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

**Authors:** Yan Gao, Rodney A. Sparapani, Sanjib Basu  
**arXiv:** [2212.06353](https://arxiv.org/abs/2212.06353)  
**Date:** 2022-12-13  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2212.06353v1/

## Key points

- The Bayesian Arc Length Survival Analysis Model (BALSAM) is a statistical framework proposed by Yan Gao, Rodney A. Sparapani, and Sanjib Basu.
- BALSAM uses arc length, a mathematical concept that quantifies cumulative variations over time, to more fully characterize stochastic volatility.
- The Cox proportional hazards model in survival analysis assumes that the hazard rate is impacted by the instantaneous value of a longitudinal variable.
- However, when cumulative variations pose a significant impact on the hazard rate, this assumption becomes questionable.
- BALSAM infuses arc length into a united statistical framework by synthesizing three parallel components: joint models, distributed lag models, and arc length.
- The authors illustrate the use of BALSAM in simulation studies and apply it to an HIV/AIDS clinical trial to assess the impact of cumulative variations of CD4 count on mortality while accounting for measurement errors and relevant variables.
- The results show that incorporating arc length into survival analysis can provide more accurate estimates of risk associated with stochastic volatility.
- Overall, BALSAM offers a promising approach for addressing challenges posed by stochastic volatility in real-world applications.

## Summary

The Bayesian Arc Length Survival Analysis Model (BALSAM) is a statistical framework proposed by Yan Gao, Rodney A. Sparapani, and Sanjib Basu to address the difficulty of capturing increasing risks associated with stochastic volatility in real-world applications. The authors propose using arc length, a mathematical concept that quantifies cumulative variations over time, to more fully characterize stochastic volatility. The Cox proportional hazards model in survival analysis assumes that the hazard rate is impacted by the instantaneous value of a longitudinal variable. However, when cumulative variations pose a significant impact on the hazard rate, this assumption becomes questionable. BALSAM infuses arc length into a united statistical framework by synthesizing three parallel components: joint models, distributed lag models, and arc length. The authors illustrate the use of BALSAM in simulation studies and 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. The results show that incorporating arc length into survival analysis can provide more accurate estimates of risk associated with stochastic volatility. Overall, BALSAM offers a promising approach for addressing challenges posed by stochastic volatility in real-world applications. By incorporating arc length into survival analysis models, researchers can better quantify cumulative variations over time and more accurately estimate risk factors associated with dynamic systems like those found in healthcare settings.