Longitudinal biomarker data and health outcomes are routinely collected in many studies to assess how biomarker trajectories predict health outcomes. Existing methods primarily focus on mean biomarker profiles, treating variability as a nuisance. However, excess variability may indicate system dysregulations that may be associated with poor outcomes. In this paper, we address the long-standing problem of using variability information of multiple longitudinal biomarkers in time-to-event analyses by formulating and studying a Bayesian joint model. We first model multiple longitudinal biomarkers, some of which are subject to limit-of-detection censoring. We then model the survival times by incorporating random effects and variances from the longitudinal component as predictors through threshold regression that admits non-proportional hazards. We demonstrate the operating characteristics of the proposed joint model through simulations and apply it to data from the Study of Women's Health Across the Nation (SWAN) to investigate the impact of the mean and variability of follicle-stimulating hormone (FSH) and anti-Mullerian hormone (AMH) on age at the final menstrual period (FMP).

翻译：纵向生物标志物数据与健康结局在许多研究中被常规收集，以评估生物标志物轨迹如何预测健康结局。现有方法主要关注生物标志物的均值特征，将变异性视为干扰因素。然而，过度的变异性可能预示着系统失调，并可能与不良结局相关。本文通过构建并研究一个贝叶斯联合模型，解决了在时间-事件分析中利用多种纵向生物标志物变异性信息这一长期存在的问题。我们首先对多种纵向生物标志物进行建模，其中部分数据受到检测限删失的影响。随后，我们通过允许非比例风险的阈值回归，将纵向模型中的随机效应和方差作为预测因子纳入生存时间建模。我们通过模拟验证了所提联合模型的运行特性，并将其应用于"全国妇女健康研究"（SWAN）的数据，以探讨促卵泡激素（FSH）和抗穆勒氏管激素（AMH）的均值及变异性对最终月经期（FMP）年龄的影响。