The absolute neutrophil count is not a state you can dose against, because by the time it moves the event that set it has already happened. The ANC measured on day 10 was decided by the kill in the proliferating compartment on days 0–2, and everything in between is a delay line:

PROL  ->  TR1  ->  TR2  ->  TR3 (marrow storage)  ->  CIRC        (Friberg 2002)

   the DELAY (mean transit time, 89.3 h)   sets WHEN the nadir arrives
   the EXPOSURE (slope x Cp)               empties the pool
   the FEEDBACK exponent gamma (0.170)     sets HOW FAST it comes back

Those three are separate parameters, and nearly every clinical rule about myelosuppression turns out to be a consequence of that separation rather than of potency. The model exists so that the rules can be derived rather than asserted — and so that the places where the derivation fails can be pointed at.

Every number below was produced by cin_reference_impl.py, a dependency-free pure-stdlib re-implementation of cin_mrgsolve_model.R. Its full 742-line output is committed as cin_numerical_report.txt. Reproduce with python3 cin_reference_impl.py.

Two parameters are fitted. Both to Vogel 2005 (PMID 15718314): febrile neutropenia 17% on placebo and 1% on pegfilgrastim after docetaxel 100 mg/m². Both are hit exactly, which is what one parameter per number always does and is evidence of nothing.

There are only two because of a trade-off the model cannot escape. The overall myelotoxic scale can be set either so that the absolute durations reported in the G-CSF trials come out right, or so that the model tells regimens apart. Not both. The duration below the 0.5 ×10⁹/L threshold saturates in this topology: the recovery limb starts from a floor set by φ that does not depend on exposure, and climbs at a rate set by the feedback exponent, so once the proliferative pool is empty at all, extra exposure buys almost no extra duration. Raising the scale until CAE reaches Crawford 1991's 6-day median puts every combination regimen at a nadir of 0.065–0.11 and a DSN of 5.4–6.8 d — it stops telling AC apart from TAC. The scale is set for discrimination, and the shortfall is reported.

Read together they say two specific things:

1. The model exaggerates how much the timing of G-CSF matters. Given on day 2, pegfilgrastim removes severe neutropenia completely (0.00 d against 1.8 observed). Given on day 4, filgrastim leaves 1.90 d where 1.0 was observed. One is −100% and the other +90%, in opposite directions, and the axis they differ on is the start day. So the timing result in A4 is right in direction and too steep in magnitude.
2. It ranks the two products in the wrong order. Green found pegfilgrastim marginally worse than daily filgrastim (1.8 vs 1.6 d); the model has it better. The mechanism responsible is the one the model is proudest of — target-mediated clearance holding the long-acting product up for exactly as long as the ANC stays low — so the same term that produces the self-titration result also produces this error.

The intact-marrow miss is forced: the steady-state ANC multiple in a Friberg loop is ((1−φ)(1+Emax_amp))^(1/γ) with 1/γ = 5.9, so a 5-fold rise needs Emax_amp = 0.320 — and at that value pegfilgrastim abolishes severe neutropenia altogether, which it demonstrably does not. Emax_amp = 0.10 sits between two observations the model cannot hold at once.

What survives all of this is everything comparative. A4–A14 change one thing at a time within a fixed regimen and patient, and the quantity being compared — timing, product, dose, cell-cycle dependence, count versus function — does not depend on the absolute scale being right. Absolute P(FN) values do, and they are anchored to a randomised-trial population, which Truong 2016 shows understates real-world rates.

A 3-fold dose range on CAE:

I expected the dose to move the depth. It moves it 1.31-fold across a 3-fold range, moves the duration 1.04-fold, and moves the nadir day by 0.21 d. Transit time, swept over the published 62–125 h range at fixed dose, moves the nadir day 7.88 → 12.63 and the depth barely at all. So the transit time owns the day, and the depth is owned by neither dose nor transit — it is floored by φ and the feedback. That is why a growth factor given on day 8 cannot help much: by day 8 the deficit has been manufactured and is in transit.

Varying only the feedback exponent — changing how fast the patient recovers and nothing about how hard the drug hit:

A 1.8-fold spread in nadir maps to a 1.7-fold spread in risk that is driven by the integral, exactly as Bodey's 1966 observation implies. Reporting a nadir without a duration discards the variable that matters.

Same fixed 6 mg dose in every row, ordered by how bad the regimen is without support:

The half-life measured during the nadir rises 3.4-fold from the mildest to the most severe regimen while the half-life measured after recovery does not move. Reported pegfilgrastim half-lives span roughly 15–80 h in exactly this way. This is not between-patient variability and not a covariate: it is the same feedback loop read from the drug's side. A patient whose marrow is in trouble automatically receives a longer exposure, because the mechanism that would have cleared the drug is the mechanism that is missing — which is why pegfilgrastim is a flat 6 mg regardless of weight while filgrastim is dosed per kilogram. Filgrastim's own exposure is identical (Cmax 7.93, AUC 80) in a mild and a severe regimen, because its renal route does not care about the ANC.

