Cancer is not a special enemy. It is a dissipative system — one that runs the same four-phase cycle as a city, a forest, an immune system, or a company. That structural fact changes how we predict treatment outcomes.
Immunotherapy has transformed cancer treatment. Checkpoint inhibitors — drugs that release the brakes on the immune system — can produce durable remissions in cancers that were previously untreatable. But they only work for some patients. Across all cancers, roughly 20–40% respond. The rest get the side effects without the benefit.
The central question in oncology today is: can we predict who will respond before treatment starts?
The current best tools:
The formula at the bottom of that chart uses two numbers measured from a tumour biopsy and one equation. No machine learning. No neural networks. No training on the patient data it predicts. It outperforms every approach above because it reads the structure of what cancer actually is.
A tumour is a system that maintains itself. That is its entire job description.
Cancer is not random chaos. A successful tumour is an organised, self-sustaining system that has solved a hard engineering problem: how to persist inside a hostile environment (your body) that is actively trying to destroy it. To do this, it runs a cycle — the same cycle every self-maintaining system runs.
Think of an invasive plant species in a garden. It doesn't just grow randomly. It signals through chemical cues to suppress nearby plants. It builds root infrastructure to capture resources. It encounters the gardener's weeding attempts and adapts. And it maintains what it has built, repairing damage and holding territory. Cut one root and it regrows from another. The plant doesn't know it's doing this. The cycle runs because the structure demands it.
A tumour does exactly the same thing, with four phases:
The tumour sends signals to avoid immune detection. It downregulates antigen presentation, secretes immunosuppressive cytokines, and hides its surface markers. The immune system tries to perceive the tumour; the tumour tries to stay invisible.
The tumour builds physical infrastructure: blood vessels (angiogenesis), extracellular matrix, metabolic pathways. It creates the supply chain that feeds its growth. This is the construction phase — turning resources into structure.
The tumour engages the immune system directly. T-cells attack. The tumour expresses PD-L1 to shut them down. This is the battle zone — the interface where the tumour and the immune system make contact and negotiate survival.
The tumour maintains what it has built. Regulatory T-cells suppress further immune attack. DNA repair mechanisms fix drug damage. The extracellular matrix is reinforced. This is the maintenance phase — holding the gains.
Every successful tumour runs this cycle. Signal → Structure → Encounter → Conservation → Signal. The cycle repeats, and with each turn the tumour becomes more entrenched. This is not a metaphor. These four phases correspond to measurable, distinct biological processes.
This cycle is not unique to cancer. Cities build infrastructure, encounter regulation, and maintain what they have. Companies signal their market, build products, encounter competition, and conserve their position. Immune systems detect pathogens, mount a response, engage the threat, and maintain memory. Every dissipative system — every system that maintains itself by processing energy — runs this same four-phase cycle. Cancer is not special. It is structural.
Every cancer drug disrupts one position in the tumour's cycle. A combination disrupts more. The question is: how much of the cycle did you actually block?
Each drug class targets a specific phase of the tumour's maintenance cycle:
| Position | What the tumour does | Drug class | What the drug disrupts |
|---|---|---|---|
| Signal | Hides from immune detection | Oncolytic viruses, BiTEs, vaccines | Forces the tumour to become visible |
| Structure | Builds blood supply and infrastructure | Anti-angiogenics, platinum chemotherapy, taxanes | Destroys the supply chain and building materials |
| Encounter | Blocks immune attack via checkpoints | Anti-PD-1, anti-PD-L1, anti-CTLA-4 | Removes the tumour's shield at the battle zone |
| Conservation | Repairs damage, maintains suppression | PARP inhibitors, CDK4/6 inhibitors, supportive care | Prevents the tumour from repairing and recovering |
Imagine a medieval castle under siege. The castle has watchtowers (Signal), walls (Structure), soldiers at the gates (Encounter), and repair crews (Conservation). An effective siege doesn't just attack the gates. It blinds the watchtowers (so the castle can't see where the next attack comes from), breaches the walls (so reinforcements can't arrive), overwhelms the soldiers (so the gate falls), and prevents repairs (so the breach stays open). Attacking only one position lets the castle recover through the others.
