bio-analytical-validation

What this skill does

## Version Compatibility

Reference examples tested with: numpy 1.26+, scipy 1.12+, statsmodels 0.14+

Before using code patterns, verify installed versions match. If versions differ:
- Python: `pip show <package>` then `help(module.function)` to check signatures

If code throws ImportError, AttributeError, or TypeError, introspect the installed
package and adapt the example to match the actual API rather than retrying.

# Analytical Validation and Detection Limits

**"What is the real limit of detection of my ctDNA assay, and can I trust the number I am about to report?"** -> Quantify the Poisson sampling ceiling, the error-suppression floor, and the LoB/LoD/LoQ that together define a defensible sensitivity claim.
- Python: `scipy.stats.poisson` for detection-probability math, `scipy.stats.norm` for CLSI LoB/LoD, `statsmodels` Probit/Logit for a dilution-series LoD95 fit.

## The Single Most Important Modern Insight -- LoD Is Set by Genome Equivalents Sampled and Error Suppression, NOT by Sequencing Depth or the Caller

A ctDNA assay is a molecule-counting experiment at the Poisson edge. The mutant signal is a fixed, tiny number of physical template molecules in the tube, and the limit of detection is governed by two ceilings: how many genome equivalents were sampled (Poisson), and how low the background error floor was driven (error suppression). 1 ng of human DNA is ~330 haploid genome equivalents; the expected mutant-molecule count is lambda = input_GE x VAF. A 0.1% variant on 1,000 GE (~3.0 ng) has lambda = 1, so e^-1 ~= 37% of the time the mutant template was never in the tube and a perfect sequencer detects nothing. Past the point where every input molecule has been read once (sampling saturation, visible as a deduplication plateau in UMI families), additional read depth re-sequences the same physical molecules and adds zero information. Reporting an LoD as a bare VAF -- with no input mass, no unique-molecule (consensus) depth, no replicate detection rate -- is reporting an undefined quantity.

The second ceiling is the per-base background error rate, which sets the VAF floor independently: a 0.1% variant cannot be distinguished from noise if the assay manufactures that base at 0.1%. Error suppression is a ladder (raw NGS ~1e-3 -> single-strand UMI consensus ~1e-4/1e-5 -> duplex <1e-7), and single-strand consensus does NOT remove template-resident damage (C->T deamination, G->T 8-oxoG) because every PCR copy of that strand inherits the lesion -- only duplex strand-concordance catches it. The achieved LoD is the *worse* of the two ceilings: error dominates above ~0.1% VAF for tumor-naive single-locus calling, sampling dominates below it. The escape hatch is integration -- a bespoke panel summing mutant molecules across 16-50 loci against summed background reaches single-ppm even though each locus alone is ~1e-3 to 1e-4 (per-locus vs panel-integrated LoD).

## Methods Landscape

| Concept | Definition | Source |
|---------|------------|--------|
| LoB (Limit of Blank) | Highest signal expected from an analyte-free blank (95th pct): LoB = mean_blank + 1.645*SD_blank; the false-positive anchor on true negatives | CLSI EP17-A2 |
| LoD (Limit of Detection) | Lowest level reliably distinguishable from LoB: LoD = LoB + 1.645*SD_low; a sample at LoD is detected ~95% of the time | CLSI EP17-A2 |
| LoD95 | The concentration/VAF where detection probability = 95%; a point on a probit/logistic detection curve, not a separate definition | CLSI EP17-A2; Newman 2016 |
| LoQ (Limit of Quantitation) | Lowest level measurable with stated precision (e.g. CV<=20%); LoQ >= LoD always, so a "VAF" near the floor is detectable but not trustworthy | CLSI EP17-A2 |
| Per-locus LoD | Single-variant LoD; sampling- and error-limited (~0.05-0.1% VAF typical) | Newman 2014/2016 |
| Panel-integrated LoD | Evidence summed across N tracked variants via a >=k-of-N positivity rule (binomial over per-locus Poisson detection), reaching single-ppm at 16-50 loci; ~sqrt(N) variance-averaging is only a loose lower bound | Reinert 2019 |
| Reference standards | Contrived defined-VAF cell-line admixtures fragmented to ~160 bp into normal cfDNA; SEQC2 Sample A / HCC1395 truth sets | Fang 2021 (SEQC2) |

