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arxiv: 2604.23393 · v1 · submitted 2026-04-25 · 📊 stat.ME · math.ST· stat.TH

Asymptotic theory of rerandomization for survival analysis

Xinyuan Chen , Fan Li This is my paper

Pith reviewed 2026-05-08 07:36 UTC · model grok-4.3

classification 📊 stat.ME math.STstat.TH
keywords rerandomizationsurvival analysisKaplan-Meier estimatorasymptotic varianceNeyman orthogonalitycensored datarandomized experimentsvariance reduction
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The pith

Rerandomization produces limiting processes with reduced pointwise asymptotic variance for Kaplan-Meier survival estimators under censoring.

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

The paper develops asymptotic theory for rerandomization in randomized experiments with survival outcomes subject to censoring. It establishes that the Kaplan-Meier estimator and the inverse probability of censoring weighted Kaplan-Meier estimator converge uniformly to tight limiting processes whose pointwise asymptotic variances are smaller than under complete randomization. By contrast, the pointwise asymptotic variance of a debiased machine learning estimator for the survival function stays the same under rerandomization, which follows from its Neyman orthogonality. This distinction clarifies when restricted randomization improves precision for functional parameters in survival analysis and when it leaves precision unchanged. The results describe the interplay between balance induced by the design and covariate adjustment performed at analysis time.

Core claim

Under rerandomization and stratified rerandomization, treatment-specific Kaplan-Meier and inverse probability of censoring weighted Kaplan-Meier estimators converge uniformly to tight limiting processes with strictly smaller pointwise asymptotic variances than under complete randomization. The pointwise asymptotic variance of the debiased machine learning survival function estimator remains invariant to the choice of randomization design because of Neyman orthogonality. These results extend existing finite-dimensional theory for M-estimators to infinite-dimensional functional parameters that arise with censored survival data.

What carries the argument

Uniform weak convergence of the treatment-specific survival function estimators to tight Gaussian processes, together with the Neyman orthogonality condition that leaves the asymptotic variance of the debiased estimator unchanged.

If this is right

  • The Kaplan-Meier estimator achieves lower pointwise asymptotic variance at every time point when rerandomization is used.
  • The inverse probability of censoring weighted Kaplan-Meier estimator exhibits the same pointwise variance reduction.
  • The debiased machine learning estimator of the survival function has unchanged asymptotic variance under rerandomization.
  • The same convergence and variance properties hold for both rerandomization and stratified rerandomization designs.

Where Pith is reading between the lines

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

  • Designers of survival trials may obtain efficiency gains from rerandomization without needing additional post-randomization adjustment for non-orthogonal estimators.
  • When orthogonality holds, the variance properties of the analysis are robust to whether the trial used complete randomization or rerandomization.
  • The geometric balance-variance relationship identified here could be checked in other functional estimation problems that involve censoring or missing data.

Load-bearing premise

The claimed variance reduction for the Kaplan-Meier estimators and the invariance for the debiased estimator both require that Neyman orthogonality holds exactly and that the standard regularity conditions for uniform convergence of Kaplan-Meier processes are satisfied.

What would settle it

A Monte Carlo study in which the empirical pointwise variance of the Kaplan-Meier estimator under rerandomization fails to match the smaller value predicted by the limiting process would falsify the variance-reduction result.

Figures

Figures reproduced from arXiv: 2604.23393 by Fan Li, Xinyuan Chen.

Figure 1
Figure 1. Figure 1: A geometric illustration of the effect of rerandomization on the limiting processes view at source ↗
read the original abstract

Rerandomization systematically reduces chance imbalance and can improve the efficiency of the average treatment effect estimator in randomized experiments. While the asymptotic properties of finite-dimensional M-estimators under rerandomization have been established, existing theory does not directly address survival outcomes under censoring, where the target estimand involves infinite-dimensional functional parameters. This article establishes the uniform weak convergence of treatment-specific survival function estimators under rerandomization and stratified rerandomization. We prove that the Kaplan-Meier and inverse probability of censoring weighted Kaplan-Meier estimators converge to tight limiting processes with reduced pointwise asymptotic variances. Furthermore, we prove that the pointwise asymptotic variance of the debiased machine learning survival function estimator remains invariant under rerandomization, a consequence of the Neyman orthogonality. Simulations and a real data example are used to illustrate the theoretical results. Our results characterize the geometric interplay between restricted randomization designs and analysis-stage covariate adjustment for functional target estimands in survival analysis.