This maps precisely to clinical data. In our analysis of standard-of-care regimens across 16 cancer types, 91% of treatment gains come from covering more positions, not from increasing the potency of drugs at positions already covered. Coverage beats potency. And the most commonly missed position? Conservation. In 9 of 16 cancers, the standard treatment has no agent at the conservation layer — leaving the tumour's repair crew untouched.
How much of a drug's potency actually gets through to the tumour? That depends on drain.
Every intervention encounters resistance. A drug enters the tumour, but the tumour fights back: it expels the drug, repairs the damage, suppresses the immune response that the drug is trying to activate. The fraction of potency that is lost to this resistance is called drain.
This is not a fitted curve. It is the algebraic form that every dissipative system follows when potency meets resistance. It was derived from first principles — two operations (hold and cross) at every scale produce four regimes, and the drain relationship follows this exact form.
Think of pushing a boat through water. M is your engine power. D is the drag. The formula says: effective speed = engine power × (1 − drag) / (1 + drag). When drag is zero, you get full power. When drag is 0.5, you lose 67% of your power. When drag approaches 1, effective speed approaches zero — no matter how powerful the engine. Drain is not subtracted. It is divided out. This is why a small reduction in drain can be more powerful than a large increase in potency.
At the population level, this formula predicts the response rate of drug combinations across 72 published clinical trials in 16 cancer types, with a mean error of 3.8 percentage points. No fitted parameters per drug — drugs with the same structural address get the same prediction.
The overlap between these two addresses determines whether the treatment works.
Just as a street address has layers of specificity (country → city → street → house number), both drugs and tumours have four-level addresses. The deeper you resolve the address, the more precise the prediction.
| Level | Drug address | Tumour address | What it determines |
|---|---|---|---|
| L1 | Which position? (Signal, Structure, Encounter, Conservation) | Which cancer type? | Where in the cycle does the drug act? |
| L2 | Which mechanism class? (Checkpoint inhibitor, platinum, taxane…) | Which stage and line? | How does the drug act? |
| L3 | Which molecular target? (Anti-PD-1 vs anti-PD-L1 vs anti-CTLA-4) | Which biomarker stratum? (PD-L1+, BRCA+, dMMR) | What specifically does the drug bind? |
| L4 | Which pharmacodynamic role? (Binding, Potency, Selectivity, Duration) | Which individual tumour profile? | What is the drug's experience at the target? |
The overlap between the drug address and the tumour address at a given depth determines M — the structural potency. At L1, you know only which position is targeted. At L4, you know the pharmacodynamic fingerprint of the specific drug meeting the specific molecular state of the individual tumour. Deeper address = more precise prediction.
This is why nivolumab and pembrolizumab produce the same clinical results in melanoma. They have the same address at L1 (Encounter), L2 (checkpoint inhibitor), and L3 (anti-PD-1). Their L4 addresses differ (pembrolizumab binds 100× stronger), but clinical dosing saturates the target, so L4 differences wash out. The address predicts this. Same address, same prediction.
The formula predicts population response rates. Can it predict which individual patients respond?
Population-level prediction says: "47% of patients with this cancer receiving this drug combination will respond." It does not say which 47%. To make that prediction, you need to resolve the system address deeper — from cancer type (L1) down to the individual tumour's immune environment (L4).
The formula remains the same. But now D and S are measured from the individual patient's tumour biopsy:
D — Conservation drain. How much is the tumour's environment suppressing or exhausting the immune response at the encounter interface? This is the thing that holds the immune system back from fighting. High drain means the drug can't break through.
S — Signal quality. Can the immune system actually perceive the tumour? Is there detection capacity present? High signal means the immune system has already identified the target.
