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

TL;DR

This paper introduces a novel TMLE approach for survival analysis in resampling studies, improving efficiency and robustness over traditional estimators by leveraging covariate data and addressing censoring.

Contribution

The paper develops a new TMLE method tailored for resampling survival data, enhancing efficiency and robustness compared to existing estimators like weighted KM.

Findings

TMLE reduced variance by up to 55% compared to weighted KM

TMLE maintained nominal confidence interval coverage

Method effectively leverages covariate information for improved estimates

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