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

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.

Figures (15)

• Figure 1: surv-iTMLE algorithm - Step 1 - Obtaining pseudo-outcomes.
• Figure 2: surv-iTMLE algorithm - Step 2 - Estimating the difference in conditional survival probabilities under two treatments for a given patient.
• Figure 3: Mean root mean squared error (RMSE) by time point for surv-iTMLE, CSFs and the T-learner when estimating the difference in conditional survival probabilities under two treatments using training data with sample size $n=2400$, with varying proportions of left truncation (LT). LSS: local survival stacking.
• Figure 4: Individual estimates of the difference in conditional survival probabilities under two treatments plotted for one individual over time, with estimates obtained by surv-iTMLE, CSFs and the T-learner using training data of samples size $n=2400$.
• Figure 5: Individual difference in conditional survival probabilities over time for three example NSCLC patients if they were to initiate immunotherapy/chemotherapy after a NSCLC diagnosis, with treatment effects estimated by surv-iTMLE, CSFs and the T-learner.

Theorems & Definitions (1)

• proof