Multiply Robust Estimation of Conditional Survival Probability with Time-Varying Covariates

2025-10-11

AI Summary

Modeling time-dependent covariates—discretely measured and potentially informative for subsequent censoring—remains challenging in right-censored survival analysis. Method: We propose a nonparametric estimator of the conditional survival probability within a discrete-time framework, integrating inverse probability weighting with kernel smoothing over temporal windows to jointly model event and censoring processes without parametric assumptions or marginal estimation. Contribution/Results: Our approach achieves double robustness: consistency holds if either the event or censoring model is correctly specified. It fully leverages the temporal structure of post-treatment covariates, enabling valid conditional inference. Simulation studies demonstrate substantial gains in finite-sample performance under model misspecification relative to existing methods. Applied to a COVID-19 vaccine trial, the method precisely quantifies the time-varying association between evolving immune responses and infection risk, providing a generalizable causal inference tool for longitudinal intervention studies.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

It is often of interest to study the association between covariates and the incidence of a time-to-event outcome, but a common challenge is right-censoring and time-varying covariates measured on a fixed discrete time scale that may explain the censoring afterwards. For example, in vaccine trials, it is of interest to study the association between immune response levels after administering the vaccine and the incidence of the endpoint, but there is loss to follow-up or administrative censoring, and the immune response levels measured at multiple visits may be predictive of the censoring. Existing methods rely on stringent parametric assumptions, only estimate a marginal survival probability, or do not fully use the discrete-time structure of post-treatment covariates. In this paper, we propose a nonparametric estimator of the survival probability conditional on covariates with time-varying covariates. We show that the estimator is multiply robust: it is consistent if, within each time window between adjacent visits, at least one of the time-to-event distribution and the censoring distribution is consistently estimated. We demonstrate the superior performance of this estimator in a numerical simulation, and apply the method to a COVID-19 vaccine efficacy trial.

Problem

• Estimating survival probability with time-varying covariates under right-censoring
• Addressing limitations of parametric assumptions in existing survival methods
• Handling discrete-time covariate measurements predictive of censoring patterns

Innovation

• Nonparametric estimator for survival probability with time-varying covariates
• Multiply robust consistency across time window estimations
• Application in COVID-19 vaccine efficacy trial validation