flowchart LR
E["Exposure(t)<br/>dose or PK-derived"] --> S["Stimulation<br/>raises hazard"]
E --> T["Tolerance(t)<br/>accumulates, then decays"]
T --> I["Inhibition<br/>lowers hazard"]
S --> H["Hazard of CRS"]
I --> H
H --> P["P(CRS after dose j)"]
CRS risk during step-up dosing of T-cell engagers
Working specification for a stimulation/tolerance model fit to public data
pharmacometrics
safety
oncology
working document
Cytokine release syndrome risk falls as step-up doses rise, which means prior exposure is doing something. This specifies a model of that effect, built by reusing the published epcoritamab repeated time-to-event model and testing how far public aggregate data can carry it.
Nothing here has been read, fit, or checked. The epcoritamab paper this project is built on has not been read; every statement below about what Li et al. did is a prediction about the paper, written from its title and abstract, and Section 3 is the work of replacing those predictions with what the paper says. The equations in Sections 6 and 7 are a candidate parameterization chosen to be replaced, not a reconstruction of the published model. The project index lists the other documents in this folder and References carries the sources and their status markers.
In brief
The question. During step-up dosing of a T-cell engager, cytokine release syndrome risk often falls as the dose rises. A model in which risk depends on the current dose alone cannot produce that, so something about the dosing history is carrying risk down while dose carries it up. This specifies a model of that something, and asks how large a dose step can be taken, given a particular dosing history, at an acceptable predicted risk.
The mechanism assumed. A dose induces a transient tolerance state that lowers the risk attached to later doses and decays between them. Risk after a dose is then the product of what the current exposure stimulates and what prior exposure has suppressed.
The starting point is somebody else’s model. Li et al. published a repeated time-to-event model of epcoritamab step-up dosing that already has this structure and was fit to patient-level data. This project reuses it. It does not build a new one unless reading the paper shows the published structure cannot be carried to the data available here.
The hard part is the data, not the model. The published model was fit to individual patients with individual pharmacokinetics and event times. What is public is counts: how many patients got a dose, how many had CRS afterwards. Whether the tolerance parameters survive that loss of resolution is the feasibility question in Section 4, and it is answered before anything is said about other drugs.
Out of scope, stated once.
- ❌ A re-analysis of the epcoritamab trials. No patient-level data is available to this project.
- ❌ A dose recommendation. Nothing here is a regulatory-grade CRS risk model, and no clinical regimen should be taken from it.
- ❌ A mechanistic cytokine model. No interleukin-6, no T-cell trafficking, no receptor-level dynamics. Tolerance is an empirical state variable fit to incidence, and its biological interpretation is not part of the claim.
How the answer is reported. Three models are fit to the same public data: current dose only, current dose plus empirical history terms, and the dynamic tolerance model. The tolerance model earns its place only by beating the other two on the same data, and by reproducing the qualification behaviours in Section 9. If it cannot be identified from aggregate counts, the finding that it cannot is the deliverable, and the objective narrows rather than the model growing.
1. Objective
Develop a quantitative model of cytokine release syndrome (CRS) risk during step-up dosing of T-cell engagers (TCEs), using the published epcoritamab repeated time-to-event (RTTE) model as the methodological template.
The model predicts the probability of CRS after each administration as a function of four things:
- the current dose, or the exposure it produces;
- the dose and exposure history before it;
- the tolerance induced by that history;
- the time since the previous dose.
Primary endpoint: CRS Grade \(\ge 2\). Grade \(\ge 1\) is the secondary endpoint. Grade \(\ge 2\) leads because it is the grade that changes clinical management and the grade the published model targets; Grade \(\ge 1\) is reported alongside because it is more frequently tabulated in public sources and carries more events.
The longer-term objective is to determine whether the framework generalizes past epcoritamab, fit to publicly available data from approved oncology TCEs.
2. Central hypothesis
CRS risk is not determined by the current dose alone. A prior TCE dose induces a transient tolerance or desensitization state that reduces the CRS risk of subsequent doses.
