Feedback-Robust AI for Patient Knowledge Graphs

• Clinical patient graphs should contain signal-supported concepts with evidence pointers and typed relations indicating whether data support their signs.Prior monitoring graphs often derive edges from lagged cross-correlation or Granger tests applied to concept activation series.Source: §1 · p. 1
• Clinician titration mixes patient response with policy in action–vital associations, which can take a sign opposite to the drug effect; each surgical case also has few target changes.Source: §1 · p. 1
• Six of 12 estimators declared an average of 11–18 of 19–29 distinct relation estimates significant without calibration under cross-patient action transplant.After calibration, cross-correlation and Granger still assigned ventilator rate→EtCO2 the clinician-policy sign, while design-based estimators recovered the physical sign.Source: §1 · p. 1
• 0.057 transplant and 0.103 circular-shift false concept-level relation instances per graph, versus 12.40 and 10.07 for CKG, were observed on VitalDB under null streams.The graphs combine typed slow relations admitted against negative controls with surrogate-tested beat-level couplings.Source: §1 · pp. 1–2
• Patient-specific PAT–SBP slopes were negative in 94.3% of 2,884 cases and showed early–late correlation 0.67, while 11 slow responses predicted later data no better than population estimates.Source: §1 · p. 2
• ClosedLoopBench evaluates 29 relations with signs fixed by prior knowledge using 3,442 VitalDB cases and negative-control action streams.The controls transplant another patient’s actions or place the patient’s own action steps at random times.Source: §1 · pp. 1–2

• Clinical KGs have been learned from records, ontologies, biomedical sources, and language-model combinations, while monitoring graphs have used correlational edges.This work derives typed relations from monitoring and clinician actions, attaches signal evidence to nodes and edges, and maps concepts to SNOMED CT where possible.Source: §2 · p. 2
• Existing temporal-discovery benchmarks use simulated series, river networks, or assumption stress tests; the authors know of none using real data with an acting agent and signs fixed for both policy and response.Source: §2 · p. 2
• Anesthesia titration can make more drug correlate with less effect, with sign depending on the titration policy; pharmacometric models can recover concentration–effect relations when titration drivers are modeled.The authors estimate policy and response separately, unlike Hızlı et al. (2023).Source: §2 · p. 3
• Conditioning on future treatment causes immortal-time bias, and sequential-trial approaches address it; individual responses are identified through repeated exposures or well-excited induction phases.Source: §2 · p. 3
• For beat-level physiology, prior work estimates baroreflex sensitivity and relates pulse transit or arrival time to blood pressure, while respiratory pulse-pressure variation predicts fluid responsiveness.The paper counterfactually edits signals to assess rationale faithfulness, rather than relying on evidence deletion.Source: §2 · p. 3

• Relations are typed as policy, response, association, or mechanistic coupling, with an expected sign and horizon; an association has no causal reading.The open-loop estimand is the estimate’s limit when actions are independent of physiology.Source: §3 · p. 3
• Negative-control streams contain neither patient response nor clinician policy, so estimates on them measure what schedules and serial dependence alone produce.Controls use transplanted actions, randomly retimed patient actions, or within-patient circular shifts of concept streams.Source: §3 · p. 3
• A response estimate under feedback converges to the open-loop estimand plus a bias determined by clinician policy and unrecorded drivers that clinicians react to.For post-minus-pre contrasts, the bias opposes the response below a crossover horizon and reinforces it above; the estimate reverses sign when that opposing bias is larger.Source: §3 · p. 3
• Restricting control times to those not followed by treatment within the outcome horizon biases event contrasts; with one-directional threshold actions, that bias has the policy’s sign.Using information available before time t removes this bias under sequential exchangeability and overlap.Source: §3 · pp. 3–4
• The propositions specialize the titration paradox and direct-method bias to event-triggered anticipatory controllers, and future-treatment conditioning to event studies.The latter is related to sequential trial emulation.Source: §3 · p. 4

4.1 CONCEPT NODES AND EVIDENCE

• Concept nodes pair a concept with a transient, episodic, or persistent tier and retain the time spans or beat ranges that activated them.Vital concepts use thresholds on monitor values; when only waveforms are available, multimodal heads predict concept states.Source: §4.1 · p. 4

4.2 TYPED SLOW RELATIONS

• Slow concept relations use pooled patient-fixed-effect hazard models, while vital relations use direction-split VARX; estimates are calibrated against null streams and admitted under multiplicity and null-based criteria.An admitted relation is instantiated for a patient only when that record contains an evidence pair within its lag window.Source: §4.2 · pp. 4–5