Five G-CSF actions switched on one at a time, in an intact marrow:

Storage release alone accounts for more than half the rise and adds no cells: it empties the marrow reserve into the blood, which is visible in the last column. Repeat the decomposition in a marrow CAE has just emptied and the ordering inverts — transit does almost all the therapeutic work (DSN 4.60 → 2.52 on its own), because release and demargination are bookkeeping operations on a pool that is empty. The pipeline, not the factory.

Pegfilgrastim 6 mg on CAE, one dose, start time swept:

Timing moves DSN across 0.53–3.79 d. A 16-fold dose range at the best timing moves it 1.74 → 1.03 d. Note also the AUC column: the same dose delivers 4-fold more exposure when the marrow needs it, which is item 3 again.

Same-day dosing is worse in the model without any parameter saying so: G-CSF raises the proliferation rate, the cytotoxic kills in proportion to that rate, and if the two overlap the drug simply gets more cells. Switching the amplification action off shrinks the penalty but does not abolish it — amplification is the larger share, not the whole mechanism.

Six cycles of CAE, expected number of FN episodes rather than P(at least one), because the latter saturates above 0.95 for every strategy:

Dose reduction buys very little FN risk and costs a great deal of tumour control. The growth factor buys almost all of it and costs none. The tumour layer is a deliberately thin log-kill and should be read as a price list, not a survival prediction — but the direction of the trade is the whole argument for prophylaxis, and it is a health-economic argument rather than a haematological one.

A13 makes that explicit. Sweeping the baseline risk and adding pegfilgrastim at each level: the risk ratio is roughly flat (9–23×) while the absolute reduction, and therefore the NNT, scales with baseline risk. There is no kink at 20%, or anywhere else. The threshold is a statement about the price of a hospital admission divided by the price of a syringe, which is exactly why it moved from 40% to 20% without any change in the biology (Calhoun 2005; Cosler 2005).

I expected the saving to rise monotonically with cell-cycle dependence. It does not. Topotecan has the highest cycle dependence of any regimen here and gains almost nothing. The missing variable is where the regimen sits relative to the threshold: trilaciclib removes a fraction of the kill, and on a regimen whose nadir is far below 0.5 a fractional reduction still leaves it below. The benefit is largest for regimens sitting near the threshold. That is a sharper claim than the one I started with, and it puts the licensed indication (etoposide/carboplatin in small-cell lung cancer) inside the favourable window while relapsed topotecan, where the drug is also used, sits outside it.

Trilaciclib is also the only intervention here that improves the cumulative column: six cycles of EP end with marrow reserve 0.9958 versus 0.9934, because the arrest protects the cycling stem fraction. A growth factor cannot do that — it accelerates the pipeline downstream of the damage.

The ordering holds for every regimen and no parameter says so — it follows from transit times of 89/200/150 h and lifespans of 7.9 h / 10 d / 120 d. Across six cycles the ANC nadir is essentially reproducible (0.169 → 0.151), the platelet nadir is flat after cycle 1, and the haemoglobin falls every cycle and never recovers (12.3 → 9.1 g/dL). A cell that lives 120 days cannot replace a cycle's losses inside 21 days; one that lives 8 hours has no memory of the previous cycle at all. Anaemia is the cumulative toxicity of a course, neutropenia the acute toxicity of a cycle, and the growth factor that fixes the second does nothing for the first.

Dexamethasone premedication, at 24 h:

The measured ANC goes up and the effective defence goes down — exactly the kind of number that gets a patient through a day-1 count gate. And in the infection module, levofloxacin changes no haematological number at all and still moves P(FN) from 0.265 to 0.215, because it acts on the other side of the race. Reporting only the ANC would make the antibiotic look inert and the steroid look protective. Both readings would be wrong. This is why the model carries neutrophil function as a state distinct from neutrophil count, and why the Shiny app never plots one without the other.

Six cycles of CAE with a controller implementing the real rules (hold for ANC < 1.5 or platelets < 100, reduce after two holds or after the cycle's FN risk crosses 20%):

Note which rule fires. Neither patient trips the day-1 count gate often — by day 21 the ANC has overshot its own baseline, which is what the feedback loop does — so almost all of the lost dose intensity comes from a clinician looking at a nadir and reducing the next dose. The intensity is being spent on a number the growth factor could have fixed without touching the dose.

And the cost that the growth factor does not fix: in the compromised patient, haemoglobin and marrow reserve are worse in the primary-prophylaxis arm precisely because it delivered more chemotherapy. Preserving dose intensity is not free; it is a decision to spend one toxicity to buy another.

Nothing above is believed before A0 passes.

