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Safe to Stop? Risk-Constrained Stopping for Sequential Clinical Diagnosis Agents

Yuexin Wu, Vasile Rus

arXiv:2609.09678v1cs.AI

TL;DR

Autonomous stopping in sequential diagnosis lacks explicit risk–coverage guarantees, so the paper introduces CROS, a frozen stop–continue–defer layer with risk ranking, disjoint policy design, and LTT-style joint tests. On a MIMIC-derived benchmark, CROS improved exploratory state-error ranking and reported lower-cost stopping outcomes, but previously accessed labels prevent a confirmatory safety claim.

  • Problem

    Sequential diagnosis agents must decide when to diagnose or defer, but existing benchmarks leave autonomous stopping reliability and finite-sample risk–coverage guarantees weakly specified.

  • Method

    CROS combines state-wise error ranking, frozen candidate-policy design, and LTT-style exact tests of selective diagnostic error and minimum autonomous coverage.

  • Results

    The full ranker achieves state-error AUROC 0.853, compared with 0.715 for the maximum-probability ranker and 0.552 for the Native-score ranker.

  • Takeaways & Limitations

    CROS provides an auditable stopping framework and supports exploratory feasibility and lower-cost deterministic–mixture trade-offs on the common clinical trajectory.

  • Takeaways & Limitations

    Previously accessed labels, structured missingness, resplit instability, subgroup failures, and benchmark limitations require a new prospectively locked study before any safety claim.

Abstract

from arXiv · show

Clinical diagnosis agents must decide not only what test to request next, but also when to diagnose or defer. Existing agent benchmarks largely evaluate accuracy after fixed or unconstrained interaction, leaving autonomous stopping reliability implicit. We present Cros, a risk-constrained stopping layer combining state-wise error ranking, policy design on disjoint development splits, and LTT-style exact tests of selective diagnostic error and minimum autonomous coverage for complete sequential policies. Its finite-sample guarantee requires the candidate family, testing rule, and any randomization to be frozen before calibration labels are accessed. On a 1,834-episode MIMIC-derived abdominal-pain benchmark, the full ranker achieves exploratory state-error AUROC 0.853, compared with 0.715 for maximum class probability and 0.552 for the backbone's native stop score. On the previously viewed 367-episode evaluation split, analytically averaging over the frozen Cros weights yields 16.9% selective error at 78.8% coverage, cost 5.57, and 0.68 tests, versus 30.8% error at 100% coverage, cost 8.14, and 1.53 tests under native stopping. Forced continuation is non-monotone: error is 28.3% with HPI alone and 34.3% after full workup. However, the uniform-weight mixture ablation is cheaper on this viewed split despite missing the locked development margins, and Cros nominally satisfies the joint criterion in only 6 of 20 development resplits. Because evaluation labels were inspected during earlier development, these findings provide exploratory feasibility and audit evidence, not a confirmatory safety certificate.

1 Introduction

The paper frames autonomous stopping as a risk–coverage problem in sequential diagnosis, where agents must decide whether to stop, continue, or defer. CROS addresses this with frozen policy design, risk ranking, and finite-sample joint testing.

  • Motivation: Sequential diagnosis requires deciding when to stop acquiring information and commit to an autonomous diagnosis.Stopping too early can miss consequential disease, while stopping too late wastes tests and may expose patients to avoidable procedures.
  • Method: CROS treats stopping as selective, risk-constrained control over diagnostic error and autonomous coverage.The stopping layer accepts, continues, or defers while minimizing resource cost subject to population constraints.
  • Method: CROS separates representation, policy design, and calibration using a risk ranker, a frozen candidate family, and LTT-style exact tests.The method does not optimize unrestricted Bellman stopping or the backbone’s test-acquisition policy.
  • Contributions: The paper contributes joint testing for complete sequential policies, sparse randomized mixtures, an auditable 1,834-episode benchmark, and negative evidence about robustness.Reported audits include non-monotone forced continuation, unstable resplit feasibility, and subgroup-safety limitations.

2 Related Work

Related work studies sequential clinical interaction, resource-aware acquisition, selective risk control, and calibrated stopping. CROS adapts these ideas to frozen clinical stop–continue–defer policies with joint error and autonomous-coverage control.