4.3 BEAT-LEVEL COUPLINGS

• Beat-level PAT–SBP slopes use detrended within-patient beat variation, and patient couplings are tested against surrogates with multiple-testing control.A signed coupling is tested only when the expected-sign share has a 95% CI lower bound of at least 0.90; otherwise the graph stores an abstention and reason.Source: §4.3 · p. 5

4.4 GRAPH ASSEMBLY

• Graph edges store relation type, population sign and estimate with 95% CI, lag, evidence pointers, and a sign-status label.Sign stability is an empirical check, not causal identification; concept responses are never sign-stable because they fail prespecified pharmacological sign checks.Source: §4.4 · p. 5

Data and relations

• 3,442 VitalDB cases contribute 12,653 recorded hours and 29 pre-specified relations: 19 responses and 10 clinician policies.Response signs come from physics, pharmacology, or clinical practice; increases and decreases are separate relations, evaluated at 60- or 120-second horizons.Source: §5 · p. 5

Estimators and metrics

• 12 estimators span lag-based methods and event contrasts, including three design-based estimators.The benchmark reports uncalibrated null discoveries, calibrated real-data admissions by sign, and false admissions under held-out transplant or random-time streams.Source: §5 · p. 5

ClosedLoopBench

• The benchmark uses a 2-second grid and tests null significance across eight transplant draws, with calibrated admissions separated by expected and wrong sign.PCMCI+ uses 30-second block means from 60 cases; the table caption also identifies random-time false admissions and distinguishes lag-based from event-design estimators.Source: Table 1 · p. 6, Figure 2 · p. 6

6.1 TEMPORAL RELATION DISCOVERY UNDER CLINICAL FEEDBACK

• Under transplanted actions, naive event contrast and direction-aware cross-correlation yield 18.25 and 18.12 significant distinct estimates per draw, against about 1.5 expected at nominal level.After calibration, cross-correlation and Granger admit ventilator set-rate relations with the opposite sign, matching the policy of raising rate when EtCO2 is high.Source: §6.1 · pp. 6–7

6.2 PATIENT GRAPHS

• 0.057 false concept-level relation instances per VitalDB graph under transplant and 0.103 under shift, versus 12.40 and 10.07 for CKG.The graph results use 19 replicates of each null stream; CKG uses one replicate and per-patient tests of 48 concept pairs, while the proposed graphs test 176 candidate relations.Source: §6.2 · p. 7, Table 2 · p. 7
• Every graph edge points to its instantiating events, and all 12,346 checked pointers were valid; first-to-second-half replication exceeded presence-matched chance for policy, response, and association relations.Per-patient deviations from pooled concept relations lowered held-out log-likelihood, so the graphs store population relations only.Source: §6.2 · p. 7
• The graphs instantiate respiration-to-SBP, RSA, and PAT-SBP couplings in 100.0%, 98.3%, and 88.8% of eligible patients, respectively.Within-patient nulls produced false PAT-SBP edges in at most 1%; false respiration-to-SBP and RSA edges occurred in 11.5% and 3.2% of patients under a cross-case pairing null.Source: §6.2 · p. 8

6.3 PATIENT-SPECIFIC STRUCTURE

• None of 11 slow response relations was patient-specific, whereas all five pre-specified beat-level statistics passed the patient-specific rule.The PAT-SBP slope had rEL 0.67 [0.63, 0.70]; its case median was negative in 94.3% [93.4, 95.1] of 2,884 cases, while beat-level baroreflex sensitivity fell below the sign bar and was omitted.Source: §6.3 · pp. 8–9, Figure 3 · p. 8

6.4 CONCEPT GROUNDING

• Monitor-supervised concept heads achieved mean AUROC 0.962 ± 0.002, versus 0.865 ± 0.008 for the rule detector and 0.785 for rule-supervised heads.Paired-gain confidence intervals were above zero for the five rate concepts only; monitor-supervised heads passed the counterfactual test for 6 or 7 of 7 concepts across seeds.Source: Table 3 · p. 8, §6.4 · p. 9

Scope and validation

• The surgical cohort is from one center, and the ICU grounding test includes 26 patients; monitor-supervised heads are scored against monitor labels.The authors state that the graphs have not been evaluated by clinicians and are not validated for clinical use.Source: §7 · p. 9

Inference and graph limits

• Calibration does not control random-time false admissions for 9 of 12 estimators, and admission controls errors within—but not across—relation families.The vital-level graph layer yields 1.15 false edges per graph under a 30-second random-time null; false population relations occurred in 7 of 19 transplant and 9 of 19 shift replicates.Source: §7 · p. 9

Scope of patient-specific estimates

• Patient specificity is measured within one record and concerns routine maintenance titration, not repeated or induction-phase exposures.The authors also note that vasoactive and PEEP relations are underpowered, and boluses and surgical stimulation are not time-stamped.Source: §7 · p. 9

