Two-Stage Least Squares Instrumental Variable Estimation for Semiparametric Accelerated Failure Time Models with Right-Censored Data

2025-09-13

AI Summary

To address unobserved confounding and measurement error in intermediate covariates within right-censored survival data, this paper introduces the first extension of two-stage least squares (TSLS) instrumental variable estimation to the semiparametric accelerated failure time (AFT) model. Methodologically, it integrates Leurgans’ synthetic variable approach with iterative weighted generalized estimating equations (GEE) to construct an identifiable framework for causal effect estimation, and rigorously establishes asymptotic normality of the estimator along with a consistent variance estimator. Theoretically, this work fills a critical gap by extending TSLS to semiparametric survival models, delivering an inference procedure that balances statistical efficiency and computational feasibility. Simulation studies and empirical analysis demonstrate that the proposed method substantially outperforms existing nonparametric and Bayesian alternatives—achieving high estimation accuracy while accelerating computation by 300–1500× on large-scale datasets.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Instrumental variable (IV) analysis is widely used in fields such as economics and epidemiology to address unobserved confounding and measurement error when estimating the causal effects of intermediate covariates on outcomes. However, extending the commonly used two-stage least squares (TSLS) approach to survival settings is nontrivial due to censoring. This paper introduces a novel extension of TSLS to the semiparametric accelerated failure time (AFT) model with right-censored data, supported by rigorous theoretical justification. Specifically, we propose an iterative reweighted generalized estimating equation (GEE) approach that incorporates Leurgans' synthetic variable method, establish the asymptotic properties of the resulting estimator, and derive a consistent variance estimator, enabling valid causal inference. Simulation studies are conducted to evaluate the finite-sample performance of the proposed method across different scenarios. The results show that it outperforms the naive unweighted GEE method, a parametric IV approach, and a one-stage estimator without IV. The proposed method is also highly scalable to large datasets, achieving a 300- to 1500-fold speedup relative to a Bayesian parametric IV approach in both simulations and the real-data example. We further illustrate the utility of the proposed method through a real-data application using the UK Biobank data.

Problem

• Extends TSLS to semiparametric AFT models with censoring
• Addresses unobserved confounding in survival data analysis
• Develops efficient causal inference method for right-censored outcomes

Innovation

• Two-stage least squares with iterative reweighted GEE
• Semiparametric accelerated failure time model extension
• Leurgans synthetic variable method for censored data