The Physics of a Negative Result

Zetobit Bioinformatics Insight Series  ·  No. 09

Liquid Biopsy · Limits of Detection

The Physics of a Negative Result

A ctDNA test that reports “no residual disease” is making a claim about molecules that may simply never have been in the tube. Understanding why is the difference between a confident call and a dangerous one.

Kanna Nandakumar, PhD Zetobit LLC 10 min read

~0.01%

Variant allele fraction at which MRD assays now aim to call disease

3,300

Approx. haploid genome copies per mL of plasma at 10 ng cfDNA input

0

Mutant molecules a negative result may actually represent

Every liquid biopsy report ends in one of two ways: a variant is called, or it is not. The first outcome invites scrutiny—is the mutation real, is it clonal hematopoiesis, does it match the tumor? The second outcome tends to be accepted at face value. But a negative ctDNA result is one of the most misunderstood numbers in clinical genomics, because it conflates two entirely different statements: the mutation is not present, and the mutation was not sampled. These are not the same claim, and the gap between them is governed less by the sophistication of the bioinformatics than by the physics of how few molecules are actually in the tube.

This article is about that gap. It walks through where the limit of detection (LOD) in circulating tumor DNA actually comes from, why it is bounded by sampling statistics long before it is bounded by sequencing chemistry, and what the analysis pipeline can and cannot do about it. The framing matters for anyone building or interpreting minimal residual disease (MRD) assays, where the entire clinical value rests on trusting a negative.

The problem

A negative result is a statement about probability

Start with the plasma itself. A typical blood draw yields a few milliliters of plasma, and each milliliter contains only a modest quantity of cell-free DNA—often in the range of 5 to 20 nanograms in a person without a large tumor burden. Because the mass of a haploid human genome is about 3.3 picograms, 10 ng of cfDNA corresponds to roughly 3,000 genome equivalents. That number is the ceiling on everything that follows. No amount of sequencing depth, error suppression, or machine learning can recover information about a molecule that was never drawn into the tube in the first place.

Now suppose a tumor is shedding DNA at a variant allele fraction (VAF) of 0.01%—a realistic target for post-surgical MRD.¹ At 3,000 genome equivalents, the expected number of mutant molecules in the sample is 0.3. Not three. Not one. Fractional. The presence or absence of tumor signal in that tube is now a coin flip governed by the Poisson distribution, and roughly three quarters of the time the answer will be zero mutant molecules present—a true negative tube from a patient with real residual disease.

A test cannot sequence a molecule that sampling never delivered. The limit of detection is set in the phlebotomy chair, not the flow cell.

This is the single most important idea in ctDNA interpretation, and it is a counting problem, not a signal-processing one. The figure below shows how the probability of capturing at least one mutant molecule collapses as VAF drops, for three realistic input amounts.

Figure 1  Detection probability is a sampling problem. At a variant allele fraction of 0.01% (dashed vertical line), even a generous 10 ng input captures at least one mutant molecule barely half the time. Curves follow the Poisson expression P = 1 − e^(−N·VAF), where N is genome equivalents. Below input thresholds, no downstream method can rescue a signal that was never sampled.

The error floor

Even when the molecule is there, chemistry adds noise

Suppose sampling cooperates and a mutant molecule does make it into the library. The second barrier is that sequencing is not error-free. Raw Illumina base-calling error rates sit near 0.1–1% per base—which is catastrophic when the signal you are hunting is a variant present at 0.01%.² Without intervention, the true mutant is buried under a far larger number of artifactual “variants” created by polymerase misincorporation, oxidative damage during library prep, and sequencing miscalls.

The field's answer is molecular barcoding. Unique molecular identifiers (UMIs) tag each original template before amplification, so that all reads descending from one molecule can be collapsed into a single consensus.⁵ A real mutation appears in every member of the family; a PCR or sequencing error appears in only some, and is voted out. Duplex sequencing extends this further by requiring the variant to be seen on both strands of the original double-stranded molecule, which suppresses the error rate to below one in ten million—because the two strands would have to fail in a correlated, complementary way to produce the same false call.³

Bioinformatics note Consensus calling is where the pipeline earns its keep. The choice of minimum family size, the strand-agreement requirement, and the base-quality thresholds for consensus all trade sensitivity against specificity directly. A family-size floor of 3 recovers more molecules but readmits noise; a duplex requirement is exquisitely clean but discards single-stranded families, shrinking your already-scarce input. There is no universally correct setting—only a setting matched to the assay's LOD claim.

The table below separates the two regimes that every ctDNA assay lives inside: the sampling-limited regime, where the constraint is how many molecules exist, and the chemistry-limited regime, where the constraint is how cleanly you can read them. Bioinformatics operates almost entirely in the second column.