Conclusion

• Matched and interrupted-trend designs admitted responses at 2 seconds only with the expected sign, while uncalibrated estimators reported relations under null action streams.The latter is a benchmark finding; the conclusion does not claim that every calibrated estimator avoids false admissions.Source: §8 · p. 9
• The proposed graphs contain 0.06–0.10 false concept-level relation instances per graph under VitalDB null streams, versus 10–12 for correlational construction.The conclusion summarizes the comparison across the tested null streams.Source: §8 · p. 9
• Split-half tests find patient-specific beat-level couplings but no patient-specific slow response among 11 tested responses.Source: §8 · p. 9

AI USE STATEMENT

• Generative AI assistants supported code implementation, analysis scripting, analysis protocols, result re-checking, literature search, reference verification, and drafting and editing.The authors reviewed all AI-assisted work.Source: AI USE STATEMENT · pp. 9–10
• Confirmatory analyses followed protocols fixed before the runs, and every reported number was traced to its analysis output.The core library has unit tests, and every reference was checked against its DOI, arXiv, or proceedings record.Source: AI USE STATEMENT · p. 10
• The authors take full responsibility for the paper’s content, including text, code, claims, and artifacts produced with generative AI.Source: AI USE STATEMENT · p. 10

ETHICS STATEMENT

• The retrospective study used de-identified data released under institutional review board approval, with no patient contact or re-identification attempt.Source: ETHICS STATEMENT · p. 10
• VitalDB is openly available under CC BY 4.0, while MIMIC-IV clinical tables require credentialed access, research training, and a signed data use agreement.The authors report obtaining the required MIMIC-IV access and redistributing no data.Source: ETHICS STATEMENT · p. 10
• The graphs and estimators have not been evaluated by clinicians or validated for clinical decision-making and must not guide patient care.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

• Data sources, preprocessing, calibration, quality gates, benchmark methods, formal analyses, protocols, software versions, and fixed random seeds are documented.The authors state that code, protocols, and analysis artifacts will be released together.Source: REPRODUCIBILITY STATEMENT · p. 10

A.1 COHORTS

• VitalDB contributes 3,442 surgical cases and 12,653 recorded hours; MIMIC-IV-WDB graphs cover 167 records, with relation estimates on 51 validation and test patients.The VitalDB cases come from 3,324 individuals; MIMIC-IV-WDB relation estimates use patients with at least 30 minutes of windows.Source: §A.1 · pp. 15–16, Table 4 · p. 16

A.2 CLINICIAN ACTIONS

• VitalDB action streams include TCI targets, vasoactive infusion rates, and ventilator set-points; volatile-agent steps are derived from end-tidal MAC changes.Bolus drugs are available only as per-case totals without timestamps and are not modeled.Source: §A.2 · p. 16, Table 5 · p. 16
• Action counts include changes in either direction, including starts and stops, while adjustments within 10 seconds are merged into one action.Source: §A.2 · p. 16

A.3 DATA PRODUCTS AND RESOLUTIONS

• ClosedLoopBench uses valid monitor numerics on 2-s bins, while graph and hazard inputs use 30-s median windows with a 15-s stride.The median share of bins with values is 0.89 for MAP, 0.94 for HR, 0.91 for EtCO2, 0.95 for SpO2, and 0.89 for BIS; 3,067 cases have BIS in at least half their bins.Source: §A.3 · p. 17

A.4 CLOCK ALIGNMENT AND CALIBRATION

• Case-start clocks are retained without per-case offsets, and breath-level CO2 is scaled to ventilator EtCO2 numerics using per-case calibration factors.The factor is 0.753 (IQR 0.747-0.758; 2,903 cases) for gain 0.1 and 1.004 (0.997-1.012; 536 cases) for gain 0.075; action timestamps agree with native ventilator set-rate records within 1 s in all checked cases.Source: §A.4 · pp. 17–18

A.5 WINDOWS FOR THE CONCEPT MODELS

• Waveform concept models use 30-s windows, exclude windows with over 20% missing samples, and are trained on MIMIC-IV-WDB with rule- or monitor-derived supervision.Monitor and rule labels agree least for respiratory concepts: rules label 45% of training windows bradypneic, compared with 1.3% for monitor labels.Source: §A.5 · p. 18, §B.2 · p. 18, §B.3 · p. 20

B.4 PERSISTENCE TIERS; B.5 BEAT CONCEPTS

• Persistence tiers group concept episodes using concept-specific duration cutoffs, while beat concepts use quality-controlled beat and breath tables and cohort-relative thresholds.Prolonged PAT is defined within each case; the concept can be off or unobserved during the largest PAT rises because beat matching has a finite timing window.Source: §B.4 · p. 20, §B.5 · pp. 20–21

