Learning Who Benefits Most: Multi-Treatment Causal Ranking for Population Health Stratification

Rocco Zaccagnino; Martina Girolamo; Alberto Lombardi; Delfina Malandrino; Donatello Telesca; Alessia Ture

cs.LGOct 14, 2026

Learning Who Benefits Most: Multi-Treatment Causal Ranking for Population Health Stratification

Authors: Rocco Zaccagnino, Martina Girolamo, Alberto Lombardi, Delfina Malandrino, Donatello Telesca, Alessia Ture

Organizations: University of Salerno, Salerno, Italy · Local Health Authority of Benevento, Benevento, Italy · University of California, Los Angeles, Los Angeles, USA

Abstract

Population health stratification frameworks, such as the Italian DM77, organize patients by clinical need and care pathways but offer limited guidance on which care changes to prioritize under constrained resources. We present PROMETHEUS (Proactive Resource Optimization through Multi-treatment Effect-based Targeting in Healthcare Environments Using Stratification), a framework that formulates population health stratification as a multi-treatment causal ranking problem. Its objective is to order eligible patient-treatment opportunities by expected incremental benefit rather than obtain perfectly calibrated individual treatment-effect estimates. Each clinically admissible care intensification is compared with maintaining the patient's current pathway. Treatments are learned jointly to produce a globally comparable ranking across patients and care profiles, within domains sharing a reference condition, outcome, follow-up horizon, and benefit scale. This separates clinical need, treatment benefit, and resource-constrained allocation. PROMETHEUS combines doubly robust causal signals with a Siamese neural ranking model and contrastive representation pretraining. The shared representation captures similarities across care transitions, supporting prioritization under capacity constraints. Synthetic experiments and semi-synthetic experiments using real administrative covariates from ASL Benevento evaluate ranking quality, allocation value, robustness, and failure modes. The results support the framework's ability to recover generated benefit orderings and prioritize care opportunities in the evaluated settings. PROMETHEUS provides a preclinical approach to actionable stratification; validation with observed treatment-outcome data is required before clinical use.

Figures & tables

Panel of Figure 1 — Figure 1. The PROMETHEUS multi-treatment causal ranking architecture. Admissible patient-profile opportunities $(u,v)$ are processed by a shared Siamese encoder $F_{\theta}$ . The latent representations $h$ are organized via uncertainty-aware contrastive pretraining based on their estimated causal responses. A ranking head $r_{\theta}$ outputs priority scores $s$ , optimized through a pairwise ranking loss $\mathcal{L}_{\mathrm{rank}}$ supervised by cross-fitted doubly robust pseudo-outcomes. Sample teaser image showing the main concept of the paper.

Element	Count
Unique assisted individuals	270,533
Hospitalization records	20,825
Diagnosis records	49,057
Curated exemption records	283,297
Adults available before sampling	230,525
Patients sampled per run	30,000

Table 1. ASL source and analytic cohort summary. Analytic counts are averages over ten partially aligned runs.

Decision layer	Metric	Estimate [95% CI]
Need	Weighted Cohen’s $\kappa$	0.705 [0.699–0.710]
Need	Ordinal MAE	0.696 [0.691–0.702]
Need	Within-one-level accuracy	0.899 [0.896–0.902]
Ranking	Held-out DR within-intervention concordance	0.502 [0.494–0.509]
Ranking	Held-out DR cross-intervention concordance	0.546 [0.534–0.561]
Ranking	Held-out DR global concordance	0.538 [0.527–0.550]

Table 2. Synthetic results over ten seeds. Values are means with 95% run-level bootstrap confidence intervals.

Scenario	Support	Abstention	Oracle global concordance	Normalized value
Poor overlap	0.798	0.630	0.734	0.949
Hidden confounding	1.000	0.462	0.567	0.893
Risk–benefit misaligned	1.000	0.490	0.681	0.975
Capacity scarcity	1.000	0.462	0.809	0.885
Sharp null	1.000	1.000	–	1.000
Placebo outcome	1.000	1.000	–	1.000

Table 3. Selected synthetic stress scenarios. Support and abstention are proportions; normalized value compares the model allocation with the oracle allocation under the same constraints.

Scenario	Held-out DR global	Oracle global	Oracle cross-profile	Within-patient accuracy	Normalized value	Selected harm
Partially aligned	0.625 [0.616–0.633]	0.766 [0.759–0.773]	0.801 [0.793–0.809]	0.800 [0.783–0.816]	0.838 [0.828–0.847]	0.001 [0.000–0.002]
Risk–benefit misaligned	0.616 [0.606–0.627]	0.776 [0.770–0.781]	0.812 [0.805–0.818]	0.788 [0.778–0.799]	0.846 [0.827–0.865]	0.006 [0.004–0.009]
Mixed response	0.578 [0.570–0.586]	0.648 [0.642–0.653]	0.673 [0.665–0.681]	0.646 [0.636–0.656]	0.660 [0.645–0.677]	0.119 [0.112–0.126]

Table 4. ASL semi-synthetic results over ten runs per scenario. Values are means with 95% run-level bootstrap confidence intervals. Oracle quantities refer only to the generated response mechanism.