Table 1 — Two limits, two toolkits

Constraint	Sampling-limited regime	Chemistry-limited regime
What bounds the LOD	Number of genome equivalents in the tube (Poisson)	Background error rate of sequencing & library prep
Dominant when	VAF is very low and input is small	Input is ample but error floor is high
Fixed by	More plasma, higher cfDNA yield, larger draw	UMIs, duplex consensus, error modeling
Pipeline can help?	No — cannot recover unsampled molecules	Yes — consensus & background suppression
Failure mode	False negative (true disease, empty tube)	False positive (artifact called as variant)

Two strategies

Fixed-panel versus tumor-informed MRD

Because the sampling limit is so punishing at a single locus, the practical route to lower LODs is to watch many loci at once. If a tumor's whole-exome or whole-genome profile is known from tissue, an MRD assay can track hundreds to thousands of patient-specific mutations simultaneously. Any individual site may fail the Poisson coin flip, but the probability that all of them come up empty falls off as the product of individual miss-probabilities. Tracking 1,000 variants is what pushes tumor-informed assays toward the parts-per-million sensitivity that fixed hotspot panels cannot reach.^6,7

This is the central design fork in the field.⁴ Tumor-naïve assays sequence a fixed panel deeply and require no tissue, at the cost of a higher LOD. Tumor-informed assays trade turnaround time and a tissue requirement for dramatically better sensitivity by aggregating signal across a personalized variant set. The second figure shows why breadth beats depth once you are sampling-limited.

Figure 2  Why tumor-informed MRD reaches lower limits. Each locus faces the same brutal sampling odds, but aggregating signal across a large personalized variant set means the assay only needs a handful of loci to land heads. Teal circles denote loci where a mutant molecule was captured; grey denotes wild-type or unsampled.

Reporting

What a defensible LOD claim actually contains

Given all of this, an LOD stated as a single percentage—“0.01% VAF”—is nearly meaningless in isolation. It is a probabilistic threshold, and a defensible claim has to state the conditions under which it holds. At minimum, a report should be able to answer: how much cfDNA was input, how many genome equivalents that represents, what detection probability the assay achieves at the claimed VAF given that input, and what the empirical false-positive rate is at the calling threshold. A “negative” without an accompanying input mass is uninterpretable, because the same result means very different things at 3 ng versus 30 ng.

“Not detected” and “confirmed absent” are different clinical statements. Only one of them is ever earned by a ctDNA assay.

This is why leading MRD frameworks report LOD as a paired quantity—the VAF at which the assay achieves a specified detection probability (commonly 95%) at a specified input—and why analytical validation studies characterize the sensitivity/input relationship rather than quoting a lone number. The bioinformatics deliverable, in a well-run pipeline, is not just a variant list. It is a variant list annotated with the sampling-informed confidence that a negative locus is truly negative.

The practical upshot for pipeline design

Three principles fall out of the physics. First, maximize input before optimizing anything else—a larger draw or better extraction buys more sensitivity than any algorithmic tuning, because it moves you along the Poisson curve directly. Second, match error suppression to the LOD claim—duplex consensus is the right tool at parts-per-million, but its molecule attrition is wasteful and counterproductive at higher VAF targets. Third, report the input alongside the call, always, so that a downstream clinician can distinguish a true negative from an empty tube. None of these are exotic. They are simply what it means to take the counting problem seriously.

The uncomfortable truth of liquid biopsy is that the most sophisticated part of the assay—the consensus calling, the background modeling, the machine-learned error profiles—operates entirely downstream of a constraint it cannot touch. The molecules either made it into the tube or they did not. Good bioinformatics does not pretend otherwise; it quantifies the uncertainty honestly and hands the clinician a negative result they can actually reason about.

Building or validating an MRD pipeline?

Zetobit designs CAP/CLIA-compliant ctDNA workflows with sampling-aware LOD characterization, UMI consensus tuning, and analytical validation support. If your negative results need to be defensible, we can help.

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References

1. Diehl F, Schmidt K, Choti MA, et al. Circulating mutant DNA to assess tumor dynamics. Nat Med. 2008;14(9):985–990. doi:10.1038/nm.1789
2. Newman AM, Bratman SV, To J, et al. An ultrasensitive method for quantitating circulating tumor DNA with broad patient coverage. Nat Med. 2014;20(5):548–554. doi:10.1038/nm.3519
3. Kennedy SR, Schmitt MW, Fox EJ, et al. Detecting ultralow-frequency mutations by Duplex Sequencing. Nat Protoc. 2014;9(11):2586–2606. doi:10.1038/nprot.2014.170
4. Wan JCM, Massie C, Garcia-Corbacho J, et al. Liquid biopsies come of age: towards implementation of circulating tumour DNA. Nat Rev Cancer. 2017;17(4):223–238. doi:10.1038/nrc.2017.7
5. Wang TT, Abelson S, Zou J, et al. High efficiency error suppression for accurate detection of low-frequency variants. Nucleic Acids Res. 2019;47(15):e87. doi:10.1093/nar/gkz474
6. Parikh AR, Van Seventer EE, Siravegna G, et al. Minimal residual disease detection using a plasma-only circulating tumor DNA assay. Clin Cancer Res. 2021;27(20):5586–5594. doi:10.1158/1078-0432.CCR-21-0410
7. Zviran A, Schulman RC, Shah M, et al. Genome-wide cell-free DNA mutational integration enables ultra-sensitive cancer monitoring. Nat Med. 2020;26(7):1114–1124. doi:10.1038/s41591-020-0915-3

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