Imagine you are a general deciding whether to send reinforcements to a battle. You need two pieces of intelligence. First: how strong is the enemy's defence? (D — conservation drain). If the enemy has built impenetrable fortifications, your reinforcements will be wasted. Second: can your scouts see the enemy? (S — signal quality). If your scouts can't even find the target, reinforcements don't know where to go. These two measurements — defence strength and intelligence quality — determine whether the reinforcements (the drug) will succeed. Everything else is detail.
The critical discovery: the structural positions are universal, but the biomarkers that read them are cancer-specific. In each cancer, a different molecular feature reads the conservation drain, because each tumour maintains itself through a different mechanism.
| Cancer | D reads from | Why |
|---|---|---|
| NSCLC | CCR8+ regulatory T-cells | The tumour recruits its own suppressive immune niche. These Tregs maintain immune silence at the encounter interface. |
| Melanoma | HAVCR2+LAG3 exhaustion markers | The immune system tried and burned out. T-cells are terminally exhausted — high effector markers co-expressed with exhaustion checkpoints. The failed encounter is the drain. |
| BCC | CD8 exhausted T-cell fraction | Same as melanoma: exhausted effectors mark a conservation state where the immune system holds a frozen, unproductive encounter. |
All three are conservation drain. The mechanism differs. The formula holds.
We tested the formula on three independent, published datasets. All used pre-treatment single-cell RNA sequencing, where immune cell proportions can be measured directly. The formula was not fitted to any of these datasets. M comes from population trial data. D and S were mapped from structural position, not from statistical optimisation.
| Dataset | Cancer | Patients | D (drain) | S (signal) | AUC | Accuracy |
|---|---|---|---|---|---|---|
| Zhang/Liu 2025 Cell | NSCLC | 159 | CCR8+ Tregs | FGFBP2+ NK cells | 0.808 | 76.7% |
| Sade-Feldman 2018 Cell | Melanoma | 19 | HAVCR2+LAG3 | (via 1−D) | 0.889 | 78.9% |
| Yost 2019 Nature Medicine | BCC | 11 | CD8 exhaustion | NK cells | 0.767 | 81.8% |
The formula uses two patient-specific measurements per patient, taken from a pre-treatment tumour biopsy. The M value is the same for all patients in a cancer type. No parameters were fitted to the patient data.
AUC (area under the receiver operating characteristic curve) measures discrimination: if you pick a random responder and a random non-responder, how often does the formula give the responder a higher score? AUC 0.808 means 81% of the time. AUC 0.5 would be a coin flip. The current clinical standard (PD-L1) achieves 0.64. Senior oncologists with full clinical records achieve 0.72.
The formula gets 77–89% of patients right. The 14–23% it misses are not random. They have structural explanations that the framework predicts.
23 patients in the NSCLC dataset had low CCR8+ Tregs (low drain D) but 36% more FOXP3+ Tregs — a second conservation mechanism. CCR8 marks tumour-resident suppression. FOXP3 without CCR8 marks the body's own regulatory machinery. Both drain the checkpoint inhibitor, but through different sub-positions within Conservation. One measurement misses the other.
14 patients had moderate CCR8+ Tregs (high drain D) but 62% more memory B-cells and 69% more VCAN+ macrophages. They responded despite T-cell suppression because the humoral arm of the immune system (B-cells, not T-cells) provided an alternative encounter pathway. The formula models T-cell encounter but misses B-cell encounter.
In framework terms: Conservation has at least two sub-positions (tumour-resident vs systemic regulation). Encounter has at least two sub-positions (T-cell pathway vs B-cell pathway). These are deeper address levels. Adding them improves AUC to 0.824 — modest, because the two-input formula already captures the dominant structural signal.