  • Clinical decision agents: Clinical-agent benchmarks increasingly model diagnosis, test requests, and hypothesis revision, motivating explicit stopping decisions.These systems include sequential, multimodal, adversarial, and reinforcement-learned clinical decision environments.
  • Resource-aware sequential diagnosis: Resource-aware methods often change which tests are selected, whereas CROS controls stopping on a common backbone-proposed trajectory.CROS therefore isolates stopping rather than end-to-end acquisition-policy improvement.
  • Selective prediction and risk control: Selective prediction and conformal methods provide risk or participation control, but these ingredients are not new in isolation.CROS applies them to stateful clinical stopping with resource costs and joint constraints.
  • Clinical stopping and calibration: Prior clinical abstention and sequential-calibration work does not provide the same frozen-policy joint control of selective diagnostic error and autonomous coverage.The distinction is methodological rather than a claim that clinical abstention or Bellman stopping is new.

3 Risk-Constrained Sequential Diagnosis

CROS defines sequential diagnosis as a common-path stop–continue–defer problem and calibrates frozen policies against selective error, coverage, and cost constraints. It also permits sparse episode-wise mixtures while preserving testability when frozen before calibration.

  • 3.1 Problem setup: The backbone proposes each test along a common trajectory, while CROS decides whether to stop, continue, or defer without selecting test identity.This separates stopping control from diagnosis and test-proposal behavior.
  • 3.1 Problem setup: CROS evaluates policies using selective diagnostic error, autonomous coverage, and expected resource cost.Risk is measured among autonomous diagnoses, coverage is the fraction diagnosed autonomously, and cost includes requested actions plus defer penalties.
  • 3.1 Problem setup: The optimization seeks the least costly candidate whose selective error is at most α and autonomous coverage is at least γ.The positive coverage requirement prevents an always-defer policy from satisfying the objective through zero participation.
  • 3.2 Risk ranking: The auxiliary risk estimator predicts whether the backbone’s current diagnosis is wrong, using diagnosis probabilities, uncertainty, trajectory, cost, latency, missingness, and native stopping features.Out-of-fold training keeps states from one patient within disjoint folds.
  • 3.2 Policy design: A disjoint selection split freezes the estimator, candidate policies, ordering, and hyperparameters before calibration labels are accessed.Validity depends on a fresh exchangeable calibration sample rather than on correct specification of the learned ranker.
  • 3.3 Exact joint tests: Calibration tests whether a frozen policy has population risk at most α and coverage at least γ using autonomous counts and error counts.The intersection-union procedure requires evidence against both failure modes, with exact binomial component tests and multiplicity control across candidates.
  • 3.3 Exact joint tests: Finite-sample validity holds when candidate policies, testing procedures, and episode-wise randomization are frozen before calibration.The guarantee does not require the risk estimator itself to be calibrated.
  • 3.4 Randomized sparse mixtures: Episode-wise randomization permits mixtures over frozen deterministic policies, with expected cost, error mass, and coverage computed from component weights.An optimal basic feasible mixture uses at most three component policies, and the random draw is independent across episodes.

4 Experimental Design

The study evaluates stopping controllers on a retrospective, patient-level MIMIC-derived benchmark using a common forced-continuation trajectory. Development-only fitting and policy construction are separated from calibration and evaluation, but prior label access makes the reported findings exploratory.

  • Benchmark and splits: 1,834 patient-level episodes span nine abdominal-pain diagnosis classes, with 1,100 development, 367 calibration, and 367 evaluation episodes without patient overlap.The development cohort is further divided into backbone and risk-ranker fitting and policy-selection partitions.
  • Benchmark and splits: The environment exposes 12 action groups, but its logged retrospective results cannot causally simulate alternative testing decisions because acquisition timestamps are unreliable.Unavailable results are represented as NO RECORDED RESULT.
  • Study status: Calibration and evaluation labels were accessed during earlier development, so the reported calibration passes, p-values, and confidence bounds are exploratory rather than prospective certificates.A new untouched cohort is required for confirmatory application of the finite-sample theorem.
  • Evaluation protocol: All stopping methods receive identical backbone outputs and forced-continuation trajectories, isolating the decision to stop, continue, or defer.Comparators include fixed-stage, confidence-threshold, native-agent, HPI-only, full-workup, and empirical cost-minimization rules.
  • Model instantiation and comparators: CROS-Det and CROS-Mix are the two named controllers, with CROS-Mix combining the same three frozen support policies using LP-optimized episode-wise randomization.Analytic expectation and realized draws are evaluation modes of one controller; the uniform-weight mixture is a design ablation.

5 Results

CROS improves state-error ranking and yields lower-cost risk-constrained stopping in exploratory comparisons, while audits reveal sensitivity to ranker features, policy design, and sequential acquisition.