Five consequences follow, and each is a prediction the model must be able to make:
- a larger first dose produces greater CRS risk;
- prior exposure reduces the risk of a later dose;
- a very small priming dose induces little tolerance;
- a large step after inadequate priming produces greater risk than the same step after adequate priming;
- tolerance decays, so a long enough interruption restores the risk of an untreated patient.
The behaviour that motivates the whole model is the fourth column of any step-up safety table: CRS risk falls while dose rises. Section 9 makes that and the four others into acceptance tests.
3. Dissecting the epcoritamab model
This is the first work, and nothing downstream of it should start before it is done. Read the main paper and the supplementary material of:
Li et al. (2026). Epcoritamab Step-Up Dosing Regimen Selection and Optimization Using Repeated Time-to-Event Modeling for Cytokine Release Syndrome Risk Mitigation. Clinical Pharmacology & Therapeutics. doi:10.1002/cpt.70362
The deliverable is one filled-in dissection, roughly a page of summary over the four subsections below. Write the answers down even where they are negative: a question the paper does not answer is a parameter this project will have to fix or drop.
3.1 What the model was fit to
- Number of patients, studies, and cohorts.
- Which epcoritamab regimens are represented, and the range of priming, intermediate and full doses in each.
- Number and timing of step-up doses.
- The modelled CRS endpoint, and whether Grade \(\ge 1\) and Grade \(\ge 2\) were both fit.
- What onset-time information was used, and at what resolution.
- How repeat CRS events within a patient were handled.
- How pharmacokinetic (PK) exposure was obtained per patient: measured, predicted from a population PK model, or a typical profile.
3.2 The mathematics
Write out the model as equations, not as a description. Seven pieces:
- the baseline hazard;
- the exposure-driven stimulation term;
- the tolerance or inhibition term;
- tolerance induction;
- tolerance recovery;
- covariates;
- the repeated-event structure.
Give every parameter its interpretation and its units, including the ones the abstract names — the maximum stimulatory effect, \(S_{50}\), \(I_{50}\), \(k_{\rm in}\), \(k_{\rm out}\), any Hill coefficients, and the baseline hazard parameters.
Settle what drives tolerance. Instantaneous concentration, cumulative exposure, an effect compartment, a turnover model, or another state variable. Everything in Section 7 depends on this answer, because it decides whether a dose-only approximation can stand in for exposure.
3.3 Estimation and identifiability
- Which parameters were estimated and which were fixed, and the stated reason for each fixing.
- Uncertainty on the tolerance parameters specifically.
- Which clinical regimens carried the information: the answer is expected to be the dose-escalation cohorts rather than the registrational regimen, and that expectation decides what Section 5 must find.
- Whether tolerance recovery was identifiable at all, or fixed.
- Parameter correlations, and any sensitivity analysis.
3.4 What the model was used to simulate
Document how the fitted model was used to compare priming doses, intermediate doses, two-step against three-step regimens, full-dose risk, prophylactic intervention, and dose delays or interruptions if they were evaluated.
3.5 The question the dissection answers
What is the minimum mathematical structure that reproduces the step-up behaviour, and which features of the data identify each part of it?
Do not design anything broader until that sentence can be answered.
4. The feasibility question
The next question is not whether the framework generalizes across drugs. It is:
Can a useful approximation to the Li et al. model be fit using only publicly available epcoritamab data?
One drug, one framework, one data-availability problem. A pooled cross-drug analysis inherits every difficulty of this question and adds its own, so it waits for the answer in Section 14.