ASL scenario	Difference [95% CI]
Partially aligned	$+0.0132$ [0.0016, 0.0243]
Risk–benefit misaligned	$+0.0155$ [0.0046, 0.0283]
Mixed response	$+0.0210$ [0.0099, 0.0326]

Table 5. Change in normalized allocation value from contrastive pretraining relative to random initialization.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Scenario	Support	Abstention	Oracle cross-profile	Oracle global	Norm. value
Baseline identifiable	1.000	0.566	0.841	0.808	0.964
Need–care alignment	0.993	0.402	0.840	0.794	0.945
Unmet need	1.000	0.099	0.905	0.871	0.887
Over-intensive care	0.864	0.907	0.363	0.538	1.000
Risk–benefit aligned	1.000	0.558	0.816	0.783	0.918
Risk–benefit misaligned	1.000	0.490	0.680	0.681	0.975

Appendix

Table 6. Synthetic scenario diagnostics for the 14 prespecified scenarios. Each row is one frozen 5,000-patient realization. Oracle concordance is undefined under tied null effects.

Analysis	Metric or comparison	Estimate [95% CI]
Restricted capacity	PROMETHEUS AUTOC	1.7487
Restricted capacity	PROMETHEUS Value@10% / Value@20%	0.8361 / 1.4981
Joint contrastive ablation	Rank-only minus rank+contrastive, held-out DR	$+0.000241$ [ $-0.000455$ , $+0.000985$ ]
Joint contrastive ablation	Rank-only minus rank+contrastive, oracle	$-0.001284$ [ $-0.003551$ , $+0.000727$ ]
Stability	Rank-score Spearman	0.738 [0.666–0.797]
Stability	Recommended-patient Jaccard	0.923 [0.905–0.941]

Appendix

Table 7. Compact supplementary results not shown in the main tables.

Source element	Count
Raw assisted-population registry rows	275,397
Unique assisted individuals	270,533
Registry identifiers appearing more than once	4,864
Curated exemption records	283,297
Hospitalization records	20,825
Diagnosis records in long format	49,057

Appendix

Table 8. Dimensions of the ASL administrative sources before application-specific sampling and semi-synthetic generation.

Diagnostic	Value
Linkable hospitalization rows	20,819
Unlinkable hospitalization rows	6
Unique patients in hospitalization data	17,949
Hospitalized patients found in registry	9,339
Hospitalization-to-registry linkage rate	52.0%
Unique patients in exemption data	190,491

Appendix

Table 9. Record-linkage and integrity diagnostics for the ASL source tables.

Variable	Missing proportion
Patient identifier	0.0%
Sex	0.0%
Age at index date	0.0%
Residence municipality	$<0.01$ %
Enrollment district	0.0%
Provider district	0.0%

Appendix

Table 10. Selected missingness diagnostics for the patient-level registry. Variables with structurally meaningful absence are marked separately.

Characteristic	Estimate
Patients sampled per run	30,000
Mean age, years	52.14
Female patients	50.96%
Income-exemption indicator	66.21%
Invalidity-exemption indicator	9.89%
Pathology-exemption indicator	22.11%

Appendix

Table 11. Selected baseline characteristics of the sampled ASL population in the partially aligned reference scenario. Values are averages across ten runs.

Scenario	Profile	Eligibility	Assignment	Mean true benefit	Negative effects
Partially aligned	Profile 1	72.18%	16.38%	1.62	7.05%
	Profile 2	22.76%	5.88%	1.72	6.62%
	Profile 3	72.00%	20.37%	2.90	6.20%
Mixed response	Profile 1	–	–	–	20.39%
	Profile 2	–	–	–	16.94%
	Profile 3	–	–	–	18.92%

Appendix

Table 12. Profile-level eligibility, simulated assignment, and oracle-only response diagnostics. Values are averages across ten runs. True-effect quantities are generated evaluation targets, not observed ASL treatment effects.

Metric	Partially aligned	Risk–benefit misaligned	Mixed response
NDCG@25%	0.917 [0.912–0.921]	–	–
Harm@25%	0.0008 [0.0004–0.0014]	–	–
Patients served	911.3 [886.9–935.5]	901.1 [870.0–930.9]	910.7 [883.1–934.8]
Allocation regret	936.7 [884.4–995.1]	–	–

Appendix

Table 13. Additional ASL semi-synthetic metrics omitted from the main result table. Values are means with 95% run-level bootstrap confidence intervals.