  • Exploratory joint calibration: 16.3% error at 78.5% coverage, with cost 5.68 and 0.68 requested actions, was achieved by the prespecified CROS-Mix realization.Table 1 reports exploratory calibration and evaluation outcomes for 367 calibration and 367 evaluation episodes.
  • Risk-ranker and stopping ablation: 0.853 state-error AUROC was achieved by the full ranker, versus 0.715 for maximum probability and 0.552 for the Native-score ranker.Only the full-ranker controller satisfied the locked selection margins and had an exploratory calibration pass.
  • Policy and matched comparisons: 0.903 cost units separated CROS-Mix from CROS-Det, while CROS-Mix requested 0.195 fewer actions and had unresolved risk difference with 0.021 lower coverage.The uniform-weight mixture was another 0.977 units cheaper on evaluation but missed both locked selection margins.
  • Policy and matched comparisons: 0.088 and 0.063 reductions in risk, and 12.54 and 4.84 reductions in cost, occurred versus confidence thresholding and native stopping with deferral, respectively.Coverage differences were unresolved in both comparisons, and cost advantages did not persist under every deferral penalty.
  • Trajectory and robustness audits: 28.3% error with HPI alone rose to 34.3% after full workup, while cost and recorded-result missingness increased along the trajectory.Across 20 development resplits, CROS-Mix passed nominally in only six, indicating design sensitivity rather than independent confirmation.

6 Discussion and Limitations

The findings support a prospectively frozen follow-up rather than deployment or a clinical safety claim, because labels were previously accessed and the benchmark and audits have important scope limitations.

  • Discussion: The results support a prospectively frozen follow-up, not deployment or a clinical safety claim.The discussion also notes that ranker, mixture, trajectory, and split-feasibility findings remain exploratory.
  • Limitations: The claims are limited by previously accessed labels, a single-center note-derived benchmark, informative missingness, proxy outcomes and costs, marginal rather than subgroup control, and dependent resplit audits.Common-path evaluation isolates stopping but does not measure end-to-end gains when agents choose different actions.
  • Follow-up: A confirmatory study should use a never-viewed temporal or external cohort with prespecified labels, costs, subgroup hypotheses, sample size, and testing graph, plus blinded clinical adjudication.It should evaluate both common-path stopping and end-to-end acquisition without changes after calibration access.

7 Conclusion

CROS frames sequential diagnosis as risk-constrained stopping and uses frozen candidate policies with exact joint tests of selective error and autonomous coverage. The retrospective results support feasibility, but label reuse and instability prevent a confirmatory safety claim.

  • Scope: The retrospective findings support feasibility and a lower-cost deterministic–mixture trade-off, but label reuse, structured missingness, resplit instability, and subgroup failures require a prospective locked study before safety claims.The present results are therefore exploratory audit evidence rather than a confirmatory safety certificate.
  • Randomized policies: At most three component policies are needed for an optimal basic feasible randomized mixture.Independent episode-wise randomization preserves compatibility with exact calibration.
  • Validity conditions: A valid finite-sample certificate requires the candidate family, testing rule, and randomization to be fixed before calibration outcomes are accessed.Testing a finite pre-frozen family controls the probability of certifying any invalid candidate.

B Benchmark, Costs, and Ranker Configuration

The benchmark uses disjoint patient-level partitions and a logged retrospective common-path environment, while CROS builds a frozen risk-ranker policy family from stage-level and episode-level development data. Costs and thresholds are fixed before calibration and evaluation analyses.

  • Benchmark and partitions: 1,834 episodes are assigned to nine abdominal-pain diagnosis classes, with 1,100 development, 367 calibration, and 367 evaluation episodes.Development contains 935 ranker-training and 165 policy-selection episodes, with all states from one episode kept together.
  • Benchmark and partitions: The retrospective environment exposes 12 action groups, but recorded results generally lack reliable acquisition timestamps and do not simulate alternative testing trajectories.CROS controls whether the backbone-proposed action is executed rather than replacing it with another action.
  • Costs: The reported cost is a normalized resource index, and the deferral penalty is a stylized downstream-review cost rather than a hospital bill or measured clinical harm.Attempted actions incur their frozen costs even when the retrospective record returns NO RECORDED RESULT.
  • Ranker configuration: The ranker uses diagnosis probabilities, uncertainty summaries, stage, missingness, cumulative cost, latency, and the native stopping score to estimate state-level diagnostic error.Cross-fitting and resampling are performed at the episode level because states from one patient are correlated.
  • Policy construction: 130 threshold-and-horizon candidates are generated, while the selection split freezes a tested family of 12 deterministic policies and one optimized randomized mixture.Thresholds are constructed only on the 165-episode policy-selection split and reused unchanged on calibration and evaluation episodes.