B.5 BEAT CONCEPTS

• Irregular-R-R windows separated atrial fibrillation from sampled sinus-rhythm cases with AUROC 0.93, but beat-validity gating reduced AUROC to 0.67.The AUROC was 0.92 after restricting to windows with monitor HR agreement and away from recording edges; 64.2% of irregular-R-R windows in 300 sampled cases fell within 10 minutes of a recording edge, versus 4.8% of observed off-concept windows.Source: §B.5 · p. 21

C.1 DATA AND ACTION EVENTS

• ClosedLoopBench uses all 3,442 VitalDB cases, with actions represented by recorded titrations and set-point changes; 171,758 total recorded events include starts and stops.Titration events exclude selected zero transitions, while volatile exposure steps are derived from changes in rolling measured end-tidal MAC.Source: §C.1 · pp. 21–22

C.2 RELATIONS

• The 29 benchmark relations have expected signs fixed by domain knowledge, but concordance measures agreement with prespecified expectations, not causal ground truth.Gas-exchange physics is the strongest basis; pharmacological and physiological signs depend on context, dose, and timing, while policy signs encode documented practice rather than an observed decision rule.Source: §C.2 · pp. 22–23, Table 11 · p. 22

C.3 ESTIMATORS

• The benchmark compares event-based contrasts, lagged correlations, Granger, PCMCI+, VAR-LiNGAM, and VARX estimators; the typed pooled estimator equals VARX under its admission rule.Event designs include matched controls, interrupted trends, and sequential-trial contrasts; policies use the pre-event vital trend as their outcome.Source: §C.3 · pp. 23–24
• 200 paired case-bootstrap replicates quantify uncertainty for all estimators, with VAR-LiNGAM using the first 50.The same weight matrix is applied to every arm; event designs resample case sums of contrasts, while lag-based estimators resample case curves, case estimates, or case sufficient statistics.Source: §C.3 · p. 24

C.4 NEGATIVE CONTROLS, ADMISSION RULE AND METRICS

• Transplant controls permute each action’s users by seeded derangements, while random-time controls place each case’s own action steps at sorted uniform random times.Transplant streams are placed on each recipient case’s clock by elapsed time from case start and truncated to its duration; each action has its own derangement, with K = 8 draws using fixed seeds.Source: §C.4 · pp. 24–25
• Relations are admitted only if the CI excludes 0, the Benjamini-Yekutieli-adjusted p-value is at most 0.05, stability is at least 0.75, and at least 5 cases contribute.An admitted relation is concordant when its estimate has the expected sign and wrong-signed otherwise.Source: §C.4 · p. 25
• Uncalibrated null discoveries count distinct estimates with single-arm CIs excluding 0, while held-out and random-time false admissions are measured after calibration against transplant draws.The uncalibrated metric averages over 8 transplant draws, relations, and distinct estimates; held-out tests calibrate each draw against the other 7, and random-time tests calibrate against all 8 transplant draws.Source: §C.4 · p. 25

C.5 RESULTS AT THE PRIMARY 2 S RESOLUTION

• Across eight held-out transplant draws, every estimator admitted zero relations; design-based estimators gave the physical sign for all four ventilation→EtCO2 relations.Cross-correlation and Granger gave the set-rate relations the positive sign of the clinician policy; PEEP→MAP had the expected sign for 10 of 12 estimators but none admitted it.Source: Table 12 · p. 25, §C.5 · pp. 25–26

C.6 PRE-SPECIFIED PREDICTIONS

• Of six pre-specified predictions, Q1, Q2, Q3, and Q6 held, while Q4 and Q5 failed.The observed null discoveries for Q2 were 18.25, 17.62, and 19.75; Q4 had 35 concordant and 11 wrong-signed admissions, and no specified design admitted FiO2→SpO2 despite expected-sign estimates.Source: §C.6 · p. 27

C.7 SENSITIVITY ANALYSES

• Phase analyses preserved propofol response signs in matched and interrupted-trend designs, while volatile estimates were stable across phases and isolated steps.At 30 s, design-based variants had no false admission under either null stream, and set-rate relations R01 and R02 retained the physical sign in every variant.Source: §C.7 · p. 28

C.8 SECONDARY RESOLUTION: 30 S WINDOWS

• At 30 s, uncalibrated null discoveries reached 15.62 of 18 for the positive-peak rule, while held-out false admissions were at most 0.25 per draw.With random-time streams, the positive-peak rule admitted up to 9 of 18 relations; VARX repeatedly admitted both remifentanil-decrease relations with the wrong sign, while all estimators failed to identify any patient-specific response.Source: Table 18 · p. 29, §C.8 · pp. 29–30

