Truncation by death in the sufficient cause framework

2026-04-06

AI Summary

This study addresses the challenge in causal inference posed by death truncation, which renders the outcome undefined for some individuals. Framing the problem within the sufficient-cause paradigm, the authors reformulate it as a comparison across distinct risk types. By integrating principal stratification, causal graphical models, and joint distribution analysis of background factors, they reveal—through a sufficient-cause lens—the non-causal nature of conventional conditional estimators and elucidate the underlying risk structure. The work establishes a formal connection between these estimators and the Survivor Average Causal Effect (SACE), provides an interpretable expression for SACE, and identifies structural sufficient conditions under which SACE equals zero. This clarifies the source of bias in naïve estimators and offers a novel pathway for causal identification in the presence of truncation due to death.

Technology Category

Reasoning under Uncertainty: CausalityMachine Learning: Causal LearningKnowledge Representation and Reasoning: Action, Change, and Causality

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metricsSecurity and Privacy: Large-scale security measurements

Abstract

The sufficient cause framework has been used for decades to improve our understanding of both basic and more complex causal concepts in epidemiology, such as mediation and interaction. Here, we make use of this framework to provide a description of truncation by death, in which the outcome of interest is undefined for individuals who die before the time of assessment at the end of follow-up. We explain the non-causal nature of the crude estimand that compares outcomes by treatment levels conditional on observed survival by showing that it corresponds to a comparison of distinct risk status types, which are defined based on the susceptibility to sufficient causes. Further, expressions for the crude estimand and for the survivor average causal effect, a causal estimand defined under the principal stratification approach, are provided in terms of population-level joint frequencies of the background factors of sufficient causes. Finally, we also describe conditions, based on background factors of sufficient causes, under which the survivor average causal effect is null. Our description of this problem, which studies truncation by death from a new perspective, might encourage further analyses of principal stratification-based estimands using sufficient causes.

Problem

• truncation by death
• sufficient cause framework
• causal inference
• principal stratification
• survivor average causal effect

Innovation

• sufficient cause framework
• truncation by death
• principal stratification
• survivor average causal effect
• causal inference