99 SMALL PROBLEMS · No. 02 RESEARCH PREVIEW · v0.1.0-alpha
Antigen-tail Check
Are two expression-matched populations actually comparable?
The average cell is a convenient fiction. Compare the cells you have, not just the mean they share.
New: paired-antigen audit, overlap bounds and mechanism-evidence map →
The distribution is the comparison
Cumulative fraction at or below each expression cutoff.
What the response assumption changes
Unresponsive share under an assumed Hill mapping. Not survival.
Here T is the half-response expression level, not a minimum recognition threshold. Both populations use the same mapping; h is not a molecular cooperativity estimate.
Keep the two claims separate
| Quantity | Population A | Population B |
|---|
Event counts are not biological replicate counts. No p-values, confidence intervals, efficacy estimates or clinical recommendations are generated.
THE TOOL, NOT THE ORACLE
A distribution audit.
Not a tumor-response simulator.
Antigen-tail Check compares two empirical or synthetic expression distributions. It measures tail differences exactly, then asks what those differences would imply under an explicitly assumed, shared response mapping. It does not learn that mapping from fluorescence.
Useful models for assumptions with expensive ambitions.
Read the complete model and validation plan →
Download the mathematics · Markdown →
Download the calculation code →
Release notes and source archive →
Why the mean is insufficient
For a nonlinear response g, averaging expression before applying the response need not agree with averaging cell-level responses. This is a mathematical property, not evidence that any particular treatment has this response.
g(a; T, h) = ah / (ah + Th)
R(T, h) = 1 − Σi wi g(ai; T, h)
A useful bound without a fitted response curve
For the same nondecreasing response g in [0, 1] applied to both populations, the absolute difference in average response is bounded by the maximum cumulative-distribution separation D. This is an exact statement about the supplied distributions, not a confidence bound on unobserved biological populations.
D = supt |FA(t) − FB(t)|
|EA[g] − EB[g]| ≤ D
The bound uses all thresholds. A small gap over a selected sweep alone does not bound responses outside that range. If the CDFs cross, which population has the larger low-expression fraction depends on the cutoff.
Mechanism matters more than the label “positive”
In a published CD20 CAR-T system, lysis and activation required different antigen-expression ranges; the lowest tested density with lysis was not the half-maximal response density. These are system-specific observations, not thresholds imported into this tool (Watanabe et al., 2015).
ADC models show how target heterogeneity interacts with payload transfer, growth and bystander effects, mechanisms that can invalidate an independent cell-by-cell response mapping (Wood et al., 2025). Fc immune-complex binding likewise depends on valency and receptor context, and binding does not by itself establish an effector response (Tan et al., 2023).
Measurement is part of the biology
ABC, MESF and relative fluorescence have different meanings; equal unit labels do not establish equal calibration or low-signal resolution (Wang & Hoffman, 2017). This preview therefore blocks comparisons when measurement comparability or tail resolution is unconfirmed, rather than manufacturing a precise answer from an unresolved tail.
A marginal antigen distribution also cannot establish equal accessibility, spatial arrangement, internalization, effector susceptibility or observation-time response. Use a held-out functional mixture experiment to test the shared-response assumption; see the validation plan.