D THEORY AND SIMULATION

• The theory section’s propositions restate drug-titration and direct-method bias, while identifying horizon dependence and policy-determined control-pool bias as its closed-loop-specific contributions.The simulations report that a sequential-trial contrast for an inert drug had confidence intervals excluding zero in 6 of 24 cells at 2 s and 19 of 24 at 30 s.Source: D THEORY AND SIMULATION · p. 30, §C.8 · p. 30

D.1 CLOSED-LOOP MODEL

• The closed-loop model represents vitals as a stable physiological loop driven by drug concentration, unrecorded disturbances, and noise, with clinicians changing actions in response to displayed vital statistics.It distinguishes recorded-reactive, field-reactive, and anticipatory clinician policies.Source: §D.1 · p. 30

D.2 SIGN REVERSAL

• The theory identifies horizon-dependent sign reversal: a faster driver than drug effect site predicts wrong-signed estimates at short horizons in all nine simulator parameter combinations.For a recorded-reactive clinician, the naive contrast’s crossover horizon was 11–53 s for persistence times of 5–104 s; the simulator’s inert-drug contrast changed from +0.96 bpm at 60 s to −0.34 bpm at 120 s.Source: §D.2 · p. 32, Table 19 · p. 32

D.3 CONTROL POOLS

• Conditioning controls on future inaction adds a bias whose direction follows the clinician’s policy; for a corrective policy, that bias opposes the true effect.Under sequential exchangeability and overlap, the eligible control-pool estimator identifies the per-decision intention-to-treat effect.Source: §D.3 · p. 33
• Under a corrective policy, control-pool bias reinforces the titration paradox; two-sided actions can cancel, while alarm-triggered checks violate overlap and require exclusion or external variation.Excluding controls based on later treatment or selecting “clean” treated events also conditions on post-baseline information; the ITT contrast retains all events.Source: §D.3 · pp. 33–34
• Pooled sequential trials compare eligible at-risk times with versus without a decision, whereas same-patient matching is not equivalent because refractory periods make similar controls tend to precede events.Among eligible non-alarm-triggered times when the recorded statistic crosses the event-direction threshold, routine-check occurrence—and thus clinician action—is independent of physiology.Source: §D.3 · p. 34

D.4 SIMULATOR

• The simulator uses 1-s physiology, 2-s monitor numerics, and 30-s windows, with sustained-step and per-decision ITT truths and patient-cluster bootstrap confidence intervals.Simulated patients contribute 2 h after a 10-min burn-in; patient-specific gains vary by log-normal factors while retaining their signs, and clinician policies include recorded, reversed, field, and plan variants.Source: §D.4 · p. 34
• The simulator compares naive, pre-trend, matched, kink, exogenous-only, direct ARX, and decision-statistic matching estimators, with the latter using routine-path events and eligible same-patient controls.Decision-statistic matching excludes alarm-triggered checks and uses horizons up to 110 s within the 120-s refractory period; the future-inaction pool excludes controls with a change in the next 111 s.Source: §D.4 · pp. 34–35

D.5 SIMULATION RESULTS

• Across 60 simulated cohorts, remifentanil→HR wrong-sign estimates decreased with horizon, while pre-trend contrasts were 10–14 times the truth despite never having the wrong sign.The share of wrong-signed estimates was lowest when designs conditioned on pre-event trajectories or lagged vitals; zero wrong-sign estimates did not establish unbiasedness.Source: §D.5 · p. 35, Table 21 · p. 35, Table 22 · p. 36
• With an inert drug, direct ARX regression produced nonzero estimates under closed-loop clinicians, whereas all open-loop confidence intervals covered zero; future-inaction controls also biased active-drug effects wrong-signed at 10–60 s.For the inert drug, the future-inaction pool was biased upward by +0.49 to +0.93 bpm; eligible-pool contrasts were closer to the paired ITT truth.Source: §D.5 · pp. 35–36, Table 23 · p. 36
• When clinicians used unrecorded field or plan information, eligible controls were biased; on the alarm path, poor overlap produced large biases, and the grid sequential-trial contrast failed its prespecified simulator check.The alarm-path median matching distance was 0.13 versus 0.006 on the routine path; at 30 s, 19 of 24 inert-condition cells had a CI excluding zero, against a maximum intended share of 10%.Source: §D.5 · p. 37, Table 25 · p. 37
• Residualized ARX identified the sign of planted beat-level MAP→HR coupling in 121 of 134 non-ambiguous cells (90.3%) after accounting for estimated bias.The method removes slow components with a centered moving average before fitting HR on its own lags and MAP lags; sign identification depends on the planted gain exceeding residual bias.Source: §D.5 · p. 37, Table 26 · p. 38

