arxiv: 2605.06581 · v1 · submitted 2026-05-07 · 📊 stat.ME

Recognition: unknown

History-Aware Conformal Prediction Sets for Censored Time-to-Event Outcomes

Alexander W. Levis, Larry Han, Shu Yang, Yuyao Wang

Pith reviewed 2026-05-08 07:18 UTC · model grok-4.3

classification 📊 stat.ME

keywords conformal predictiontime-to-event datacensored outcomesprediction setsinverse probability weightingdoubly robust estimationsurvival analysis

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The pith

History-aware conformal sets use covariate histories and censoring weights to produce shorter prediction intervals for event times that cover the truth among survivors.

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

The paper develops History-Aware Prediction Sets to overcome the limits of standard conformal methods for time-to-event outcomes that rely only on baseline information. It builds sets for the individual event time by conditioning on the full covariate history observed up to a chosen decision point and applies inverse probability of censoring weighting to handle right censoring. When the weights are estimated consistently the sets deliver probably asymptotically approximately correct coverage specifically among those who have survived to the decision point. This matters because the resulting intervals are substantially narrower than baseline-only versions, which can support more precise timing decisions in settings such as medical follow-up. Simulations and two real benchmark datasets confirm large reductions in interval length while coverage stays near the nominal level.

Core claim

The central claim is that conformal prediction sets for right-censored time-to-event outcomes can be constructed to achieve PAAC coverage among survivors by incorporating the observed covariate history up to the decision time and reweighting uncensored observations by the inverse probability of remaining uncensored; two doubly robust variants are also given that protect the coverage guarantee if either the censoring or outcome model is correct.

What carries the argument

History-Aware Prediction Sets (HAPS) that condition the nonconformity score on the full observed covariate process up to the decision time and reweight by inverse probability of censoring.

If this is right

The sets remain valid conditionally on survival to the decision time rather than only unconditionally from baseline.
Doubly robust extensions preserve the coverage property even when one of the two models is misspecified.
Interval lengths shrink because the method uses updated, individual-specific information instead of fixed baseline data alone.
The same weighting approach can be applied at multiple decision times to produce a sequence of updating forecasts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could be extended to streaming settings where new covariate measurements arrive continuously and predictions are refreshed in real time.
It may improve resource planning in clinical cohorts by supplying tighter bounds on remaining time for patients still under observation.
The framework suggests a general route for bringing dynamic histories into other conformal procedures that currently use only static features.

Load-bearing premise

The censoring weights must be estimated consistently or at least one model in the doubly robust version must be correct.

What would settle it

A simulation or dataset in which both the censoring and outcome models are misspecified in a manner not protected by double robustness, and the empirical coverage among survivors falls materially below the target probability.

Figures

Figures reproduced from arXiv: 2605.06581 by Alexander W. Levis, Larry Han, Shu Yang, Yuyao Wang.

**Figure 2.** Figure 2: Summary of 90% prediction intervals across 200 Monte Carlo replications comparing view at source ↗

**Figure 3.** Figure 3: Summary of 80% prediction intervals across 200 random splits for data applications. view at source ↗

**Figure 4.** Figure 4: Illustration for the data structure and the definitions of view at source ↗

**Figure 5.** Figure 5: Summaries for the 90% prediction intervals in Setup A of the main paper. view at source ↗

**Figure 6.** Figure 6: Summaries for the 90% prediction intervals in Setup B of the main paper. view at source ↗

**Figure 7.** Figure 7: Summary of 90% prediction intervals with DDH prediction model and a misspecified view at source ↗

**Figure 8.** Figure 8: Mean coverage and median interval length of 80% prediction intervals from HAPS, HAPS view at source ↗

**Figure 9.** Figure 9: Summary of 90% prediction intervals for HAPS and its two extensions in DGM2 under two view at source ↗

**Figure 10.** Figure 10: Summary of 80% prediction intervals across 200 random splits for the colon cancer data. view at source ↗

