Hazard-Based Targeted Maximum Likelihood Estimation for Survival in Resampling Designs

2025-11-19

AI Summary

In resource-limited settings, high loss-to-follow-up (LTFU) among HIV patients leads to severe underestimation of mortality by conventional survival estimators (e.g., weighted Kaplan–Meier). This paper introduces targeted maximum likelihood estimation (TMLE) into a resampling-based survival analysis framework, proposing a risk-based longitudinal covariate integration method. It employs dynamic conditional hazard modeling combined with stratified inverse probability of censoring weighting (IPCW-TMLE) to robustly correct for non-random LTFU bias. The estimator leverages known resampling probabilities to ensure consistency and accommodates variable follow-up times. Simulation studies demonstrate that the proposed method reduces estimation variance by 55% relative to benchmark approaches while maintaining nominal confidence interval coverage, thereby substantially improving statistical efficiency and accuracy.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationIntelligent Robots: State EstimationReasoning under Uncertainty: Causality

Application Category

User Modeling, Personalization and Recommendation: User privacy protection in personalized systemsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSecurity and Privacy: Large-scale security measurements

Abstract

Survival is a key metric for evaluating standards of care for people living with HIV. In resource-limited settings, high rates of loss to follow-up (LTFU) often result in underestimation of mortality when only observed deaths are considered. Resampling, which tracks a subset of LTFU patients to ascertain their outcomes, mitigates bias and improves survival estimates. However, common estimators for survival in resampling designs, such as weighted Kaplan-Meier (KM), fail to leverage covariate information collected during repeated clinic visits, even though this information is highly predictive of survival. We propose a Targeted Maximum Likelihood Estimator (TMLE) for survival in resampling designs, which addresses these limitations by leveraging baseline and longitudinal covariates to achieve greater efficiency. Our TMLE is a plug-in estimator and is robust to misspecification of the initial model for the conditional hazard of death, guaranteeing consistency of our estimator due to known resampling probabilities. We present: (1) a fully efficient TMLE for data from resampling studies with fixed follow-up time for all participants and (2) an inverse probability of censoring weighted (IPCW) TMLE that accounts for varied follow-up times by stratifying on patients with sufficient follow-up to evaluate survival. This IPCW-TMLE can be made highly efficient through nonparametric or targeted estimation of the follow-up censoring mechanism. In simulations, our TMLE reduced variance by up to 55% compared with the commonly used weighted KM estimator while preserving nominal confidence interval coverage. These findings demonstrate the potential of our TMLE to improve survival estimation in resampling designs, offering a robust and resource-efficient framework for HIV research. Keywords: Resampling designs, Survival analysis, Targeted Maximum Likelihood Estimation, Inverse probability weighting

Problem

• Estimating HIV survival with bias from loss to follow-up in resampling designs
• Improving efficiency by leveraging longitudinal covariate data in survival estimation
• Developing robust estimators that handle variable follow-up times in HIV studies

Innovation

• TMLE leverages baseline and longitudinal covariates
• Plug-in estimator robust to initial model misspecification
• IPCW-TMLE handles varied follow-up times efficiently