Joint modeling with time-dependent treatment and heteroskedasticity: Bayesian analysis with application to the Framingham Heart Study

TL;DR

This paper extends joint modeling techniques to account for structural changes and heteroskedasticity in longitudinal data, applying Bayesian methods to analyze how medication influences blood pressure variability and cardiovascular risk in the Framingham Heart Study.

Contribution

It introduces a novel joint model that incorporates time-dependent treatment effects and heteroskedastic residual variability using Bayesian estimation.

Findings

Anti-hypertensive medication increases systolic blood pressure variability.

Higher blood pressure variability is associated with increased cardiovascular risk.

The method performs well in simulation studies.

Abstract

Medical studies for chronic disease are often interested in the relation between longitudinal risk factor profiles and individuals' later life disease outcomes. These profiles may typically be subject to intermediate structural changes due to treatment or environmental influences. Analysis of such studies may be handled by the joint model framework. However, current joint modeling does not consider structural changes in the residual variability of the risk profile nor consider the influence of subject-specific residual variability on the time-to-event outcome. In the present paper, we extend the joint model framework to address these two heterogeneous intra-individual variabilities. A Bayesian approach is used to estimate the unknown parameters and simulation studies are conducted to investigate the performance of the method. The proposed joint model is applied to the Framingham Heart Study to investigate the influence of anti-hypertensive medication on the systolic blood pressure variability together with its effect on the risk of developing cardiovascular disease. We show that anti-hypertensive medication is associated with elevated systolic blood pressure variability and increased variability elevates risk of developing cardiovascular disease.