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arxiv: 2606.31954 · v1 · pith:SVF7KF7Mnew · submitted 2026-06-30 · 📊 stat.ME

A Conformal Selection Framework for Individual Treatment Beneficiaries with Auxiliary External Data

Jiajun Liu , Ke Zhu , Xiaofei Wang This is my paper

Pith reviewed 2026-07-01 03:57 UTC · model grok-4.3

classification 📊 stat.ME
keywords conformal inferenceFDR controlheterogeneous treatment effectsprecision medicinerandomized controlled trialsreal-world datamultiple testing
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The pith

Conformal p-values calibrated on RCT data allow FDR-controlled selection of treatment beneficiaries using models trained on external data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a framework to select individual patients likely to benefit from a treatment while controlling the false discovery rate. It reformulates the problem of identifying beneficiaries based on conditional average treatment effects as a multiple-testing task. Conformal p-values are constructed using calibration from randomized controlled trial data, and the Benjamini-Hochberg procedure adjusts them for FDR control. External real-world data can train the underlying models to increase power when RCT samples are limited. Simulations verify FDR control, and a lung cancer case study demonstrates practical application in identifying profiles that benefit from limited resection.

Core claim

The framework reformulates CATE-based treatment-benefit selection as a multiple-testing problem. For each candidate, it tests whether the conditional treatment benefit exceeds a clinically meaningful threshold and constructs a conformal p-value using RCT-based calibration. These p-values are adjusted by the Benjamini-Hochberg procedure to control the false discovery rate among selected beneficiaries. External data can be used to train the treatment effect models while conformal calibration remains anchored in the RCT data.

What carries the argument

The conformal inference framework that constructs RCT-calibrated conformal p-values for testing if conditional treatment benefit exceeds a threshold, enabling FDR control via Benjamini-Hochberg adjustment.

Load-bearing premise

Conformal p-values constructed from RCT calibration remain valid for FDR control even when the treatment-effect model is trained on external data whose distribution may differ from the RCT.

What would settle it

A simulation study where the external data distribution differs substantially from the RCT and the realized false discovery rate among selected beneficiaries exceeds the target level.

Figures

Figures reproduced from arXiv: 2606.31954 by Jiajun Liu, Ke Zhu, Xiaofei Wang.

Figure 1
Figure 1. Figure 1: Flowchart of the proposed framework for identifying treatment beneficiaries [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FDR across different scenarios given covariate shift [PITH_FULL_IMAGE:figures/full_fig_p025_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Power across different scenarios given covariate shift [PITH_FULL_IMAGE:figures/full_fig_p026_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FDR across different scenarios given outcome drift ( [PITH_FULL_IMAGE:figures/full_fig_p028_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Power across different scenarios given outcome drift ( [PITH_FULL_IMAGE:figures/full_fig_p029_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of conformal 𝑝-value surfaces under ID and ED when limited resection is treatment of interest and Super Learner is base learner We use Restricted Mean Survival Time (RMST) as the outcome of interest. RMST is defined as 𝑌 = min(𝑇, 𝑡∗ ), where 𝑇 denotes survival time and 𝑡 ∗ is a pre-specified truncation time. RMST represents the expected survival time restricted to 𝑡 ∗ and is commonly used as an … view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of conformal 𝑝-values regarding age and tumor sizes when using Super Learner as the base learner Here, we present the case study results using Super Learner as the base learner, with corre￾sponding BART results provided in Supplementary Material D [PITH_FULL_IMAGE:figures/full_fig_p034_7.png] view at source ↗
read the original abstract

Identifying patients who are likely to benefit from a treatment is central to precision medicine and can guide follow-up trials, enrichment designs, and individualized decisions. Although randomized controlled trials (RCTs) provide evidence on efficacy, they are usually powered to estimate average treatment effects rather than patient-level benefit. Meanwhile, artificial intelligence and machine learning methods offer flexible tools for estimating heterogeneous treatment effects, especially when augmented by real-world data (RWD). However, in practice, these estimated effects are often translated into decisions through simple ranking or thresholding rules, which can ignore uncertainty and multiplicity when many patients are evaluated simultaneously. Motivated by this, we propose a model-agnostic conformal inference framework for uncertainty-aware beneficiary selection. The framework reformulates CATE-based treatment-benefit selection as a multiple-testing problem. For each candidate, we test whether the conditional treatment benefit exceeds a clinically meaningful threshold and construct a conformal p-value using RCT-based calibration. These p-values are then adjusted by the Benjamini-Hochberg procedure to control the false discovery rate (FDR) among selected beneficiaries. To improve efficiency when RCT sample sizes are limited, external data, such as RWD, can be used to train flexible treatment effect models, while conformal calibration remains anchored in the RCT data. It can be paired with conventional machine learning algorithms and emerging tabular foundation models. Simulations show that the framework maintains FDR control, with power depending on the base learner and external-data comparability. A case study in early-stage non-small-cell lung cancer illustrates how the method identifies candidate profiles with evidence of benefit from limited resection to reduce overtreatment.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper proposes a model-agnostic conformal inference framework for selecting individual treatment beneficiaries. It reformulates CATE-based selection as a multiple-testing problem, constructs conformal p-values calibrated exclusively on RCT data, and applies the Benjamini-Hochberg procedure to control FDR among selected beneficiaries. External data may be used to train the underlying treatment-effect model, while calibration and p-value construction remain anchored in the RCT; simulations are reported to confirm FDR control, and the method is illustrated in an early-stage non-small-cell lung cancer case study identifying profiles that may benefit from limited resection.

Significance. If the FDR guarantee holds, the framework supplies a statistically principled route to uncertainty-aware beneficiary selection that respects the limited size of RCTs while allowing flexible model training on external data. The explicit separation of training and calibration data, together with the reduction to standard conformal validity under RCT exchangeability, is a clean contribution that could be paired with existing CATE estimators or tabular foundation models.

minor comments (3)
  1. [Abstract] The abstract states that simulations confirm FDR control but supplies no quantitative results, error bars, or description of the simulation design; adding a brief summary table or figure reference would strengthen the claim.
  2. The construction of the conformal score and the precise definition of the conformal p-value (including any dependence on the estimated CATE) should be stated explicitly in the main text with an equation or algorithm box, even if the validity argument is standard.
  3. The lung-cancer case study would benefit from a table reporting the number of discoveries, estimated FDR, and a short description of the selected profiles to make the practical output concrete.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our work and the recommendation for minor revision. The report lists no specific major comments under the MAJOR COMMENTS section.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The framework separates model training on external data from conformal p-value calibration and FDR control on RCT data. Standard conformal validity (exchangeability of calibration and test points) holds independently of how the score function is obtained, so the FDR guarantee does not reduce to a fitted quantity defined by the same data. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided description or abstract. The central claim rests on established conformal properties rather than internal redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the framework implicitly relies on standard conformal-inference exchangeability assumptions and RCT external-data comparability that are not stated or justified here.

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