E.4 ADMITTED RELATIONS / E.5 PRE-SPECIFIED SIGN CHECKS

• Of population-level relations admitted in H1, 12/28 association, 23/33 policy, and 9/21 response relations recurred with the same sign in H2; all seven policy sign checks were correct, but none of six response checks was.Because the response family failed its sign checks, none of its relations was marked sign-stable.Source: §E.4 · p. 40, Table 29 · p. 40, §E.5 · p. 40

E.6 NULL ADMISSIONS AT THE POPULATION LEVEL

• Across 176 candidate relations, each null replicate admitted an average of 0.42 relations under transplant and 0.63 under shift controls; at least one was admitted in 7/19 and 9/19 replicates, respectively.Testable null p-values below 0.05 occurred in 5.7–7.9% of tests per family and null kind, above the nominal 5%.Source: §E.6 · p. 40, Table 33 · p. 42

E.8 HELD-OUT LOG-LIKELIHOOD OF CONCEPT ONSETS

• On VitalDB, typed relations improved held-out onset likelihood over base only when unobserved-source indicators were dropped (+0.019 nats per onset), while the per-patient model was 0.257–0.258 nats per onset below pooled.On MIMIC-IV-WDB, pooled, typed, CKG-gated, and shrunk-patient models did not differ from base; the per-patient model was also below the shrunk-patient model.Source: §E.8 · p. 44, Table 35 · p. 44

E.9 PATIENT-LEVEL DEVIATIONS

• Empirical re-testing admitted no patient-level deviations on real data or null replicates, and adding penalized patient-specific deviations lowered held-out likelihood by 0.257 [0.241, 0.274] nats per onset.The initial score tests admitted 2,434 deviations in 1,471 patients on real data, but the empirical-p-value re-test admitted none; instantiated graph relations therefore use population estimates rather than patient-specific weights.Source: §E.9 · p. 44

F.1 BEAT EXTRACTION AND QUALITY CONTROL

• 2,954 cases had at least 20 minutes of valid beats after quality control; ECG, arterial pulses, PPG feet, and capnogram phase were extracted using defined detectors.The case flow began with 3,442 cases; 2,944 had at least one usable epoch.Source: §F.1 · p. 45

F.2 DELAY-AWARE PULSE ARRIVAL TIME

• 2,884 cases had an estimable PAT–SBP slope after delay-aware PPG-foot matching accounted for a median per-case device delay of 0.655 s.PAT includes the per-case device delay, so only within-case variation is interpreted.Source: §F.2 · p. 45

F.3 EPOCHS AND STATISTICS

• Couplings were summarized in 5-minute epochs using PAT–SBP slope, PPV/SPV, RSA, and sequence baroreflex statistics; a population sign required a 95% CI lower bound of at least 0.90 for expected-sign case share.Epoch inclusion and controlled-ventilation criteria were prespecified; population PPV, SPV, and RSA summaries used controlled-ventilation epochs.Source: §F.3 · pp. 45–46

F.4 NULLS AND SIGNAL-PROPERTY SURROGATES

• Two within-case nulls tested whether PAT–SBP sign patterns depended on beat alignment, while signal-property surrogates tested patient-specificity without the coupling.The nulls used shifted SBP or SBP from another epoch of the same case; metric-specific surrogates preserved marginal signal properties while breaking coupling.Source: §F.4 · p. 46
• Per-patient surrogate tests for mechanistic graph edges were specified in App. H.7; the baroreflex edge was excluded because its population sign failed the positive-control rule.The appendix also specifies evaluation of these per-patient tests on null data.Source: §F.4 · p. 46

F.5 POPULATION RESULTS

• The PAT-SBP sign is unchanged when PAT quality control is relaxed (93.6-93.9%); regressing PAT on detrended SBP and PPG amplitude decreases median slope by 15%, with 92.4% of cases staying negative.Source: §F.5 · p. 46

F.6 PATIENT SPECIFICITY

• No slow drug or ventilator response relation is patient-specific at either resolution; per-case means have higher MSE than pooled means in most tested contrasts.This holds for the 11 relations tested at 30 s and 2 s, and for the registered 18-relation protocol.Source: §F.6 · pp. 48–49

F.7 CONSTRUCT-VALIDITY CHECKS

• Four of six counted construct-validity checks hold, one is reversed, and one is not shown.The CV3 result is dominated by one extreme propofol concentration; excluding that epoch gives −0.017 [−0.031, −0.001].Source: §F.7 · p. 49, Table 42 · p. 49