**Figure 11.** Figure 11: Summary of 80% prediction intervals across 200 random splits for the PBC data. view at source ↗

read the original abstract

Existing conformal prediction methods for time-to-event outcomes leverage only baseline covariates, producing prediction intervals that are insufficiently informative to facilitate decision making. We propose History-Aware Prediction Sets (HAPS), a conformal framework that constructs prediction sets for individual event times using covariate histories observed up to a decision time, targeting coverage among individuals who have survived to this time. HAPS handles right censoring adjusted for time-varying confounders via inverse probability of censoring weighting. When the censoring weights are consistently estimated, it achieves PAAC (probably asymptotically approximately correct) coverage among survivors. We further propose two doubly robust extensions of HAPS to weaken reliance on consistent estimation of the censoring distribution. In simulations, HAPS and its extensions reduce median prediction interval length by up to 75\% relative to baseline comparators while maintaining close to nominal coverage. On two public benchmark data sets, HAPS reduces the median interval length by up to 60\% for predictions at year 5, compared to the baseline comparators.

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.

Desk Editor's Note private letter to a colleague

HAPS adds history-aware conformal sets to censored survival data via IPCW and DR extensions, with clear empirical gains on interval length, but the coverage under joint nuisance misspecification needs explicit proof details.

read the letter

The paper introduces HAPS, a conformal framework that constructs prediction sets for event times using covariate histories observed up to a decision time and targets coverage among survivors. It adjusts for right censoring with inverse probability of censoring weights and adds two doubly robust extensions to reduce dependence on the censoring model alone. This is the main new piece: moving beyond baseline-only conformal methods to history-dependent sets in time-to-event settings with censoring. The simulations report up to 75% shorter median intervals while holding coverage near nominal, and the two public datasets show up to 60% length reductions at year 5. Those numbers are the strongest evidence the paper supplies for practical value. The targeting of survivor-specific coverage at the decision time is a sensible choice for applications like ongoing medical monitoring. The soft spots sit in the theoretical backing. The abstract claims PAAC coverage when censoring weights are consistent and says the DR versions weaken that reliance, yet it does not lay out how the conformity scores built from history-dependent residuals or pseudo-outcomes preserve the necessary exchangeability or asymptotic quantile properties when both the outcome and censoring models are misspecified in correlated ways. The stress-test concern about the rank distribution of scores under joint error is reasonable to raise until the full argument is checked. Sensitivity to weight estimation errors is also left unaddressed in the summary. This is for statisticians and methodologists working on uncertainty quantification in longitudinal survival data. A reader who needs shorter, still-valid intervals for time-varying covariates will get concrete ideas and benchmarks from it. The work has enough substance and addresses a genuine gap, so it deserves peer review even if the theory section will likely need tightening and extra robustness checks.

Referee Report

2 major / 2 minor

Summary. The paper proposes History-Aware Prediction Sets (HAPS), a conformal prediction framework for right-censored time-to-event outcomes that incorporates covariate histories observed up to a decision time and targets coverage among survivors. It adjusts for censoring via inverse probability of censoring weighting (IPCW) with time-varying confounders, claims probably asymptotically approximately correct (PAAC) coverage when censoring weights are consistent, introduces two doubly robust extensions, and reports up to 75% reduction in median interval length in simulations and up to 60% at year 5 on real data while maintaining nominal coverage.

Significance. If the coverage guarantees are rigorously established, the work would meaningfully extend conformal prediction to dynamic, history-dependent survival settings, enabling tighter and more actionable intervals for time-specific decisions. The empirical gains in interval efficiency and the attempt to weaken reliance on censoring model correctness via double robustness are clear strengths relative to baseline-only conformal methods.

major comments (2)

