Bayesian joint modelling using semiparametric accelerated failure time approaches

2026-06-14

AI Summary

This study addresses the limitations of traditional joint models in clinical longitudinal studies, where repeatedly measured biomarkers or quality-of-life outcomes are often associated with event times but constrained by the proportional hazards assumption, hindering interpretability on the time scale. The authors propose a class of Bayesian semiparametric accelerated failure time joint models that integrate linear mixed-effects models for the longitudinal process and employ Bernstein polynomials to flexibly model the baseline hazard. A time-warping rescaling strategy is introduced to enhance numerical stability and parameter identifiability. By relaxing the proportional hazards assumption, the proposed approach offers more intuitive time-scale interpretations. Simulation studies demonstrate that, when event risk depends on underlying longitudinal trajectories, the method yields more accurate estimates of treatment effects compared to separate modeling approaches and exhibits excellent finite-sample performance.

Abstract

Longitudinal clinical studies often collect repeated measurements of biomarkers or health-related quality of life together with a time-to-event outcome. These processes are intrinsically linked: longitudinal trajectories may predict event risk, while event occurrence, or its anticipation, can induce informative censoring of the longitudinal process. Joint models provide a principled framework for handling this dependence, but most existing formulations rely on proportional hazards assumptions that may be restrictive and offer limited interpretability on the time scale. We propose a class of semiparametric accelerated failure time joint models that directly model covariate effects on event timing while flexibly capturing longitudinal-event associations. The survival component is specified through an accelerated failure time model with the baseline component represented by a flexible basis expansion, allowing a broad class of smooth baseline specifications. We illustrate the framework using Bernstein polynomial baseline representations and introduce rescaling strategies to improve numerical stability and parameter identifiability under time-warping. Estimation is conducted within a Bayesian framework, enabling joint inference for longitudinal, survival, and association parameters. Simulation studies reflecting realistic longitudinal trajectories, censoring mechanisms, and dependence structures are used to evaluate finite-sample performance. The proposed models show improved recovery of longitudinal treatment effects compared with a standalone linear mixed model when event risk depends on the underlying longitudinal process. Overall, the framework extends existing joint modelling methodology by offering a flexible and interpretable alternative to proportional hazards-based approaches.

Problem

• joint modelling
• accelerated failure time
• longitudinal data
• time-to-event
• informative censoring

Innovation

• semiparametric accelerated failure time
• joint modelling
• Bayesian inference
• Bernstein polynomials
• informative censoring