On inference in parametric survival data models

2026-03-23

AI Summary

This study addresses the failure of conventional inference methods in parametric survival models under model misspecification, where both the estimand and limiting distribution may deviate from their nominal forms. Adopting a model-agnostic perspective, the work integrates asymptotic theory with a robust inference framework, extending influence functions to censored data settings and developing bootstrap strategies tailored to complex life history models—including regression frameworks and Markov chains. The research rigorously characterizes the true probability limit and asymptotic distribution of estimators under misspecification, proposes novel approaches to enhance inferential robustness, and demonstrates through both theoretical analysis and simulation studies the effectiveness and applicability of the proposed framework in complex survival analysis scenarios.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The usual parametric models for survival data are of the following form. Some parametrically specified hazard rate $α(s,θ)$ is assumed for possibly censored random life times $X_1^0,\ldots,X_n^0$; one observes only $X_i=\min\{X_i^0,c_i\}$ and $δ_i=I\{X_i^0\le c_i\}$ for certain censoring times $c_i$ that either are given or come from some censoring distribution. We study the following problems: What do the maximum likelihood estimator and other estimators really estimate when the true hazard rate $α(s)$ is different from the parametric hazard rates? What is the limit distribution of an estimator under such outside-the-model circumstances? How can traditional model-based analyses be made model-robust? Does the model-agnostic viewpoint invite alternative estimation approaches? What are the consequences of carrying out model-based and model-robust bootstrapping? How do theoretical and empirical influence functions generalise to situations with censored data? How do methods and results carry over to more complex models for life history data like regression models and Markov chains?

Problem

• parametric survival models
• model misspecification
• censored data
• robust inference
• hazard rate

Innovation

• model misspecification
• robust inference
• censored survival data
• influence function
• parametric hazard models