C Detailed Baseline and Masking Results

The common-path controller comparisons and masking analyses show that explicit-language removal changes CROS-Mix performance while preserving the controller, but deterministic masking cannot establish that diagnostic leakage is absent.

  • Common-path comparisons: All controllers receive the same backbone diagnoses, action proposals, native stopping scores, and forced-continuation observations, so comparisons isolate stopping and deferral.Baseline calibration p-values are descriptive and do not place every baseline in the multiplicity-controlled CROS family.
  • Masking results: Diagnosis-name and expanded masking increase CROS-Mix selective risk by +.015 and +.013, reduce coverage by −.018 and −.020, and increase cost by +.504 and +.632, respectively.These are masked-minus-original changes under analytic-expectation evaluation.
  • Masking results: Evaluation ranker AUROCs are .853, .839, and .840 for original, diagnosis-name, and expanded masking, respectively.The corresponding calibration AUROCs are .840, .842, and .842.
  • Masking results: Explicit-language removal weakens ranking and efficiency without collapsing the frozen controller, but deterministic masking cannot remove every implicit cue or establish that no diagnostic leakage remains.Versioned artifacts include the regex list, replacement rules, split-level match counts, and immutable input/output hashes.

D Expanded Paired Bootstrap and Trajectory Details

Paired bootstrap analyses compare CROS-Mix with common-path controllers, while forced continuation shows that diagnostic error is non-monotone across the shared 367-episode trajectory. The mixture offers a narrow cost advantage rather than a universal dominance claim.

  • Paired comparisons: Paired differences use 10,000 patient-level bootstrap resamples, with all states and outcomes from each patient resampled together.Replicates without autonomous diagnoses are omitted only when the selective-risk difference is undefined.
  • Paired comparisons: CROS-Mix analytic expectation is less costly than CROS-Det, fixed-sequence LTT, confidence thresholding, and native stopping with deferral, but more costly than the uniform-weight mixture and ERM.Its selective-risk difference from CROS-Det, fixed-sequence LTT, and the uniform-weight mixture is unresolved.
  • Forced-continuation trajectory: Forced-continuation diagnostic error reaches its minimum after one requested action and then becomes non-monotone as cumulative cost and recorded-result missingness increase.The same 367 patients appear at every stage, so later-stage degradation is not caused by changing patient composition.
  • Forced-continuation trajectory: The trajectory characterizes the frozen backbone and retrospective benchmark rather than establishing that clinical testing is generally harmful.The benchmark records shared-backbone trajectories instead of counterfactual outcomes from alternative test ordering.

E Exact Bounds and Frozen Frontiers

Exact joint testing combines risk and coverage evidence, while frozen frontiers and post-freeze analyses assess candidate behavior and randomization sensitivity. Evaluation bounds remain descriptive because labels were previously viewed, and population guarantees do not imply subgroup control.

  • Exact Bounds: p_j = max(p_R,j, p_C,j) is small only when both selective-risk and autonomous-coverage requirements receive sufficient evidence.The joint value is computed from the two exact component p-values.
  • Exact Bounds: The Single-candidate test, Fixed-sequence LTT, Holm, and Bonferroni procedures evaluate frozen candidates with prespecified multiplicity handling.Bonferroni uses threshold .00417; its returned controller has adjusted p = 0.00530 in this run.
  • Frozen Frontiers: The frozen mixture assigns weights 0.322, 0.044, and 0.633 to three threshold-and-horizon policies, with full-precision weights used for analysis.The displayed weights sum to 0.999 because of rounding.
  • Frozen Frontiers: The displayed randomized draw yields 280 autonomous diagnoses with 51 calibration errors and 288 autonomous diagnoses with 47 evaluation errors.Exact testing uses realized episode-level outcomes, whereas analytic mixture quantities integrate component contributions over frozen weights.
  • Frozen Frontiers: All 1,000 post-freeze evaluation realizations fall below the numerical risk target and above the numerical coverage target, without constituting independent calibration experiments.The analysis measures sensitivity to episode-wise random draws rather than selecting a favorable seed.
  • Exact Bounds: Evaluation bounds are descriptive because evaluation labels were previously viewed, and the bounds address marginal population risk and coverage rather than disease-class or demographic control.Frozen frontiers select marked operating points using development or selection data rather than favorable evaluation outcomes.