Scenario	Comparator	Oracle difference [95% CI]	Non-oracle validation difference [95% CI]
Partially aligned	Random initialization	$+0.0132$ [ $+0.0016$ , $+0.0243$ ]	$+0.0032$ [ $+0.0014$ , $+0.0051$ ]
	Joint UACT	$+0.0133$ [ $+0.0017$ , $+0.0246$ ]	$+0.0032$ [ $+0.0014$ , $+0.0052$ ]
	Legacy triplet	$+0.0106$ [ $+0.0010$ , $+0.0197$ ]	$+0.0033$ [ $+0.0013$ , $+0.0056$ ]
	Pretrained and fine-tuned	$0.0000$ [ $0.0000$ , $0.0000$ ]	$0.0000$ [ $-0.0000$ , $0.0000$ ]
Risk–benefit misaligned	Random initialization	$+0.0155$ [ $+0.0046$ , $+0.0283$ ]	$+0.0013$ [ $-0.0021$ , $+0.0042$ ]
	Joint UACT	$+0.0156$ [ $+0.0048$ , $+0.0286$ ]	$+0.0013$ [ $-0.0021$ , $+0.0042$ ]

Appendix

Table 14. Paired normalized-allocation-value differences over ten ASL runs per scenario. Positive differences favor the contrastively pretrained configuration.

Setting	Value	Interpretation
Main sample size	30,000	Number of adult ASL patients used in a complete experimental run.
Smoke-test sample size	6,000	Reduced sample used only to verify execution and diagnostic outputs.
Minimum age	18 years	Patients younger than 18 years were excluded before sampling.
Default response scenario	partially_aligned	Default semi-synthetic relationship between baseline risk and profile-specific benefit. Campaign experiments additionally considered risk_benefit_misaligned and mixed_response .
Patient-level split proportions	30/30/15/10/15%	Proportions assigned respectively to nuisance training, ranking training, validation, calibration, and testing.
Data-generation seed	8101	Controls patient sampling, simulated treatment assignment, potential outcomes, and patient-level partitioning.

Appendix

Table 15. Semi-synthetic study and reproducibility settings. The smoke-test configuration was used only for engineering diagnostics and not for the reported confirmation results.

Hyperparameter	Value	Role
Nuisance fitting mode	full_bootstrap	Fits every nuisance repetition on a treatment-stratified bootstrap sample of the nuisance-training partition.
Number of nuisance repetitions	3	Number of independently fitted propensity and outcome-model sets. The resulting repeated DR contrasts are used to measure sign agreement and uncertainty.
Minimum observations per arm	20	Minimum number of nuisance-training observations required for each treatment arm. The run is rejected when this support condition is not satisfied.
Minimum stabilized propensity	0.04	Lower bound imposed on every multinomial treatment probability. Probabilities are shrunk toward the uniform distribution while preserving a unit row sum.
Propensity boosting iterations	65	Maximum number of iterations for the multinomial histogram gradient-boosting classifier.
Outcome boosting iterations	70	Maximum number of iterations for each treatment-specific histogram gradient-boosting outcome model.

Appendix

Table 16. Hyperparameters used to estimate the repeated doubly robust supervision signals.

Hyperparameter	Value	Role
Shared hidden width	96	Width of the clinical encoder, FiLM-conditioned representation, and post-conditioning layer.
Profile-embedding dimension	16	Dimension of the learned embedding associated with each candidate care profile.
Projection dimension	24	Dimension of the normalized representation used by the contrastive losses.
Dropout probability	0.12	Dropout applied in the clinical encoder and after FiLM conditioning.
Optimizer	AdamW	Optimizer used for both contrastive pretraining and ranking fine-tuning.
Global weight decay	$5\times 10^{-4}$	Weight decay used during ranking fine-tuning.

Appendix

Table 17. Architecture and ranking-optimization hyperparameters.

Hyperparameter	Value	Role
Maximum training pairs	30,000	Maximum number of stable pairs sampled from the ranking-training partition.
Maximum validation pairs	9,000	Maximum number of independently sampled stable pairs used for held-out model selection.
Minimum DR-signal gap	0.15	Minimum absolute difference between the average repeated DR signals of the two opportunities.
Minimum repeat agreement	0.70	At least 70% of nuisance repetitions must support the direction indicated by the average DR difference.
Within-patient pair fraction	0.50	Target proportion of comparisons involving different profiles for the same patient.
Within-profile pair fraction	0.20	Target proportion comparing different patients for the same profile.

Appendix

Table 18. Hyperparameters controlling ranking-pair construction and weighting.

