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arxiv: 2604.03502 · v1 · submitted 2026-04-03 · 📊 stat.ML · cs.LG· stat.ME

Recognition: 2 theorem links

· Lean Theorem

Nonparametric Regression Discontinuity Designs with Survival Outcomes

Erik Sverdrup, Maximilian Schuessler, Robert Tibshirani, Stefan Wager

Authors on Pith no claims yet

Pith reviewed 2026-05-13 17:50 UTC · model grok-4.3

classification 📊 stat.ML cs.LGstat.ME
keywords regression discontinuity designsurvival analysiscensoringdoubly robust estimationcausal inferencenonparametric methodstime-to-event datamedical decision making
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The pith

Nonparametric regression discontinuity designs can now handle survival outcomes with censoring using doubly robust corrections.

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

The paper establishes a nonparametric method for estimating causal effects in regression discontinuity designs when the outcome is a survival time subject to right-censoring. Standard RD methods assume fully observed outcomes, but survival data often have patients lost to follow-up before the event occurs. The proposed approach uses doubly robust corrections for the censoring to adjust the estimation while preserving flexibility for long follow-up and covariate effects. This is relevant for evaluating threshold-based treatment rules in medicine, such as biomarker cutoffs that determine who receives a therapy. The method is shown to be more efficient and robust in simulations and in data from a large cancer screening trial.

Core claim

The authors claim that by applying doubly robust censoring corrections to nonparametric regression discontinuity estimators, one can obtain consistent estimates of treatment effects on survival outcomes at a cutoff threshold, even under complex censoring patterns. This extends standard RD methods to time-to-event settings common in medical research, handling multiple endpoints, long follow-up, and covariate-dependent variation in survival and censoring.

What carries the argument

Doubly robust censoring corrections paired with existing RD estimators to adjust for loss to follow-up while remaining consistent if either the censoring or survival model is correct.

If this is right

  • Survival outcomes with censoring can be analyzed in RD designs without assuming complete data.
  • Multiple endpoints and long follow-up periods become feasible to study.
  • Estimates gain efficiency and robustness to misspecification in applications like cancer screening trials.
  • Implementation is supported by an open-source R package.

Where Pith is reading between the lines

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

  • Similar corrections could be developed for other designs like difference-in-differences with censored outcomes.
  • Using flexible machine learning models for the nuisance functions might further improve performance in high-dimensional settings.
  • Applying the method to policy thresholds in non-health domains with time-to-event data could reveal new insights.
  • Validation in settings with known true effects from randomized trials would strengthen confidence in the approach.

Load-bearing premise

At least one of the censoring mechanism or the conditional survival model must be correctly specified.

What would settle it

A Monte Carlo simulation in which both nuisance models are misspecified and the resulting RD estimate deviates significantly from the known true causal effect.

Figures

Figures reproduced from arXiv: 2604.03502 by Erik Sverdrup, Maximilian Schuessler, Robert Tibshirani, Stefan Wager.

Figure 1
Figure 1. Figure 1: Illustration of the canonical RD design. Survival is declining as the prognostic [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the estimands π h and τ h . For the population with running variable Zi equal to the threshold c, π h is the vertical distance between to counterfactual survival curves P [Ti(w) > h | Zi = c], w ∈ {0, 1}, at time point h, while τ h is the area between the counterfactual survival curves up to time point h. sides near the threshold. From an estimation perspective, this overlooks a core insigh… view at source ↗
Figure 3
Figure 3. Figure 3: The figure shows two scenarios with a total of around 70 months of follow-up. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example of bias using an IPCW approach compared with a more flexible dou [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Uptake of prostate biopsy as a function of the running variable PSA. The [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Event and censoring distributions for prostate cancer-free and overall survival. [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of events and right-censoring for overall survival stratified by [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Effect of prostate biopsy on survival endpoints. The dashed line indicates [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Effect of prostate biopsy on overall survival at varying time horizons. Point [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Relationship between the horizon h and units’ probabilities of remaining un￾censored when analyzing overall survival. At the horizontal dashed line, the probability of remaining uncensored becomes critically low. Units below this line (red color) and near the threshold (vertical dashed line) may cause instabilities in the DR scores and thus RD estimates. results from the PLCO trial suggest that prostate b… view at source ↗
read the original abstract

Quasi-experimental evaluations are central for generating real-world causal evidence and complementing insights from randomized trials. The regression discontinuity design (RDD) is a quasi-experimental design that can be used to estimate the causal effect of treatments that are assigned based on a running variable crossing a threshold. Such threshold-based rules are ubiquitous in healthcare, where predictive and prognostic biomarkers frequently guide treatment decisions. However, standard RD estimators rely on complete outcome data, an assumption often violated in time-to-event analyses where censoring arises from loss to follow-up. To address this issue, we propose a nonparametric approach that leverages doubly robust censoring corrections and can be paired with existing RD estimators. Our approach can handle multiple survival endpoints, long follow-up times, and covariate-dependent variation in survival and censoring. We discuss the relevance of our approach across multiple areas of applications and demonstrate its usefulness through simulations and the prostate component of the Prostate, Lung, Colorectal and Ovarian (PLCO) Cancer Screening Trial where our new approach offers several advantages, including higher efficiency and robustness to misspecification. We have also developed an open-source software package, $\texttt{rdsurvival}$, for the $\texttt{R}$ language.

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

2 major / 2 minor

Summary. The manuscript proposes a nonparametric approach to regression discontinuity designs (RDD) for survival outcomes subject to right-censoring. It pairs existing RD estimators (local polynomials or kernels) with doubly robust censoring corrections that require consistent estimation of either the conditional survival or censoring hazard. The method is claimed to handle multiple survival endpoints, long follow-up, and covariate-dependent variation in survival and censoring. The authors report advantages in simulations and an application to the prostate component of the PLCO Cancer Screening Trial, including higher efficiency and robustness to misspecification, and provide an open-source R package rdsurvival.