[Abstract] Abstract: the claim that HAPS achieves PAAC coverage among survivors when censoring weights are consistently estimated is load-bearing, yet the abstract provides no definition of the history-aware conformity scores, the precise form of the IPCW-adjusted residuals, or the argument establishing (asymptotic) exchangeability of the weighted scores conditional on survival to the decision time.
[Abstract] Abstract: for the doubly robust extensions, it is not indicated whether the coverage argument uses the standard DR expansion (which debiases the point estimate but does not automatically protect the quantile of the score distribution) or a conformal-specific argument; without this, it remains possible that joint misspecification of the censoring and outcome models in correlated ways (e.g., shared time-varying confounders) can distort the rank distribution of the scores and invalidate PAAC coverage among survivors.

minor comments (2)

[Abstract] The abstract refers to 'two public benchmark data sets' without naming them or providing access details, which hinders immediate reproducibility assessment.
Simulation results are summarized only at a high level (up to 75% length reduction); reporting the number of Monte Carlo replications, exact censoring mechanisms, and the precise baseline comparators would strengthen the empirical section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight opportunities to improve the clarity of the abstract. We address each point below and have revised the abstract to incorporate more precise technical descriptions while preserving its conciseness.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that HAPS achieves PAAC coverage among survivors when censoring weights are consistently estimated is load-bearing, yet the abstract provides no definition of the history-aware conformity scores, the precise form of the IPCW-adjusted residuals, or the argument establishing (asymptotic) exchangeability of the weighted scores conditional on survival to the decision time.

Authors: We agree that the abstract should supply sufficient context for the coverage claim. In the revision we have expanded the abstract to define the history-aware conformity scores as the IPCW-weighted residuals that incorporate the full covariate history up to the decision time. We also state the form of the IPCW-adjusted residuals and indicate that the PAAC coverage follows from the asymptotic exchangeability of these weighted scores conditional on survival, as proved in Theorem 1. These additions make the abstract self-contained without exceeding length limits. revision: yes
Referee: [Abstract] Abstract: for the doubly robust extensions, it is not indicated whether the coverage argument uses the standard DR expansion (which debiases the point estimate but does not automatically protect the quantile of the score distribution) or a conformal-specific argument; without this, it remains possible that joint misspecification of the censoring and outcome models in correlated ways (e.g., shared time-varying confounders) can distort the rank distribution of the scores and invalidate PAAC coverage among survivors.

Authors: We thank the referee for this distinction. The coverage guarantee for the doubly robust extensions rests on a conformal-specific argument: double robustness ensures the weighted scores remain asymptotically exchangeable conditional on survival, thereby preserving the quantile properties required for conformal validity. This is distinct from the standard DR expansion for point estimation. We have added a clarifying sentence to the revised abstract and expanded the discussion in Section 4.2 to state the conditions under which joint misspecification (including correlated errors) may invalidate coverage. We have also added simulation results under partial misspecification to illustrate the practical behavior. revision: partial

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper proposes HAPS, a history-aware conformal prediction framework for censored time-to-event data. Its core coverage guarantee relies on standard conformal prediction exchangeability arguments applied to IPCW-weighted or doubly-robust pseudo-residuals. The abstract and claimed derivations invoke established IPCW and DR theory rather than re-deriving coverage from fitted quantities by construction. No self-definitional reduction, fitted-input-called-prediction, or load-bearing self-citation chain appears in the provided text. The length-reduction claims are simulation- and data-based rather than tautological. Overall, the derivation is self-contained against external benchmarks (standard CP + IPCW/DR).

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard conformal prediction assumptions plus survival-specific conditions for censoring adjustment; no new entities are invented.

axioms (2)

domain assumption Data satisfy approximate exchangeability conditional on histories for conformal coverage to hold
Core requirement for any conformal prediction method to deliver valid coverage.
domain assumption Censoring mechanism is correctly modeled or the doubly robust property protects against misspecification
Explicitly required for the stated PAAC coverage among survivors.

pith-pipeline@v0.9.0 · 5479 in / 1340 out tokens · 92093 ms · 2026-05-08T07:18:51.878896+00:00 · methodology

discussion (0)

Reference graph

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