## Decision Tree by Scenario

| Scenario | Recommended | Why |
|----------|-------------|-----|
| "How many GE for 95% detection at VAF X?" | Solve lambda = input_GE x VAF >= 3, so input_GE >= 3/VAF | 1 - e^-3 = 0.95; ~30,000 GE (~91 ng at 330 GE/ng) for a single 1e-4 variant -- often more than one tube provides |
| "Why is more depth not helping?" | Report unique (consensus) molecular coverage, not raw depth; check the dedup plateau | Past sampling saturation, depth re-reads the same molecules; the ceiling is GE in the tube |
| Single hotspot vs bespoke panel for low VAF | Single locus: error/sampling-limited ~0.1%; need ppm -> integrate across 16-50 clonal loci | Per-locus Poisson/error floor is escaped only by summing independent detections (panel-integrated LoD) |
| Reporting an LoD | Condition on input mass (GE) + consensus depth + replicate detection rate (e.g. "LoD95 0.1% VAF at 30 ng / 2x duplex / 95% of 20 replicates") | A bare VAF omits the input mass, the unique depth, and per-locus vs integrated -- it is undefined |
| Estimating LoD95 from a dilution series | Probit (or logistic) regression of detection (0/1) on VAF; read off the 95% point with a CI | CLSI EP17-A2 detection-curve method; binary detection is a clean GLM target |
| Distinguishing detection from quantitation | Set LoD for yes/no calls; set LoQ (CV<=20%) separately for any reported VAF/TF | MRD calls are binary and can sit far below LoQ; a near-floor VAF number is not quantitative |
| Validating against truth | Contrived SEQC2 Sample A / HCC1395 admixtures, fragmented to cfDNA-like ~160 bp | Real low-VAF patient material is scarce/unverifiable; commutability with plasma is the caveat |

## Genome-Equivalent and Poisson Detection Calculator

**Goal:** Convert an input mass and target VAF into an expected mutant-molecule count and a detection probability, so a sensitivity claim is anchored to molecules rather than to a VAF alone.

**Approach:** Convert ng to haploid genome equivalents (~330/ng), set lambda = input_GE x VAF, and read the detection probability as a Poisson tail P(X >= k) = 1 - cdf(k-1, lambda); invert for the minimum GE that puts lambda at the >=3 sampling-detection threshold.

```python
import numpy as np
from scipy.stats import poisson

GE_PER_NG = 330  # haploid ~3.3 pg -> strict 1 ng / 3.3 pg = 303; 330 is the common diploid-6.6 pg/rounding convention

def genome_equivalents(input_ng):
    return input_ng * GE_PER_NG

def detection_probability(input_ng, vaf, min_mutant_molecules=1):
    '''P(at least min_mutant_molecules present) under Poisson(lambda = GE * VAF).'''
    lam = genome_equivalents(input_ng) * vaf
    return float(poisson.sf(min_mutant_molecules - 1, lam))

def ge_for_sampling_detection(vaf, target_lambda=3.0):
    '''GE needed so lambda >= 3 -> ~95% chance the mutant molecule is present at all.'''
    return target_lambda / vaf

# A 0.1% variant on 3.0 ng (~990 GE) has lambda ~= 1 -> ~63% detected, ~37% missed by sampling alone.
detection_probability(3.0, 0.001)          # ~0.63
ge_for_sampling_detection(1e-4)            # 30000 GE (~91 ng) for a single 0.01% variant
```

## LoB and LoD95 from a Dilution Series (CLSI EP17 style)

**Goal:** Estimate the VAF at which the assay detects 95% of the time, from a contrived dilution series, and anchor it to the blank-derived false-positive floor.

**Approach:** Compute LoB from blank replicates (mean + 1.645*SD, one-sided 95th pct), then fit a probit GLM of binary detection on log10(VAF) (CLSI EP17 fits on log concentration) across the dilution series and invert it for the 95% detection point. The series must bracket the 0.95 crossing — all-detected upper levels cause near-complete separation and an unstable slope.

```python
import numpy a