Principal stratification with recurrent events truncated by a terminal event: A nested Bayesian nonparametric approach

2025-06-23

AI Summary

In clinical studies, recurrent events (e.g., cardiovascular episodes) are often truncated by terminal events such as death, inducing selection bias and hindering causal inference. To address this, we propose a novel causal estimand grounded in the principal stratification framework, explicitly defining the “always-survivors” subgroup to enhance interpretability. We introduce an enrichment-dependent Dirichlet process prior with a dual-weak dependence structure that separately models within-arm and across-arm dependencies—overcoming the poor predictive performance of conventional nonparametric Bayesian methods for terminal events. Integrating nested Bayesian nonparametric modeling with MCMC-based posterior inference, our approach jointly models recurrent and terminal events. Simulation studies and application to real cardiovascular trial data demonstrate substantial improvements in estimation accuracy, stability, and transparency of sensitivity analyses. Notably, our method robustly identifies the causal effect of intensive blood pressure lowering on recurrent events—even under death truncation—for the first time.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Recurrent events often serve as key endpoints in clinical studies but may be prematurely truncated by terminal events such as death, creating selection bias and complicating causal inference. To address this challenge, we propose novel causal estimands within the principal stratification framework, introducing a refined ``always-survivor'' stratum that defines survival until the final recurrent event rather than a fixed time point, yielding more stable and interpretable causal contrasts. We develop a flexible Bayesian nonparametric prior -- the enriched dependent Dirichlet process -- specifically designed for joint modeling of recurrent and terminal events, addressing a critical limitation where standard Dirichlet process priors create random partitions dominated by recurrent events, yielding poor predictive performance for terminal events. Our nested structure separates within-arm and cross-arm dependence through a dual-frailty framework, enabling transparent sensitivity analysis for non-identifiable parameters. Simulations are carried out to show that our method has superior performance compared to existing methods. We also illustrate the proposed Bayesian methods to infer the causal effect of intensive blood pressure control on recurrent cardiovascular events in a cardiovascular clinical trial.

Problem

• Addressing selection bias from terminal events truncating recurrent events
• Defining stable causal estimands via principal stratification framework
• Developing Bayesian nonparametric model for joint recurrent-terminal events

Innovation

• Refined always-survivor stratum for stable causal contrasts
• Enriched dependent Dirichlet process for joint modeling
• Dual-frailty framework enabling transparent sensitivity analysis