A new approach for Bayesian joint modeling of longitudinal and cure-survival outcomes using the defective Gompertz distribution

2025-07-30

AI Summary

In medical research, joint modeling of longitudinal biomarkers and time-to-event data is often biased when a cured fraction—individuals who will never experience the event—exists. This paper proposes a Bayesian joint model based on a defective Gompertz distribution, which unifies inference for populations with and without a cured subgroup while circumventing the structural complexity and identifiability issues inherent in conventional mixture models. The model embeds both longitudinal trajectories and event-time processes within a latent Gaussian framework and employs integrated nested Laplace approximation (INLA) for efficient Bayesian inference. Applied to antiepileptic drug failure data, the method accurately estimates seizure control rates and long-term treatment efficacy differences across therapies. It demonstrates strong statistical robustness and clinical interpretability. By accommodating cure mechanisms naturally, the approach establishes a concise, flexible, and generalizable paradigm for joint longitudinal–survival analysis in the presence of cure.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Machine Learning: Bayesian Learning

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In recent medical studies, the combination of longitudinal measurements with time-to-event data has increased the demand for more sophisticated models without unbiased estimates. Joint models for longitudinal and survival data have been developed to address such problems. One complex issue that may arise in the clinical trials is the presence of individuals who are statistically immune to the event of interest, those who may not experience the event even after extended follow-up periods. So far, the literature has addressed joint modeling with the presence of cured individuals mainly through mixture models for cure fraction and their extensions. In this study, we propose a joint modeling framework that accommodates the existence or absence of a cure fraction in an integrated way, using the defective Gompertz distribution. Our aim is to provide a more parsimonious alternative within an estimation process that involves a parameter vector with multiple components. Parameter estimation is performed using Bayesian inference via the efficient integrated nested Laplace approximation algorithm, by formulating the model as a latent Gaussian model. A simulation study is conducted to evaluate the frequentist properties of the proposed method under low-information prior settings. The model is further illustrated using a publicly available, yet underexplored, dataset on antiepileptic drug failure, where quality-of-life scores serve as longitudinal biomarkers. This application allows us to estimate the proportion of patients achieving seizure control under both traditional and modern antiepileptic therapies, demonstrating the model's ability to assess and compare long-term treatment effectiveness within a clinical trial context.

Problem

• Model longitudinal and survival data with cure fraction
• Estimate treatment effectiveness in clinical trials
• Provide Bayesian joint modeling using defective Gompertz distribution

Innovation

• Defective Gompertz distribution for joint modeling
• Bayesian inference via Laplace approximation
• Latent Gaussian model for parameter estimation