Characterizing Survivor Principal Strata Over Time: Identification, Efficient Estimation, and Sensitivity Analysis
Abstract
Longitudinal studies with functional outcomes subject to truncation-by-death frequently report time-indexed survivor average causal effect estimates, defined among individuals who would survive regardless of treatment assignment. Because the survivor stratum can change over time, the resulting effect estimates may pertain to populations with different characteristics. We propose accompanying survivor average causal effect estimates with measures of covariate divergence between the survivor and baseline populations. We study standardized mean differences (SMDs) and the Kullback-Leibler (KL) divergence as moment-based and distributional summaries, respectively. We show that these divergence measures are identified under a subset of standard principal stratification assumptions and that their identification involves nuisance functions already estimated in survivor analyses. We derive the efficient influence functions, enabling construction of one-step bias-corrected estimators with appealing large-sample properties and allowing machine learning for nuisance estimation. We demonstrate that in randomized studies, one-step estimation of SMDs is robust to arbitrary nuisance model misspecification, whereas the KL divergence and broader density ratio estimands are more sensitive to nuisance misspecification. Additionally, we provide a sensitivity analysis framework that partially relaxes a monotonicity assumption required for identification, and construct one-step estimators for the resulting bounds. Through simulation studies, we demonstrate the finite-sample performance of the proposed estimators and illustrate how divergence measures can improve the interpretability of survivor analyses. Finally, we assess covariate divergence in survivor strata over time in amyotrophic lateral sclerosis (ALS) trials, using data from the Pooled Resource Open-Access ALS Clinical Trials database.
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BibTeX
@misc{barnatchez2026characterizing,
title = {{Characterizing Survivor Principal Strata Over Time: Identification, Efficient Estimation, and Sensitivity Analysis}},
author = {Keith Barnatchez and Willow Butler and Julia A. Geller and Elizabeth A. Stuart},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37821},
eprint = {2609.37821},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37821},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Characterizing Survivor Principal Strata Over Time: Identification, Efficient Estimation, and Sensitivity Analysis
AU - Keith Barnatchez
AU - Willow Butler
AU - Julia A. Geller
AU - Elizabeth A. Stuart
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37821
UR - https://arxiv.org/abs/2609.37821
AB - Longitudinal studies with functional outcomes subject to truncation-by-death frequently report time-indexed survivor average causal effect estimates, defined among individuals who would survive regardless of treatment assignment. Because the survivor stratum can change over time, the resulting effect estimates may pertain to populations with different characteristics. We propose accompanying survivor average causal effect estimates with measures of covariate divergence between the survivor and baseline populations. We study standardized mean differences (SMDs) and the Kullback-Leibler (KL) divergence as moment-based and distributional summaries, respectively. We show that these divergence measures are identified under a subset of standard principal stratification assumptions and that their identification involves nuisance functions already estimated in survivor analyses. We derive the efficient influence functions, enabling construction of one-step bias-corrected estimators with appealing large-sample properties and allowing machine learning for nuisance estimation. We demonstrate that in randomized studies, one-step estimation of SMDs is robust to arbitrary nuisance model misspecification, whereas the KL divergence and broader density ratio estimands are more sensitive to nuisance misspecification. Additionally, we provide a sensitivity analysis framework that partially relaxes a monotonicity assumption required for identification, and construct one-step estimators for the resulting bounds. Through simulation studies, we demonstrate the finite-sample performance of the proposed estimators and illustrate how divergence measures can improve the interpretability of survivor analyses. Finally, we assess covariate divergence in survivor strata over time in amyotrophic lateral sclerosis (ALS) trials, using data from the Pooled Resource Open-Access ALS Clinical Trials database.
ER -