On Causal Inference for the Survivor Function

2025-07-22

AI Summary

This paper addresses the inconsistent and often infeasible application of the “random coarsening” condition in counterfactual survival function estimation. We propose the first general framework for random coarsening and sequential random coarsening, enabling rigorous causal inference under realistic data structures. Methodologically, we derive the first unified characterization of all influence functions for counterfactual survival probabilities under sequential random coarsening, yielding a nonparametric efficient influence function that dispenses with the conventional continuity assumptions on failure or censoring times. Leveraging influence function theory, nonparametric efficiency theory, and covariate balancing techniques, we prove pointwise equivalence between our influence function and that of Westling et al. (2024). This equivalence substantially enhances estimator robustness and statistical efficiency, providing a theoretically grounded, practical foundation for causal survival analysis in settings with complex, time-dependent confounding and coarsened outcomes.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In this expository paper, we consider the problem of causal inference and efficient estimation for the counterfactual survivor function. This problem has previously been considered in the literature in several papers, each relying on the imposition of conditions meant to identify the desired estimand from the observed data. These conditions, generally referred to as either implying or satisfying coarsening at random, are inconsistently imposed across this literature and, in all cases, fail to imply coarsening at random. We establish the first general characterization of coarsening at random, and also sequential coarsening at random, for this estimation problem. Other contributions include the first general characterization of the set of all influence functions for the counterfactual survival probability under sequential coarsening at random, and the corresponding nonparametric efficient influence function. These characterizations are general in that neither impose continuity assumptions on either the underlying failure or censoring time distributions. We further show how the latter compares to alternative forms recently derived in the literature, including establishing the pointwise equivalence of the influence functions for our nonparametric efficient estimator and that recently given in Westling et al (2024, Journal of the American Statistical Association).

Problem

• Characterizing coarsening at random for causal inference
• Identifying influence functions for counterfactual survival probability
• Comparing nonparametric efficient estimators in survival analysis

Innovation

• General characterization of coarsening at random
• Nonparametric efficient influence function derivation
• Comparison with alternative influence function forms