Hyperparameter	Value	Role
Pretraining enabled	True	Initializes the shared representation before fitting the ranking score.
Contrastive mode	uncertainty_aware_ordinal_triplet	Uses reliable positive, neutral, and negative ordinal response neighborhoods.
Maximum pretraining epochs	30	Maximum number of encoder-only contrastive epochs.
Pretraining patience	8	Number of validation epochs without improvement before stopping pretraining.
Pretraining learning rate	$1\times 10^{-3}$	AdamW learning rate for the representation parameters during pretraining.
Pretraining weight decay	$5\times 10^{-4}$	Weight decay applied during contrastive pretraining.

Appendix

Table 19. Hyperparameters of uncertainty-aware contrastive pretraining.

Hyperparameter	Value	Role
Calibration objective	Enabled	Adds a reliability-weighted pointwise loss between ranking scores and standardized learner-safe DR signals.
Calibration weight	0.10	Coefficient multiplying the calibration regularizer.
Calibration batch size	256	Number of opportunities used in each calibration update.
Huber transition parameter	1.0	Parameter $\beta$ of the smooth $L_{1}$ calibration loss.
Minimum calibration reliability	0.25	Lower bound on the reliability weight assigned to a calibration target.
Within-patient auxiliary	Enabled	Adds an additional pairwise objective over alternative profiles available to the same patient.

Appendix

Table 20. Active auxiliary objectives used during ranking fine-tuning. The contrastive retention loss was excluded from the selected final configuration.

Validation component	Weight or value	Interpretation
Global pair concordance	0.20	Agreement over all held-out ranking comparisons.
Cross-profile concordance	0.25	Agreement over pairs involving different patients and different profiles.
Within-patient concordance	0.30	Agreement when ranking alternative profiles for the same patient.
NDCG fraction	0.25	Computes NDCG over the upper 25% of validation opportunities.
NDCG weight	0.15	Contribution of top-region ranking quality to checkpoint selection.
Top- $k$ DR-value fractions	0.10, 0.25, 0.50	Fractions used to evaluate the benefit captured by the highest-ranked opportunities.

Appendix

Table 21. Hyperparameters of non-oracle checkpoint selection.

Parameter	Value	Interpretation
Monitoring capacity fraction	0.18	Monitoring capacity is set to 18% of the number of test patients.
Home-care capacity fraction	0.10	Home-care capacity is set to 10% of the number of test patients.
Case-management capacity fraction	0.06	Case-management capacity is set to 6% of the number of test patients.
Budget multiplier	0.85	The available budget equals 85% of the cost required to fill all profile-specific capacity pools.

Appendix

Table 22. Operational capacity and budget parameters.

Baseline	Hyperparameters	Description
Prospective-utilization Ridge	$\alpha=1.0$	Ridge regression fitted to the simulated prospective-utilization outcome.
Prospective-utilization GBDT	80 iterations; 15 leaf nodes	Histogram gradient-boosting risk model.
T-learner GBDT	70 iterations per outcome model; 15 leaf nodes	Separate outcome regressions for the reference and candidate treatment arms.
X-learner GBDT	60 outcome iterations; 50 pseudo-effect iterations; 50 propensity iterations; 15 leaf nodes	Profile-specific X-learners. Binary propensities are clipped to $[0.05,0.95]$ .
DR-learner GBDT	70 iterations; 15 leaf nodes	Profile-specific regressors fitted to the mean repeated DR signal.
DR Random Forest	120 trees; minimum leaf size 12	Profile-specific random-forest regressors fitted to the mean repeated DR signal.

Appendix

Table 23. Main baseline-model hyperparameters used in the full ASL experiments.

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Precedence-Aware Resource Allocation: Extending the AUTOC Framework to Multi-Level Treatments

Olin E. Gilster, Shengpu Tang

Emory University, USA

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Many real-world decision problems require allocating limited resources across individuals to maximize total benefit often through interventions that vary in intensity rather than binary treat-or-not decisions. In these settings, higher levels treatments require first applying lower levels of treatment, inducing a precedence constraint that complicates allocation under a fixed budget. While the causal inference literature has largely emphasized accurate estimation of conditional average treatment effects (CATE), recent work has shown that estimation accuracy alone does not guarantee effective resource allocation, motivating ranking-based evaluation frameworks. The Area Under the Targeting Operating Characteristic (AUTOC) provides an effective way to evaluate prioritization rules across budget levels, but existing formulations are limited to binary treatments. We introduce Multi-Level AUTOC (ML-AUTOC), which is a generalization for AUTOC designed for multi-level treatment settings with precedence. We also propose precedence-aware policies for mapping true marginal treatment effects to feasible treatment assignments under fixed budget constraints. Our results show that in the setting of multi-level treatments, maximizing realized treatment effects may require re-allocation of treatments across individuals.

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