Bayesian Arc Length Survival Analysis Model (BALSAM): Theory and Application to an HIV/AIDS Clinical Trial

TL;DR

This paper introduces BALSAM, a Bayesian survival analysis model that incorporates arc length to better capture the impact of cumulative variations in longitudinal data, demonstrated through simulations and an HIV/AIDS clinical trial.

Contribution

BALSAM uniquely integrates arc length with joint and distributed lag models within a Bayesian framework to improve survival analysis of longitudinal biomarkers.

Findings

BALSAM effectively captures the impact of cumulative variations on hazard rates.

Simulation studies show improved model performance over traditional methods.

Application to HIV/AIDS data reveals significant effects of CD4 count variability on mortality.

Abstract

Stochastic volatility often implies increasing risks that are difficult to capture given the dynamic nature of real-world applications. We propose using arc length, a mathematical concept, to quantify cumulative variations (the total variability over time) to more fully characterize stochastic volatility. The hazard rate, as defined by the Cox proportional hazards model in survival analysis, is assumed to be impacted by the instantaneous value of a longitudinal variable. However, when cumulative variations pose a significant impact on the hazard, this assumption is questionable. Our proposed Bayesian Arc Length Survival Analysis Model (BALSAM) infuses arc length into a united statistical framework by synthesizing three parallel components (joint models, distributed lag models, and arc length). We illustrate the use of BALSAM in simulation studies and also apply it to an HIV/AIDS clinical trial to assess the impact of cumulative variations of CD4 count (a critical longitudinal biomarker) on mortality while accounting for measurement errors and relevant variables.