Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring

TL;DR

This work tackles the challenge of estimating heterogeneous treatment effects in survival data when censoring is informative. By reframing the problem with partial identification, the authors derive informative lower and upper bounds on the conditional average treatment effect (CATE) and its component survival quantities, incorporating censoring strength and a domain-knowledge post-dropout survival function. They introduce SurvB-learner, a model-agnostic two-stage meta-learner that produces consistent, double-robust, and quasi-oracle-efficient estimates of these bounds, applicable to discrete and continuous treatments and adaptable to real-world data with hidden confounding. Through synthetic experiments and an application to the ADJUVANT gefitinib trial in NSCLC, the framework reveals genomically defined subgroups with robust treatment benefits despite dropout, illustrating its practical value for robust, individualized evidence generation in medicine and epidemiology.

Abstract

Dropout is common in clinical studies, with up to half of patients leaving early due to side effects or other reasons. When dropout is informative (i.e., dependent on survival time), it introduces censoring bias, because of which treatment effect estimates are also biased. In this paper, we propose an assumption-lean framework to assess the robustness of conditional average treatment effect (CATE) estimates in survival analysis when facing censoring bias. Unlike existing works that rely on strong assumptions, such as non-informative censoring, to obtain point estimation, we use partial identification to derive informative bounds on the CATE. Thereby, our framework helps to identify patient subgroups where treatment is effective despite informative censoring. We further develop a novel meta-learner that estimates the bounds using arbitrary machine learning models and with favorable theoretical properties, including double robustness and quasi-oracle efficiency. We demonstrate the practical value of our meta-learner through numerical experiments and in an application to a cancer drug trial. Together, our framework offers a practical tool for assessing the robustness of estimated treatment effects in the presence of censoring and thus promotes the reliable use of survival data for evidence generation in medicine and epidemiology.

Figures (9)

• Figure 1: Overview of our framework.(A) Data: A key challenge in survival analysis is censoring, where follow-up information about patient outcomes is incomplete. In practice, this can be due to various reasons such as patients dropping out of clinical studies for side effects gupta.2025wiegrebe.2024. As a result, the exact event time (e.g., of death or disease progression) for censored patients is unknown. (B) Intuition behind our framework: Under informative censoring (i.e., when dropout depends on survival time), unbiased point estimation of the CATE $\tau_{a_1, a_2}(x)$ is generally not possible. We therefore reframe the estimation task using partial identification, which allows us to construct informative bounds (i.e., LB and UB) for the CATE, while explicitly accounting for censoring bias. (C) Output example: We propose a two-stage meta-learner called SurvB-learner to efficiently estimate these bounds. The result can be assessed through survival curves of expected survival time, which provide intuitive insights into how unknown censoring may affect CATE estimates. (D) Theoretical property: We show theoretically that (i) the bounds shrink to the point estimate as the censoring bias goes to zero, and that (ii) the bounds are asymptotically consistent with the true CATE (see Proposition \ref{['prop:width_of_bounds']}). Altogether, our framework generates individualized bounds to generate clinical evidence for personalized treatment decision-making.
• Figure 2: Causal graph for survival data under informative censoring. Variables in yellow are observed, while variables in blue are unobserved. Solid edges denote causal relationships, and dashed edges reflect dependence. Note that the absence of arrows encodes causal assumptions, not their presence.
• Figure 4: Findings for the ADJUVANT trial. The ADJUVANT trial zhong.2018liu.2021 assesses the effect of adjuvant gefitinib in $N=171$ patients with EGFR-mutant stage II--IIIA non-small cell lung cancer (NSCLC), yet the original study was subject to large censoring (37.06% for DFS and 63.53% for OS). Hence, our aim is to identify subgroups of patients that have a robust treatment benefit despite potential informative censoring. To do so, we report the proportion of patients where the lower bounds (LBs) of the CATE are strictly greater than zero (i.e., "LBs > 0"), expressed as percentages (%). So, a value close to 100% indicates that nearly all patients in this subgroup benefit from treatment, with a CATE above zero despite potential informative censoring. (A) Patient characteristics: The table on the left reports the baseline characteristics and genetic alterations of the patient population, while the survival curves on the right show the expected survival time for both chemotheropy and gefitinib groups, where the x-axis is time since randomization in months, and the y-axis is the probability that the conditional average survival time beyond that time point. The solid line represents the point estimate from the causal survival forest cui.2023, while the lower and upper bounds (shaded areas) are estimated by the SurvB-learner. (B) Single-covariate analysis: The forest plots show the mean and standard deviation of the estimated lower bounds of the CATE within subgroups defined by baseline characteristics or genetic covariates by bootstrap. For each subgroup on the x-axis, we performed $2000$ bootstrap replications. The background scatter points represent the CATE lower bound estimates without bootstrapping. (C) Data-driven analysis: Using a tailored recursive partition algorithm, we select subgroups with the highest percentage of LBs above zero. Method details are in Supplement \ref{['app:implementation_detail']}. (D) Co-alteration analysis: The heatmap (left) reports the probabilities that the conservative lower bounds are above zero ("LBs > 0") for pairs of genetic biomarkers, while the table (right, sorted alphabetically) summarizes these probabilities for both disease-free survival (DFS) and overall survival (OS) for selected genetic co-alterations. Hence, our framework provides robust evidence of treatment benefit for certain subgroups, even for the efficacy outcome (OS), despite the original study not being able to confirm this and in the presence of informative censoring that could otherwise bias the results.
• Figure 6: Survival curves of conditional average DFS time. These curves show the expected survival time for SMAD4 (top line), CDK4 (middle line), and MYC (bottom line), for patients with alteration (right) and without alteration (left). The x-axis is time since randomization in months, and the y-axis is the probability of conditional average survival time beyond that time point. The lower and upper bounds (shaded areas) are estimated by the SurvB-learner.
• Figure 7: Single-covariate analysis for OS. The forest plot (left) shows the mean and standard deviation of the estimated lower bounds of the CATE within subgroups defined by baseline characteristics or genetic covariates by bootstrap. For each subgroup on the x-axis, we performed $2000$ bootstrap replications. The background scatter points represent the CATE lower bound estimates without bootstrapping. The table (right) reports the probabilities that the conservative lower bounds are above zero ("LBs > 0").

Theorems & Definitions (23)

• Lemma 2.1
• Proof
• Theorem 2.2
• Proof
• Proposition 2.3
• Proof
• Theorem 2.4: Consistency and double robustness
• Proof
• Theorem 2.5: Quasi-oracle efficiency
• Proof