• Baseline steady state — with no drug and no growth factor, every state is stationary to 0.00e+00 over 42 simulated days. Any drift would mean the results are a mixture of pharmacology and numerical error.
• Step-size convergence — the cytotoxic PK is stiff (docetaxel's central compartment empties at ~9.7 /h) so it is pre-integrated on a 0.025 h grid and interpolated; the biology is stepped with a time-local bound of 1.2/λ(t) recomputed every step. dt 0.25 → 0.05 moves the CAE nadir from 0.06520 to 0.06509 and DSN from 6.1250 to 6.1271 d.
• DSN as a state versus the output grid — agreement to 8.9e-16 on CAE.

Four defects found by these checks and fixed rather than absorbed, all recorded in the source at the line that caused them:

1. G-CSF's transit acceleration was applied to the outflow but not the proliferation term — so more G-CSF deepened the nadir.
2. The reserve term multiplied the self-renewal gain, so through the 1/γ exponent a 12% stem-cell loss halved the baseline ANC.
3. The thrombopoietin ceiling was applied to both branches of its own equation, making it a sign trap: above the ceiling both factors were negative and TPO grew faster the further past its limit it went.
4. The megakaryocyte pool was self-renewing with gain > 1 behind an 8-day feedback delay — a delayed positive loop that drove the platelet rebound to 7118 ×10⁹/L before the count caught up.

A calibration search was also silently fooled once: min() over a list containing NaN returns the first element, which reads as "no neutropenia at all", so a diverging integration pushed the search to a docetaxel slope of 2713. Non-finite states now raise.

53 ODE compartments. 4 cytotoxic PK slots (A 3-compartment, B/C/D 2-compartment) covering 8 parameterised agents across 13 regimens, with threshold-driven PD for paclitaxel; G-CSF depot/central/peripheral/effect with target-mediated clearance; trilaciclib; dexamethasone; levofloxacin; a quiescent stem pool feeding three lineages each with its own transit chain; marrow storage and marginated pools kept separate from circulating; mucosal barrier → bacterial translocation → IL-6 → CRP → temperature; the DSN counter and FN hazard; a tumour with sensitive and resistant clones; and neutrophil function as a state distinct from count.

Structural choices worth arguing with

• φ = 2⁻⁸ is the reciprocal of the mitotic amplification factor and sets an ANC floor that no cytotoxic can push through. It is the single most consequential number in the model: n_div = 5 puts the floor at 0.236 and no grade 4 nadir is reachable at any exposure; n_div = 9 gives DSN 5.33 d. The value 8 is the smallest that reaches grade 4 nadirs on the regimens that produce them clinically. It should be read as chosen, not measured.
• (1 − E_drug) is not clamped at zero. At the published Friberg slopes the term goes negative during the infusion and the proliferative pool is actively depleted rather than merely stopped. Clamping caps the achievable nadir far above what is observed.
• Reserve acts on the influx, not the self-renewal gain, so reduced marrow reserve barely moves the baseline count and markedly slows recovery — which is what a previously-treated patient actually looks like.
• γ_P = 1.0 and γ_E = 0.6, larger than the neutrophil's 0.170. Reusing so weak an exponent for the slower lineages makes their steady state absurdly sensitive, because it enters as 1/γ.
• The inflammatory gains are set analytically, from what florid Gram-negative sepsis looks like at the bacterial carrying capacity (IL-6 500 pg/mL, CRP 250 mg/L, +3.0 °C). The first version used gains an order of magnitude too high and reported a core temperature of 83 °C.
• kkill_B is set so that neutrophil killing exactly balances bacterial growth at ANC 0.5, i.e. the clinical threshold is a property of the model rather than a number written into it.

• It cannot reproduce an agent-specific nadir day — the nadir day is a function of MTT alone, and carboplatin's is reported near day 21.
• It cannot assign a regimen to a guideline risk band (A1, miss 6). Use it to compare within a regimen, not across the band boundary.
• It does not reproduce which lineage is dose-limiting for the platelet-limited agents. Carboplatin and gemcitabine come out neutrophil-limited because a global scale right for a three-drug regimen is too large for a mild single agent. A version that got this right would need per-agent slopes fitted to per-agent data rather than to ratios.
• The tumour layer is a price list, not a survival model. The dose-intensity/survival association is observational and confounded.
• Absolute P(FN) values are trial-population numbers and read low against registry data (Truong 2016).

# Full numerical report (~2 min, standard library only)
python3 cin_reference_impl.py

# One analysis, or refit the calibration from the anchors
python3 cin_reference_impl.py --only A7
python3 cin_reference_impl.py --recalibrate

# Re-render the map
dot -Tsvg cin_qsp_model.dot -o cin_qsp_model.svg
dot -Tpng -Gdpi=150 cin_qsp_model.dot -o cin_qsp_model.png

library(mrgsolve)
mod <- mread("cin_mrgsolve_model.R")
# agent/regimen tables and 18 prebuilt scenarios are in the usage block
# at the foot of the model file
shiny::runApp("cin_shiny_app.R")

Research, education and hypothesis generation only. Not validated for clinical decisions, prescribing, or regulatory submission. Parameters are illustrative approximations; the six named misses above are the model's own account of where it disagrees with the literature.