5. Public epcoritamab data inventory
Search publications, supplements, conference abstracts and posters, regulatory review documents, and prescribing information for CRS data reported per dosing occasion. For every cohort or regimen found, record one row per dosing occasion with these fields.
| Field | What it holds |
|---|---|
study, cohort, indication |
Provenance of the row |
dose_number |
Position in the step-up sequence, 1 for the priming dose |
dose, dose_unit, route |
The administration this row is about |
time_since_previous_dose |
Days; blank for dose_number 1 |
previous_dose |
The dose before this one |
priming_dose, intermediate_dose, full_dose |
The regimen this row sits in |
n_dosed |
Patients who received this administration |
n_crs_ge1, n_crs_ge2 |
Patients with CRS at each threshold after it |
crs_grading_system |
Lee 2014, ASTCT 2019, CTCAE, or as stated |
steroid_prophylaxis, tocilizumab_prophylaxis, other_crs_prophylaxis |
Premedication, as reported |
source, table_or_figure, notes |
Where the numbers came from |
Prioritize the dose-escalation cohorts over the registrational regimen. The feasibility question depends on variation in dosing history, not on the approved schedule, and the approved schedule contributes one history no matter how many patients received it. Early-phase cohorts in which several priming and intermediate dose combinations were tried are where the information is; published summaries indicate 17 such combinations were explored in EPCORE NHL-1. Confirming that count, and finding the CRS numerator and denominator behind each combination, is the first extraction to attempt.
Record what cannot be found, in the same table. A regimen reported only as a pooled all-cycles CRS rate is a row that cannot be used, and Section 13 needs the count of those.
6. Model formulation for aggregate data
The published analysis is a patient-level RTTE model. Public data give aggregate incidence after a dosing occasion, so the likelihood changes even where the hazard does not.
For dosing occasion \(j\):
\[ y_j \sim \mathrm{Binomial}(N_j, p_j) \]
with \(N_j\) the number of patients who received that dose, \(y_j\) the number with CRS above the chosen grade threshold, and \(p_j\) the model-predicted probability of CRS after that dose.
Retaining the hazard model, \(p_j\) is the probability of at least one event in the interval before the next dose:
\[ p_j = 1 - \exp\left(-\int_{t_j}^{t_{j+1}} h(t)\,dt\right) \]
and the hazard keeps the published structure:
\[ h(t) = h_0(t) \times \mathrm{STIM}\big(E(t)\big) \times \mathrm{INH}\big(A(t)\big) \]
where \(E(t)\) is the exposure driver of Section 7 and \(A(t)\) is the tolerance state.
Take the functional forms from the paper. Pending Section 3, the placeholders below are the conventional ones,
\[ \mathrm{STIM}(E) = 1 + \frac{S_{\max}\,E^{\gamma}}{S_{50}^{\gamma} + E^{\gamma}}, \qquad \mathrm{INH}(A) = 1 - \frac{I_{\max}\,A}{I_{50} + A}, \qquad \frac{dA}{dt} = k_{\rm in}\,E(t) - k_{\rm out}\,A \]
with \(I_{\max} < 1\) and \(A(0) = 0\) in a treatment-naive patient. In the turnover form, \(k_{\rm out}\) alone sets the tolerance recovery half-life, \(\ln 2 / k_{\rm out}\), which is the parameter that decides what a dose delay does. Replace all three with the published equations at Milestone 1 and note in the same commit anything the substitution changes downstream.
7. The exposure driver
Two implementations, fit in this order.
Version A, dose as the driver. Substitute dose for exposure. This is the simplest test of whether the tolerance structure is estimable from public data, and it is the version that works for every drug and cohort in the inventory, because dose is always reported and PK usually is not.
Version B, typical PK. Generate a typical concentration-time profile per regimen from a published population PK model and drive the model with it, or with a summary of it: early area under the curve, \(C_{\max}\), the concentration at 24 hours, or receptor occupancy where a model for it exists. Version B is closer to the published analysis and is preferred wherever a usable population PK model is public.
Write the code so the driver is an argument. \(E(t)\) enters the hazard and the tolerance equation at one place each; nothing in the tolerance architecture should know which version produced it. That is what makes Version B a substitution rather than a rewrite, and it is also what makes the Section 14 comparison of the two possible.
