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Abstract:
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Fluctuations often imply increasing risks in numerous applications, such as stock market volatility, global temperature change, heart rate variability, and mood swings in mental health. To characterize fluctuations, we propose a new measurement defined by arc length, originated from mathematics, to quantify cumulative variations, that is, the total amount of variability over the longitudinal history. Our proposed Bayesian Lag Joint Model (BLJM) infuses arc length into statistical modeling to address the research problem associated with cumulative variations. In survival modeling, hazard rate is often assumed to be impacted by the instantaneous value of a covariate, especially for the Cox proportional hazards models. However, when cumulative variations impose a significant impact, this assumption is often questionable. In BLJM, three parallel components (joint model, distributed lag model, and arc length) are synthesized into one united framework. When cumulative variations cast a notable influence, BLJM outperforms current joint models. The proposed model can be utilized in diverse disciplines and applications. We illustrate its usage in both simulation and clinical studies.
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