F Cost, Missingness, and Resplit Details

Cost accounting preserves the frozen stopping decisions while revealing scenario-dependent trade-offs, and missingness provides weak information about diagnosis and backbone error. Resplit and disease-class audits expose exploratory instability and inadequate support for subgroup certificates.

  • Cost: Risk, coverage, requested actions, thresholds, trajectories, deferral outcomes, and mixture weights remain unchanged when the cost-accounting vector changes.The sensitivity analysis therefore changes cost accounting without redesigning stopping decisions.
  • Cost: 5.77 is the CROS-Mix total cost when laboratory costs are doubled, while the break-even deferral penalty against native stopping is approximately 22.15.These quantities come from the frozen-decision cost analysis.
  • Cost: CROS-Mix remains less costly than the listed comparators across primary, imaging-sensitive, and missingness-sensitive scenarios, but native stopping becomes less costly at deferral penalty 25.ERM remains less costly throughout but fails exploratory calibration.
  • Missingness: Missingness-only indicators achieve diagnosis macro-AUROC 0.597 and state-error AUROC 0.535, indicating weak information about diagnosis and backbone error.The observed association is consistent with historical ordering behavior but does not identify a causal missingness mechanism.
  • Resplit Audit: Five of 20 CROS-Mix development resplits are infeasible, and reused outer cohorts make the resplit scores dependent exploratory checks rather than independent confirmations.Failures remain in the denominator and the audit did not replace or modify the primary frozen policy.
  • Disease-Class Audit: Coverage is below 70% for biliary disease, diverticulitis, and nonspecific abdominal pain, with selective error 0.500 for diverticulitis and 1.000 for a small nonspecific-pain subgroup.The denominators do not support simultaneous class-level certificates at α = .25 while maintaining useful coverage.
  • Disease-Class Audit: The theorem concerns aggregate selective risk and coverage unless subgroup constraints are explicitly included in the frozen testing family.Groups lacking adequate sample size should be reported as unsupported rather than safe.

H Frozen Protocol and Confirmatory Extension

The study evaluates frozen stopping controllers on shared backbone trajectories, separating stopping and deferral decisions from acquisition. Its confirmatory boundary is limited by exploratory design, common-path assumptions, sample-size requirements, and the theoretical scope of frozen-policy guarantees.

  • Frozen Protocol: The backbone is Qwen2.5-7B-Instruct adapted through decision-agent GRPO, hypothesis-agent supervised fine-tuning, and confidence-calibration GRPO.Training uses LoRA adaptation and the official LA-CDM implementation at frozen commit 3f435a1.
  • Frozen Protocol: The training manifest loads only the 935-episode ranker-training and 165-episode development-selection partitions, while later controllers use the resulting logged backbone quantities.Canonical calibration and evaluation files are not loaded by the backbone-training pipeline.
  • Frozen Protocol: Each episode follows a maximum forced-continuation trajectory of 12 action opportunities recording information state, probabilities, proposed actions, observations, and accumulated cost.Controllers later accept, continue, or defer on this stored trajectory.
  • Frozen Protocol: All controllers are applied to the same stored backbone trajectory, so paired primary comparisons isolate stopping and deferral decisions while holding backbone proposals fixed.Requested-action count and cost are truncated at the terminal stage, with deferral penalties added when applicable.
  • Frozen Protocol: HPI-only, full workup, and fixed-stage controls compare fixed information budgets, while confidence, native-agent, ERM, and CROS controllers implement distinct stopping policies.CROS-Det is the least-cost deterministic candidate satisfying selection-stage constraints; CROS-Mix is the LP-optimized mixture over the frozen family.
  • Frozen Protocol: The calibration procedures test frozen policies with single-candidate, fixed-sequence LTT, Holm, or Bonferroni multiplicity handling.Holm and fixed-sequence LTT return the same deterministic controller in this run, whereas Bonferroni returns a different one.
  • Frozen Protocol: The ranker ablations remove history features, use the native stopping score, or assign uniform mixture weights to test ranking and weight-design choices.Resource outcomes are total relative cost and attempted actions, including actions returning NO RECORDED RESULT.
  • Confirmatory Extension: A separate post-freeze branch provides negative exploratory evidence rather than independent confirmation, including no improvement from Full-Ensemble-UCB over the No-history ranker.The branch was not pooled with or used to modify the canonical analysis.
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