Asymptotic theory of rerandomization for survival analysis

2026-04-25

AI Summary

This study addresses the lack of asymptotic theory for functional parameters—such as survival functions—under rerandomization designs with censored data. It develops a unified asymptotic framework based on uniform weak convergence, inverse probability censoring weighting, and debiased machine learning. The work establishes, for the first time, that Kaplan–Meier–type estimators under rerandomization (and stratified rerandomization) achieve strictly smaller pointwise asymptotic variance. Moreover, it demonstrates that Neyman orthogonality renders the variance of debiased machine learning estimators invariant to the randomization scheme. These theoretical findings are corroborated through simulations and empirical analysis, clarifying that while rerandomization enhances the efficiency of conventional estimators, it offers no such gain for orthogonalized machine learning estimators—thereby elucidating the distinct roles of covariate adjustment and constrained randomization in estimation efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• rerandomization
• survival analysis
• censoring
• infinite-dimensional parameters
• asymptotic theory

Innovation

• rerandomization
• survival analysis
• asymptotic theory
• Kaplan-Meier estimator
• Neyman orthogonality