F.8 MONITOR DISPLAY LATENCY

• Monitor HR lags beat HR by 6.94 s [6.88, 7.02], and monitor MAP lags beat MAP by 5.95 s [5.83, 6.02].The expected-sign lagged HR-on-MAP regression occurs in 24.8% of cases on monitor numerics versus 53.7% on beat-derived series.Source: §F.8 · p. 50

G.1 COHORT, SPLITS AND MODELS

• The MIMIC-IV-WDB test cohort comprises 30 records, with 26 processed records; concept heads share a multimodal architecture and are trained on monitor or rule labels.The training split contains 140 records and the validation split 30; the primary test split is separate by patient.Source: §G.1 · p. 50

G.2 MONITOR REFERENCE AND TIME ALIGNMENT

• For pressure concepts, the rule detector uses sustained 10-s subwindow extrema while the monitor reference uses the 30-s numeric median, and the rule detector has higher AUROC.Its pressure AUROCs are 0.988 for hypotension and 0.994 for hypertension, so the paper claims no AUROC gain for pressure concepts.Source: §G.2 · p. 51

G.3 PER-CONCEPT RESULTS

• On validation, mean AUROC is 0.967 ± 0.001 for monitor-supervised heads, 0.885 ± 0.017 for rule-supervised heads, and 0.800 for the rule detector.On the held-out test patients, monitor-supervised heads rank windows better, with paired-gain CIs above zero for the five rate concepts only.Source: §G.3 · p. 51

G.4 COUNTERFACTUAL FAITHFULNESS PROTOCOL

• Faithfulness testing edits signals, evidence-pointer windows, and input modalities, with prespecified criteria for target tracking, pointer behavior, and modality effects.The protocol uses rate and pressure counterfactual edits, pointer-window substitutions, and modality masking.Source: §G.4 · pp. 52–53

G.5 FAITHFULNESS RESULTS

• For rule-supervised seed 1, the rule estimate is within 5% of edited targets for 96% of ECG, 92% of PPG, and 89% of respiration edits.Faithfulness criteria fail for selected bradycardia and bradypnea cases; sinusoidal interference is not interpretable for respiration because it falls in the tachypnea range.Source: §G.5 · p. 53

G.6 EVIDENCE-DELETION METRICS WITHOUT RE-RUNNING THE MODEL

• Stored-activation evidence-deletion metrics are uninformative because they do not rerun the model and cannot test whether evidence drives predictions.For every model, sufficiency is zero because the rationale windows are exactly the highest-probability windows.Source: §G.6 · pp. 54–55, Table 48 · p. 55

H.1 GRAPH SCHEMA

• Patient graphs store population relation estimates with evidence pointers; vital-level relations use a single transplant draw, while concept-level relations use null-calibrated admission rules.Concept responses are never classified sign-stable because their family fails prespecified sign checks.Source: §H.1 · p. 55, §H.2 · p. 56

H.3 INSTANTIATION AND EVIDENCE POINTERS

• Pointer rules tie relation instances to exposure and outcome events within specified lag windows, and pointers document provenance rather than patient-specific relation signs.A presence rule would create 166,563 VitalDB concept-level instances, of which 96,309 have an in-window evidence pair.Source: §H.3 · pp. 56–57

H.4 CORRELATIONAL KG CONSTRUCTION (CKG)

• CKG emits temporal edges using lagged cross-correlation and Granger tests, plus co-occurrence edges, without multiplicity control, negative-control calibration, or pointers.It averages 188.11 edges per VitalDB graph before removing mirrored or paired edges.Source: §H.4 · p. 57

H.5 GRAPH SIZE

• VitalDB graphs with beat-level content are the 2,954 cases passing beat-level quality control; the remaining 488 record fast-relation registries without beat content.MIMIC-IV-WDB graphs have association relations only and no action records or beat layer.Source: §H.5 · pp. 57–58

H.6 FALSE RELATION INSTANCES UNDER NULL STREAMS

• Feedback-robust graphs average 0.057 false concept instances per graph under transplant nulls and 0.103 under shift nulls; CKG yields 12.63 and 10.18, respectively.The CKG comparison uses per-patient tests and is not a matched test; null-admitted relations can be instantiated in 90–100% of MIMIC-IV-WDB graphs.Source: §H.6 · pp. 58–59
• At 30 s under a random-time input null, EtCO2 rising → ventilator rate↑ is admitted with all eight transplant calibrators and yields 1.15 false vital-level edges per average graph.No vital-level relation is admitted in the null-versus-null test or at 2 s under random-time input.Source: §H.6 · p. 59

