Targeted learning of heterogeneous treatment effect curves for right censored or left truncated time-to-event data

2026-03-27

AI Summary

This work proposes surv-iTMLE, a novel method for estimating individualized treatment effects in time-to-event data subject to right censoring and left truncation—a setting where existing causal machine learning approaches often yield biased and non-smooth effect estimates due to neglect of temporal structure. Built upon the targeted maximum likelihood estimation (TMLE) framework, surv-iTMLE integrates machine learning with causal inference to model differences in conditional survival probabilities while enforcing temporal smoothness constraints to enhance finite-sample stability. The resulting estimator produces bounded, smooth curves that reflect heterogeneous treatment effects over time. Simulation studies demonstrate that surv-iTMLE substantially outperforms current methods in both bias reduction and smoothness of estimated effect trajectories. Applied to real-world data on immune checkpoint inhibitors in non-small cell lung cancer, the method successfully uncovers clinically meaningful time-varying treatment effects.

Abstract

In recent years, there has been growing interest in causal machine learning estimators for quantifying subject-specific effects of a binary treatment on time-to-event outcomes. Estimation approaches have been proposed which attenuate the inherent regularisation bias in machine learning predictions, with each of these estimators addressing measured confounding, right censoring, and in some cases, left truncation. However, the existing approaches are found to exhibit suboptimal finite-sample performance, with none of the existing estimators fully leveraging the temporal structure of the data, yielding non-smooth treatment effects over time. We address these limitations by introducing surv-iTMLE, a targeted learning procedure for estimating the difference in the conditional survival probabilities under two treatments. Unlike existing estimators, surv-iTMLE accommodates both left truncation and right censoring while enforcing smoothness and boundedness of the estimated treatment effect curve over time. Through extensive simulation studies under both right censoring and left truncation scenarios, we demonstrate that surv-iTMLE outperforms existing methods in terms of bias and smoothness of time-varying effect estimates in finite samples. We then illustrate surv-iTMLE's practical utility by exploring heterogeneity in the effects of immunotherapy on survival among non-small cell lung cancer (NSCLC) patients, revealing clinically meaningful temporal patterns that existing estimators may obscure.

Problem

• heterogeneous treatment effect
• right censoring
• left truncation
• time-to-event data
• causal machine learning

Innovation

• heterogeneous treatment effect
• time-to-event data
• right censoring
• left truncation
• targeted maximum likelihood estimation