaries as algorithm-dependent.

Quantitative Thresholds

Threshold	Value	Source / Rationale
CBS alpha	0.01	DNAcopy default; breakpoint significance
CBS undo.SD	2-3	Merges segments within N noise SD; guards oversegmentation
Depth where CBS recall degrades	< ~5x WGS	Zhang 2024; CBS recall falls sharply (HMM is depth-robust)
GC range kept for loess	0.3-0.7	Extreme-GC bins are unreliable; standard restriction
Bin size, shallow WGS CNV	~500 kb - 1 Mb	Larger bins raise per-bin counts for stable segmentation
Sample MAD usable	< 0.5	Above this, segmentation chases noise regardless of algorithm

Common Errors

Error / symptom	Cause	Solution
Hundreds of tiny segments	Oversegmentation (liberal alpha / low cval / noisy input)	Tighten alpha, raise undo.SD, denoise input
Whole genome wrong-signed	Baseline centered on a non-diploid mode	Anchor ploidy with BAF; do not depth-center aneuploid genomes
Real events missed at low depth	CBS recall degrades	Use HMM/HaarSeg or larger bins
Breakpoints clustered at centromeres	CBS bridging assembly gaps	Segment per arm; supply gap-aware coordinates
Segmentation not reproducible	HMM local optima / unfixed seed	Fix seeds; multiple initializations
Wave artifact remains after GC correction	Replication-timing bias, not GC	Use a matched normal or PoN

References

• Olshen AB et al 2004. Circular binary segmentation for the analysis of array-based DNA copy number data. Biostatistics 5:557
• Venkatraman ES, Olshen AB 2007. A faster circular binary segmentation algorithm. Bioinformatics 23:657
• Zhang Y, Liu W, Duan J 2024. On the core segmentation algorithms of copy number variation detection tools. Brief Bioinform 25:bbae022
• Ben-Yaacov E, Eldar YC 2008. A fast and flexible method for the segmentation of aCGH data (HaarSeg). Bioinformatics 24:i139
• Scheinin I et al 2014. DNA copy number analysis of fresh and FFPE specimens by shallow WGS (QDNAseq). Genome Res 24:2022

Related Skills

• copy-number/cnvkit-analysis - Read-depth caller exposing CBS/HMM/HaarSeg choices
• copy-number/gatk-cnv - Tangent normalization and ModelSegments segmentation
• copy-number/allele-specific-copy-number - ASPCF joint logR+BAF segmentation
• copy-number/recurrent-cnv - Copy-number signatures sensitive to segmentation quality
• copy-number/cnv-visualization - Visual diagnosis of oversegmentation and baseline shift
• genome-intervals/coverage-analysis - Per-bin depth computation upstream of segmentation