8. The model hierarchy
Fit three models to the same data and the same endpoint, in this order.
| Model | Structure | What it establishes |
|---|---|---|
| 0 | \(\mathrm{logit}(p_j) = \alpha + \beta \log D_j\) | The benchmark. Current dose only, no history |
| 1 | Model 0 plus empirical history terms, such as \(\log(D_j/D_{j-1})\) or cumulative prior dose | Whether history improves prediction at all, without a tolerance state |
| 2 | The dynamic tolerance model of Section 6 | The target model |
Model 0 is the null and must be reported whatever happens to the others. Model 1 is descriptive and is not the intended final model; its purpose is to separate two claims that are otherwise confounded, that history matters and that a tolerance state is the right description of how it matters. Model 2 has to beat Model 1 as well as Model 0 to be worth its parameters.
Compare on the same criterion across all three, on the primary endpoint, and report the secondary endpoint fit for each.
9. Qualification behaviours
Five behaviours a useful model reproduces. These are simulation checks on the fitted model, run before any conclusion is drawn from it, and a model that fails one has failed a test rather than revealed a finding about biology.
| # | Behaviour | What it tests |
|---|---|---|
| 1 | The same full dose carries higher risk on first administration than after prior exposure to that dose | That current dose alone is inadequate |
| 2 | \(D_1 < D_2 < D_3\) with \(P(\mathrm{CRS}_1) > P(\mathrm{CRS}_2) > P(\mathrm{CRS}_3)\) | Tolerance can outrun the dose increase |
| 3 | An excessively small priming dose lowers risk at dose 1 and raises it at dose 2 | Tolerance induction saturates at low exposure |
| 4 | Two regimens reaching the same target dose by different paths give it different risk | The path to a dose changes its risk |
| 5 | A long enough gap before a dose restores something close to naive risk | Tolerance recovery is in the model and is signed correctly |
Behaviour 3 is the external one. The published elranatamab dose-optimization work compared alternative priming regimens, and whether a smaller first priming dose left more CRS at the second dose is a qualitative result this model can be held to without being fit to it. Behaviour 4 is the one that matters for the use case in Section 16: for the paths \(1 \to 10 \to 100\) and \(10 \to 30 \to 100\), the 100-unit dose need not carry the same risk.
10. Extension to other T-cell engagers
Only after Section 14 is answered. Candidates, in priority order:
- Elranatamab. First, because alternative priming regimens were studied and published, which is the variation this model needs.
- Teclistamab.
- Glofitamab.
- Mosunetuzumab.
- Talquetamab.
Include a drug only where public sources report CRS by individual dosing occasion, across more than one dosing history. Approval status is not the criterion. A drug reported only as a total CRS rate for one approved regimen contributes a single point and no information about tolerance.
11. The cross-drug dataset
The Section 5 schema, with these fields added:
| Field | What it holds |
|---|---|
drug, target |
Molecule and target antigen |
normalized_dose |
Dose on a scale comparable across drugs |
previous_previous_dose |
Two doses back, for three-step regimens |
anti_target_pretreatment |
Prior therapy against the same target, such as chimeric antigen receptor (CAR) T-cell therapy |
The initial normalization is dose as a fraction of the target dose,
\[ D^{*} = \frac{D}{D_{\rm target}} \]
which is an empirical scaling and nothing more. An exposure-based normalization is preferable and is what Version B of Section 7 makes possible.
anti_target_pretreatment earns its column. Prior CAR T-cell therapy is reported to reduce the maximum stimulatory effect in the epcoritamab model by about 70%, in a fifth of the modelled patients (References, entry 1, unverified). A pooled fit that ignores it will attribute that reduction to a tolerance parameter instead.
12. The cross-drug question
Can one structural stimulation/tolerance model describe step-up CRS behaviour across several T-cell engagers, using drug-specific exposure scaling with common or partially shared tolerance parameters?
The parameters that plausibly differ by drug are exposure-response potency, baseline CRS propensity, PK, route, and maximum CRS risk. The parameters that plausibly do not are the shape of tolerance induction, the tolerance recovery half-life, and the maximum tolerance effect.
