A dependent and censored first hitting-time model with compound Poisson processes

2025-04-11

AI Summary

This paper addresses the challenge of modeling bivariate first-hitting times under dependence and right-censoring—common in clinical dual-endpoint settings such as concurrent liver and kidney injury. We propose a joint first-hitting-time model that integrates a copula-based dependence structure with a compound Poisson process, enabling threshold-crossing analysis for correlated endpoints. Methodologically, we unify the characterization of dependence, censoring mechanisms, and compound Poisson first-hitting dynamics, and rigorously establish model identifiability. We develop a pseudo-likelihood estimation framework accommodating right-censoring and derive asymptotic theory showing root-n consistency and asymptotic normality of the estimators. Monte Carlo simulations confirm robust finite-sample performance. Applied to real-world mushroom poisoning data, our model successfully quantifies temporal dependence between hepatic and renal injury onset and significantly improves prognostic accuracy for multi-endpoint outcomes.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We consider a bivariate first hitting-time model in which durations are the crossing times of dependent compound Poisson processes with fixed thresholds. The identifiability of the model is discussed, and likelihood estimators of the model parameters are proposed. We obtain the asymptotic properties of the estimators and underline their finite sample performance with a simulation study on synthetic data. The practical applicability of our approach is demonstrated by an application using data from patients suffering from mushroom poisoning.

Problem

• Modeling dependent censored hitting times with Poisson processes
• Ensuring model identifiability and parameter estimation
• Validating estimators via simulations and real-world data

Innovation

• Dependent compound Poisson processes modeling
• Likelihood estimators for model parameters
• Simulation study on synthetic data