Significance. If the central construction preserves double robustness and achieves the required convergence rates under local nonparametric estimation, the work would fill a practical gap for causal inference with censored time-to-event data in threshold-based healthcare settings. The provision of reproducible software strengthens potential impact and adoption.

major comments (2)
  1. The manuscript does not jointly optimize or theoretically justify the bandwidth for the auxiliary nonparametric estimators of the survival and censoring functions with the main RD bandwidth. Under standard regularity conditions, the bias from these auxiliary models can remain of the same order as the leading RD bias term when the censoring or survival surface is not smoother than the outcome regression, potentially invalidating the double-robustness property for the RD estimand. A rate calculation or simulation isolating this issue is needed.
  2. The simulation results claim advantages in efficiency and robustness, but the reported scenarios do not appear to include cases where both the survival and censoring models are misspecified simultaneously while the RD bandwidth is selected via cross-validation on the observed outcome. This leaves the double-robustness claim under-supported for the most relevant practical case.
minor comments (2)
  1. Notation for the doubly robust correction term and the local RD estimator should be aligned more explicitly with standard references (e.g., Hahn et al. or Calonico et al.) to improve readability.
  2. The abstract states advantages on the PLCO data but does not report specific numerical comparisons (e.g., standard errors or confidence interval widths); adding these would clarify the efficiency gain.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify key aspects of our nonparametric RD approach for censored survival data. We address each major comment below and outline targeted revisions that strengthen the theoretical and empirical support without altering the core contributions.

read point-by-point responses

  1. Referee: The manuscript does not jointly optimize or theoretically justify the bandwidth for the auxiliary nonparametric estimators of the survival and censoring functions with the main RD bandwidth. Under standard regularity conditions, the bias from these auxiliary models can remain of the same order as the leading RD bias term when the censoring or survival surface is not smoother than the outcome regression, potentially invalidating the double-robustness property for the RD estimand. A rate calculation or simulation isolating this issue is needed.

    Authors: We thank the referee for this important observation on bandwidth interplay. In the revised manuscript we will add a dedicated subsection deriving the required convergence rates: under standard Hölder smoothness assumptions on the conditional survival and censoring functions (of order at least as high as the main RD regression), the auxiliary nonparametric estimators can be tuned (via separate cross-validation or undersmoothing) so that their bias and variance contributions are o_p of the leading RD bias term, thereby preserving the double-robustness property for the RD estimand. We will also include a focused simulation that isolates auxiliary bandwidth choice while holding the main RD bandwidth fixed, confirming that the double-robustness is maintained in finite samples. revision: yes

  2. Referee: The simulation results claim advantages in efficiency and robustness, but the reported scenarios do not appear to include cases where both the survival and censoring models are misspecified simultaneously while the RD bandwidth is selected via cross-validation on the observed outcome. This leaves the double-robustness claim under-supported for the most relevant practical case.

    Authors: We agree that simultaneous misspecification of both auxiliary models, combined with data-driven bandwidth selection on the observed (censored) outcome, represents the most practically relevant stress test. In the revision we will expand the simulation section with exactly these scenarios: both the survival and censoring hazard models are deliberately misspecified (e.g., via incorrect functional forms or omitted covariates), while the main RD bandwidth is chosen by cross-validation on the observed data. Results will be reported alongside the existing correctly-specified and singly-misspecified cases to directly illustrate the double-robustness property under realistic bandwidth selection. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation builds on external RD estimators and standard DR techniques

full rationale

The paper proposes pairing existing nonparametric RD estimators (local polynomials or kernels) with doubly robust censoring corrections for survival outcomes. The abstract and description explicitly state that the approach 'can be paired with existing RD estimators' and leverages 'doubly robust censoring corrections' without re-deriving or redefining the core RD identification or the DR property from within the paper's own fitted quantities. No equations are presented that reduce the target RD estimand to a self-defined fit, a bandwidth chosen solely on the outcome, or a self-citation chain that bears the identification load. The method is presented as an extension that inherits rates and robustness properties from prior literature on RD and DR censoring, with the main contribution being the practical pairing for survival data. This is self-contained against external benchmarks and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are detailed beyond reliance on standard RDD assumptions and doubly robust estimation properties.

pith-pipeline@v0.9.0 · 5519 in / 1043 out tokens · 151789 ms · 2026-05-13T17:50:30.599352+00:00 · methodology

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

  1. [1]

    censoring

    ISSN 1368-4221. 23 Youngjoo Cho, Chen Hu, and Debashis Ghosh. Analysis of regression discontinuity designs using censored data.Journal of Statistical Research, 55(1):225, 2021. Yifan Cui, Michael R Kosorok, Erik Sverdrup, Stefan Wager, and Ruoqing Zhu. Esti- mating heterogeneous treatment effects with right-censored data via causal survival forests.Journa...

    work page doi:10.1093/jrsssb/qkac001 2021

  2. [2]

    Mark J van der Laan and James M Robins.Unified methods for censored longitudinal data and causality

    doi: 10.1007/0-387-37345-4. Mark J van der Laan and James M Robins.Unified methods for censored longitudinal data and causality. Springer, 2003. Mark J van der Laan, Sherri Rose, Eric C Polley, and Mark J van der Laan. Super learn- ing for right-censored data.Targeted Learning: Causal Inference for Observational and Experimental Data, pages 249–258, 2011....

    work page doi:10.1007/0-387-37345-4 2003