Do not assume the second list is shared. Test it. Fit shared and drug-specific versions of each candidate and report which pooling the data support. A shared tolerance half-life that is assumed rather than tested is the finding this project would most easily fake.
13. Limitations of public aggregate data
The public-data model is not equivalent to the original RTTE analysis, and the gap is stated rather than modelled away.
- No exact CRS event times.
- No individual PK.
- No recurrent-event history within a patient.
- Different patients contribute to different dosing occasions, because of discontinuation between steps, so \(N_j\) falls with \(j\) for reasons unrelated to risk.
- No within-patient correlation can be represented.
- Grade \(\ge 1\) and Grade \(\ge 2\) are inconsistently reported.
- Grading systems differ across studies and eras.
- Prophylaxis is incompletely reported and is confounded with dose level and calendar time.
- Some tolerance parameters will not be independently estimable.
Where a parameter cannot be identified, say so and fix it. Four acceptable responses, in order of preference: fix it to the Li et al. estimate; place an informative prior on it from Li et al.; estimate only relative tolerance effects; or simplify the structure until what remains is identifiable. Adding complexity to cover an identifiability failure is not on that list.
14. Decision point
Answer these before broadening the project. Each has a written answer in the project, not an impression.
- Recovery. Can public epcoritamab data recover the qualitative behaviour of the published RTTE model?
- Separation. Can the data distinguish a current-exposure effect from a prior-exposure effect, or do the two trade off along a ridge?
- Identifiability. Which tolerance parameters are estimable from aggregate counts, and which have to be fixed?
- Cost of aggregation. How much information is lost by using aggregate incidence instead of patient-level RTTE data? Simulate patient-level data from the Section 6 model, aggregate it to the shape of the public data, refit, and compare. That comparison answers this question without any patient-level data.
- Exposure. Does published PK materially improve the fit over dose alone?
If the answers are unfavourable, narrow the scientific objective. A qualitative model that reproduces Section 9 with fixed tolerance parameters is a result. An unidentifiable pooled model fit to force the original objective through is not.
15. Milestones
| # | Milestone | Deliverable |
|---|---|---|
| 1 | Understand the published model | The Section 3 dissection: the mathematics, which parameters were estimated against fixed, and which data features identify tolerance |
| 2 | Public epcoritamab inventory | The Section 5 table, filled, with the count of unusable rows, and a verdict on whether there is enough to fit an aggregate model |
| 3 | Reproduce the structure | The published model implemented and simulated, not fit. Verify that risk rises with exposure in a naive patient, that tolerance develops after exposure, that successive doses are attenuated, and that a gap restores risk |
| 4 | Aggregate-data fit | Models 0, 1 and 2 of Section 8 fit to the Section 5 data, on Grade \(\ge 2\) with Grade \(\ge 1\) reported alongside |
| 5 | External test | Section 9 behaviour 3, tested against published elranatamab priming data with no refitting |
| 6 | Cross-drug model | Only if Section 14 justifies it: a pooled or hierarchical fit across drugs |
Milestone 3 comes before Milestone 4 deliberately. A structural implementation that reproduces the four qualitative behaviours by simulation is a working model of the mechanism, and it is worth having even if Milestone 4 shows the public data cannot estimate the parameters.
16. The intended use
Given a proposed first dose, one or more step-up doses, a target dose, and the intervals between them, predict:
- the probability of Grade \(\ge 1\) CRS after each administration;
- the probability of Grade \(\ge 2\) CRS after each administration;
- the tolerance state before each dose;
- the effect of changing the size of any one step;
- the effect of changing any one interval;
- whether adding a priming dose materially reduces risk at the target dose.
The practical question all of that serves:
How large a dose step can be taken, given the dosing history, while holding predicted CRS risk at an acceptable level?
17. Guiding principle
Start by reusing and simplifying a clinically validated model, then find out how far public data carry it. Build a new CRS tolerance model from scratch only if reading the epcoritamab paper shows its structure is unsuitable for that application, and record what made it unsuitable if that happens.