Same formula. Different address depth. The address determines the prediction. The depth determines the resolution.
| Scale | What we measure | What it predicts | Accuracy |
|---|---|---|---|
| Population (72 trials) | Drug address + tumour state | Response rate of drug combinations | MAE 3.8 pts |
| Drug class (38 agents) | Pharmacodynamic profile | L4 role assignment | 24/24 mapped |
| Patient (189 individuals) | 2 immune measurements per patient | Individual treatment response | AUC 0.77–0.89 |
The clinical implication is direct. If you can measure a patient's conservation drain and signal quality — from a standard flow cytometry panel, not expensive single-cell sequencing — you can predict immunotherapy response with 77–89% discrimination before the first dose. The formula tells you what to measure, because the structural positions tell you where the drain and the signal live.
In NSCLC, measure CCR8+ Tregs and FGFBP2+ NK cells. In melanoma, measure HAVCR2 and LAG3 co-expression. Two numbers per patient. One equation. Arithmetic that fits in an Excel cell.
The formula was not designed for cancer. It was derived from the geometry of how any dissipative system resists and responds to intervention. That it predicts individual patient outcomes in immunotherapy — with two inputs and one equation, across three cancer types — is a consequence of the structure being real at every scale.
A reasonable question: are these obscure markers chosen to make the formula look good? The answer is the opposite. Every biomarker used in this study is at the cutting edge of current immuno-oncology research. The field is investing billions in them — but as therapeutic targets, not as predictive tools. That gap is what this work fills.
CCR8 is one of the most actively pursued next-generation immunotherapy targets. Multiple pharmaceutical companies have anti-CCR8 antibodies in Phase 1/2 clinical trials, including Coherus Oncology (tagmokitug/CHS-114), AbbVie (ABBV-514), Bayer (BAY 3375968), Domain Therapeutics (DT-7012), and Zymeworks. At SITC 2025, CHS-114 showed selective depletion of CCR8+ Tregs and a >50% increase in intratumoral CD8 T-cells in HNSCC patients.
The field is building drugs to deplete CCR8+ Tregs. We show that measuring them predicts who will respond to existing checkpoint inhibitors — before any drug is given. The measurement is cheaper than the drug and tells you whether the drug will work.
Both are active therapeutic targets with drugs in clinical trials. Anti-LAG3 (relatlimab) is already FDA-approved in combination with nivolumab for melanoma. Multiple anti-TIM-3 antibodies are in Phase 2/3 trials. The field uses these as molecules to block. We use them as molecules to measure — their expression level predicts the conservation drain state of the tumour's immune environment.
FGFBP2 was specifically identified in the Zhang/Liu 2025 Cell paper as significantly associated with immunotherapy response in 234 NSCLC patients. NK cell biology is an increasingly active area of immuno-oncology, with multiple NK cell-based therapies in clinical development.
The biomarkers are not new. The formula is. The field has established that CCR8+ Tregs suppress the immune response, that HAVCR2/LAG3 mark exhaustion, and that NK cells detect tumours. What was missing is the structural relationship between these measurements and treatment outcome — a formula that connects conservation drain to effective potency. One equation that turns known biology into a prediction.
The formula, the datasets, and the code are publicly available. GEO accession numbers: GSE243013 (NSCLC), GSE120575 (melanoma), GSE123813 (BCC). The Python script, the data CSVs, and an Excel calculator are downloadable from this page. Anyone can reproduce the result in an afternoon.
Pick a cancer type. Select the drugs. See the prediction build — position by position, layer by layer. Watch what happens when you leave a position uncovered. Watch what happens when you add one.
The Treatment Map covers 16 cancer types, 138 drug groups, and 72 validated trials.
It runs entirely in your browser. No data is sent anywhere.
The four-position cycle is not specific to cancer. It is the structure of every dissipative system. To understand why the formula works — and where else it applies — start with the addressing system.
Reproduce the results
Python script · Patient data (CSV) · Excel calculator
GEO: GSE243013 · GSE120575 · GSE123813
Generative Geometry (van der Klein, 2026).
Treatment Map · Geometry of Intervention · Four-State Observer Protocol