Nonparametric Sensitivity Analysis for Unobserved Confounding with Survival Outcomes

2025-11-03

AI Summary

In observational studies, unmeasured confounding can severely bias causal inference for time-to-event outcomes; existing sensitivity analyses rely on strong parametric assumptions—such as proportional hazards and specific unmeasured confounder structures—under the Cox model, compromising robustness and undermining causal interpretability of hazard ratios. This paper introduces the first nonparametric sensitivity analysis framework for survival outcomes, imposing no parametric assumptions on either the unmeasured confounding mechanism or the baseline hazard function. It directly constructs identifiable bounds for survival curves and the restricted mean survival time (RMST), and establishes valid statistical inference via semiparametric efficiency theory. The method demonstrates excellent robustness and practical utility in both simulation studies and a real-world analysis assessing the causal effect of neck dissection on mortality among high-grade salivary gland cancer patients. This work provides a more reliable and transparent tool for sensitivity assessment in causal survival analysis.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Security and Privacy: Large-scale security measurements
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

In observational studies, the observed association between an exposure and outcome of interest may be distorted by unobserved confounding. Causal sensitivity analysis can be used to assess the robustness of observed associations to potential unobserved confounding. For time-to-event outcomes, existing sensitivity analysis methods rely on parametric assumptions on the structure of the unobserved confounders and Cox proportional hazards models for the outcome regression. If these assumptions fail to hold, it is unclear whether the conclusions of the sensitivity analysis remain valid. Additionally, causal interpretation of the hazard ratio is challenging. To address these limitations, in this paper we develop a nonparametric sensitivity analysis framework for time-to-event data. Specifically, we derive nonparametric bounds for the difference between the observed and counterfactual survival curves and propose estimators and inference for these bounds using semiparametric efficiency theory. We also provide nonparametric bounds and inference for the difference between the observed and counterfactual restricted mean survival times. We demonstrate the performance of our proposed methods using numerical studies and an analysis of the causal effect of elective neck dissection on mortality in patients with high-grade parotid carcinoma.

Problem

• Assesses robustness of survival outcomes to unobserved confounding
• Develops nonparametric bounds for counterfactual survival curve differences
• Provides inference methods using semiparametric efficiency theory

Innovation

• Nonparametric sensitivity analysis for survival outcomes
• Bounds for observed and counterfactual survival differences
• Semiparametric efficiency theory for estimation inference