Evidence

Struck-through cells are the original manuscript draft's figures, superseded after two extraction bugs were found and fixed — not hidden, just clearly marked as historical.

The 11,354-stay cohort size above is the published Sepsis-3 table this manuscript draft used — now a sensitivity cohort. The primary cohort is 13,192 stays (MIMIC-IV v3.1, Sepsis-3 recomputed; see docs/DECISIONS_H3.md), which this historical verification predates.

The AUROC gap (0.900 → 0.791) survived a 15× difference in underlying vasopressor-dose row counts almost untouched — 0.109 verified vs. ≈0.108 in the original, inflated-data run, so the gap itself is not an artifact of the data bug. Exploratory work in review (exp-persistence, not pre-registered) finds what the gap is actually made of: SOFA's dose-coded cardiovascular and total terms carry the currently running treatment's dose tier into the state, and that effect runs largely through treatment persistence rather than a SOFA-specific mechanism. Once an "infusion running right now" indicator is included, SOFA's own terms add almost nothing on top of it — (A+I) minus (E+I) is 0.000 [-0.000, +0.001] at the decision point, and under 0.01 at every offset tested.

Full diagnostic trail — including the false starts — in ROADMAP.md.

Everything on this page evaluates a feature's relationship to next-action prediction specifically. That's a deliberate scope, not an oversight — the same feature's status can differ entirely for a different task. A cardiovascular-subscore value that's treatment-confounded for predicting the next vasopressor action may be exactly the right feature for predicting mortality: mortality prediction doesn't carry the "was this information available before the decision" constraint that action-prediction does. None of the figures above should be read as "this feature is bad" in general — only "this feature's value for predicting the next action is inflated by treatment history, by this much." See Terminology for the full distinction this depends on.

Variant D's fix (recompute the total from a MAP-only cardiovascular proxy) removes the treatment-confounding this project measures — but it isn't free. The MAP-only branch of the scoring rule (score_map = 1 if MAP < 70 else 0) is a two-level signal that cannot distinguish a patient who is healthy and untreated from one who is successfully treated and still critically ill — the second patient's MAP looks the same as the first's once vasopressors have done their job.

This is a genuine tradeoff, not an argument that sanitization is the wrong approach: predictive purity (Variant D/E's lower action-recoverability) is bought at a real cost in clinical validity (losing the "needed treatment to reach this value" signal). Whether that cost is acceptable is task-dependent (see the scope note above) — and is exactly what motivates disentangling severity from treatment history as two separate, explicit terms, rather than collapsing them into one composite score either way.

The concrete example above is real, but does it add up to variant D/E being meaningfully worse at predicting mortality across the whole cohort? Trained the same way as Experiment 2 (logistic regression / random forest / gradient boosting, clustered bootstrap CIs) but predicting in-hospital mortality from the state at a single fixed 24h decision point — matching SOFA's own original validation convention — rather than the next action at every timestep:

Reported as the actual result, not adjusted toward the anticipated one: sanitizing the state costs almost nothing in mortality-prediction accuracy, despite costing a lot in next-action predictability. This does not confirm the qualitative concern above — at least not as measured by whole-cohort mortality prediction at a fixed timepoint. The individual-patient failure mode is still mathematically real; it just doesn't appear to aggregate into a large mortality-AUROC loss. Full figures: results/experiment6_mortality_vs_action_recoverability.json.

Theorems 1–2 are proofs about the cardiovascular subscore specifically. Does the diagnostic generalize to a different SOFA subscore, or was it a one-off property? Checked against respiratory SOFA — deliberately isolated: this does not modify the shared `sofa_resp` function or any of Experiments 1, 2, 3, or 6's already-published figures, all of which continue to use the existing implementation unchanged.

The official rule (Vincent et al., 1996) scores respiratory SOFA from the PaO₂/FiO₂ ratio, but its two highest tiers (3, 4) additionally require the patient to be on mechanical ventilation — a conditional this project's own sofa_resp does not implement. Checking whether the same non-identifiability pattern as Theorem 1 holds here turned up something more precise: it doesn't, not in the same form. Fixing ventilation status doesn't collapse the score to a constant the way fixing any nonzero dose does for cardiovascular SOFA — a ventilated patient's score still varies across all five PF tiers. What actually happens is narrower: a score-shift collision — for PF in [100, 200), two patients with the identical PF ratio get different official scores (3 vs. 2) purely as a function of treatment status.

What this means for the general framework: the diagnostic generalizes, but not uniformly — a second confirmed instance with a genuinely different mathematical shape (a bounded-range collision, not an unbounded-range constancy) is what starts to separate "an audit of one score" from "a methodology." Full figures: results/experiment7_respiratory_sofa_summary.json, proof: FORMAL_ANALYSIS.md §4.5.

A reviewer suggestion proposed a specific alternative to Variant D: instead of stripping treatment signal out of the severity term, keep severity untouched and add explicit treatment-history features alongside it — testing whether that recovers Variant D's small mortality-predictive-validity loss (0.011 AUROC, above) without reintroducing Experiment 2's action-recoverability gap. Full design: docs/PHASE4_VARIANT_F_SPEC.md.

Variant F = Variant D's severity term (unchanged) plus two explicit treatment-history features, deliberately chosen to avoid re-exposing the raw dose value Variant D removes: hours on vasopressor (continuous duration, ending at the decision boundary) and hours since dose-tier change (regimen recency, tied to the same tier thresholds the SOFA score itself uses — not raw rate, which titrates too often to carry signal). The success criterion was stated before the experiment ran: F would be useful if its mortality AUROC moved toward A's while its action-recoverability stayed close to D's — action-recoverability rising toward A instead was named in advance as evidence against the hypothesis.

The pre-registered falsification condition was met, unambiguously: F's action-recoverability didn't drift toward A's, it exceeded it. Two purely temporal features — how long a patient has been on a vasopressor, and how long since their dose tier last changed — are on their own more predictive of the next vasopressor decision than the entire physiology-plus-severity state. This sharpens the treatment-persistence mechanism already visible in the offset-decay curve below: vasopressor courses are highly autocorrelated, and duration/recency features encode that autocorrelation almost losslessly, independent of physiology. It's independent confirmation of a point made elsewhere on this site: the predictive power this project measures was never really about SOFA's construction quirk specifically — it's ordinary treatment persistence, and this experiment just gives a cleaner, more direct instrument for it than the original AUROC gap. This is not evidence that Variant D's own design is wrong — it shows that any specific choice of history feature carries a real risk of reconstructing the action independent of physiology, and that risk has to be tested per feature set, not assumed away. Full figures: results/experiment8_variant_f_summary.json, discussion: FORMAL_ANALYSIS.md §7.5.

The pre-registered paired-bootstrap test has been run: Delta = AUROC(0) minus AUROC(8) = 0.147, 95% CI [0.140, 0.154] (bin-index offsets, common rows, logreg) — Prediction A, per docs/DECISIONS_H3.md. A synthetic ground-truth check (exploratory work in review, exp-simulation) finds this same rule fires whenever a state encodes a currently-running treatment under realistic persistence, whether or not a SOFA-specific mechanism is present — so Prediction A on its own does not separate the SOFA-construction mechanism from ordinary treatment persistence. Exploratory work in review, none of which changes the decision: persistence, label alignment, paired CIs, dose decisions, simulation. See Status for the full run.