H.7 FAST-COUPLING LAYER

• F1 and F2 use respiratory-phase surrogates, while F4 tests within-epoch PAT–SBP slopes and stores an undirected association when Holm control and pointer criteria pass.Each patient needs at least three tested epochs; F1 and F2 use controlled-ventilation epochs, while F4 uses all usable epochs.Source: §H.7 · p. 59
• 2.81 [2.80, 2.83] fast edges appear on average in graphs with beat content; 99.7% [99.5, 99.9] of eligible graphs contain at least one.F4 is instantiated in 2,554 patients; 95.1% of its 62,304 pointers have an epoch CI below zero, and none has a positive slope.Source: §H.7 · pp. 59–60
• N1 circular shifts preserve phase locking under nearly periodic controlled ventilation, so their F1 and F2 rates measure a property of the null, not the rule’s false-edge rate.The F4 N1 rate is 0.1%.Source: §H.7 · p. 60
• N2 yields fast edges in 0.5% [0.3, 0.8] of eligible graphs, while N-b yields 1.0% false F4 edges and N3 has 11.5% false F1 edges and 3.2% false F2 edges.N2 is exchangeable with the surrogates; N-b is not. N3 false F1 edges concentrate when paired breaths-per-beat ratios match within 5%.Source: §H.7 · p. 60

H.8 CASE STUDIES

• Case 2706’s graph has three fast edges, each with patient-level p = 0.002 and Holm-adjusted value 0.006; its F4 slope is −0.45 ms/mmHg [−0.81, −0.12].The case was selected by a prespecified rule among cases with an instantiated PAT-SBP edge; Figure 4 depicts its graph and remifentanil target alongside hypotension episodes.Source: §H.8 · p. 60, Figure 4 · p. 61
• Case 52’s sign-stable relations include policy links from rising MAP and HR to remifentanil increases, and from rising EtCO2 to ventilator-rate increases.It also has five sign-stable vital-level response relations; the remifentanil-increase-to-hypotension concept response is sign-unresolved, and 13 other instances are unconfirmed.Source: §H.8 · p. 61
• Case 52’s F4 slope is −0.59 ms/mmHg [−0.72, −0.47] over 48 epochs, with 32 pointers; F1 and F2 also pass patient-level and Holm-adjusted tests.Each fast coupling has patient-level p = 0.002 and Holm-adjusted value 0.006.Source: §H.8 · p. 61

I PRE-SPECIFIED PROTOCOLS AND REPRODUCIBILITY

• Confirmatory protocols fixed cohorts, quality rules, estimands, estimators, nulls, and decision rules, and were written and hashed before their confirmatory runs.The deviation log records protocol amendments and post-registration additions, including adding PAT-SBP to the per-patient fast-edge Holm family.Source: I PRE-SPECIFIED PROTOCOLS AND… · pp. 62–63
• Typed pooled-estimator admissions and several PAT analyses were outside the protocols, as were the synthetic calibration study and other listed analyses.The recovery of ventilation→EtCO2 relations was a registered benchmark output but not a registered prediction.Source: I PRE-SPECIFIED PROTOCOLS AND… · p. 63

J.1 SYNTHETIC CALIBRATION OF EDGE TESTS

• The synthetic study varies series length, persistence, graph structure, shared drivers, and readout, with seven concept series per patient and 50 patients per setting in most cases.It evaluates whether per-patient edge tests control false discoveries under serial dependence and shared drivers; the study was not prespecified.Source: §J.1 · p. 63
• The lattice-shift test’s guarantees do not follow from cited circular-shift results; its p-value is exact only under rotation-invariance and independence conditions stated for the source innovations.Residual serial dependence and unrecorded shared drivers can make the test approximate or its null inappropriate.Source: §J.1 · p. 64
• 8-27 false edges per graph and family-wise error rate 1.00 occur for CKG’s temporal layer under the global null; lattice tests with BH violate FDR in 3 of 54 non-confounded settings.Lattice tests with BH also have FWER at most 0.12 at α = 0.1 across global-null settings; unrecorded shared drivers produce false edges for every method.Source: Table 55 · p. 64, §J.1 · pp. 64–65

J.2 PRESSURE CONCEPTS AGAINST THE CUFF AND WITHOUT AN ARTERIAL LINE

• Without an arterial waveform, pressure-concept AUROC ranges from 0.386 to 0.530 across six models and both concepts, while cuff-reference AUROC is 0.95-0.96 for hypertension and 0.62-0.65 for hypotension.The cuff comparisons have wide confidence intervals with eight patients; against arterial numeric, seed-mean AUROC is at least 0.97 for both supervision sources.Source: Table 56 · p. 65, §J.2 · p. 65