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 / 4 minor

Summary. The paper develops asymptotic theory for rerandomization in randomized experiments with survival outcomes subject to censoring. It establishes uniform weak convergence of treatment-specific Kaplan-Meier and inverse-probability-of-censoring-weighted Kaplan-Meier estimators to tight limiting Gaussian processes under both rerandomization and stratified rerandomization, with explicit pointwise asymptotic variance reductions relative to complete randomization. It further shows that the pointwise asymptotic variance of a debiased machine-learning estimator for the survival function remains invariant under rerandomization, owing to Neyman orthogonality. The theoretical results are illustrated via simulations and a real-data example, and the work characterizes the geometric interaction between restricted randomization designs and covariate-adjusted functional estimation.

Significance. If the derivations hold, the manuscript supplies the first rigorous extension of rerandomization asymptotics to infinite-dimensional survival estimators. The variance-reduction and invariance results, together with the explicit limiting processes, provide a foundation for more efficient design and analysis of clinical trials with time-to-event endpoints. The emphasis on Neyman orthogonality as a mechanism that preserves asymptotic variance under design restrictions is a useful conceptual contribution that may generalize to other functional estimands.

minor comments (4)
  1. The statement of the uniform weak-convergence result (likely in the main theorem) should explicitly list the regularity conditions on the censoring distribution and the support of the survival times that are needed to preserve the martingale structure under the rerandomization constraint.
  2. In the section deriving the reduced asymptotic variance for the IPCW-KM estimator, the expression for the variance reduction factor should be written out explicitly rather than left in operator notation, to facilitate direct comparison with the complete-randomization case.
  3. The simulation study would benefit from reporting the empirical coverage of the pointwise confidence intervals constructed from the derived limiting variances, in addition to the variance estimates themselves.
  4. Notation for the treatment-specific at-risk processes and the rerandomization balance constraint should be introduced with a single consolidated table or display to avoid repeated re-definition across sections.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation and recommendation for minor revision. The provided summary accurately captures our contributions on the uniform weak convergence of the Kaplan-Meier and IPCW Kaplan-Meier estimators under rerandomization and stratified rerandomization, the explicit pointwise variance reductions, and the invariance result for the debiased machine-learning estimator stemming from Neyman orthogonality. As the report contains no specific major comments, we have no point-by-point responses or revisions to propose based on this feedback.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivations rely on standard weak-convergence theory for Kaplan-Meier estimators under censoring and established results for rerandomization designs, without any reduction of target quantities to fitted parameters, self-definitional constructions, or load-bearing self-citations that collapse the central claims. The uniform convergence, variance reduction for KM and IPCW-KM estimators, and invariance for the debiased ML estimator via Neyman orthogonality are obtained by applying existing martingale and functional central limit theorem arguments to the restricted randomization setting, keeping the argument self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard regularity conditions from survival analysis and semiparametric statistics; no new free parameters or invented entities are introduced.

axioms (2)
  • domain assumption Standard regularity conditions for uniform weak convergence of Kaplan-Meier and IPCW Kaplan-Meier processes under censoring
    Invoked to obtain the tight limiting Gaussian processes with reduced variances.
  • domain assumption Neyman orthogonality of the debiased machine-learning survival estimator
    Used to conclude that its pointwise asymptotic variance is invariant to rerandomization.

pith-pipeline@v0.9.0 · 5458 in / 1285 out tokens · 51069 ms · 2026-05-08T07:36:46.191784+00:00 · methodology

discussion (0)

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Reference graph

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