Intensive longitudinal biomarker data are increasingly common in scientific studies that seek temporally granular understanding of the role of behavioral and physiological factors in relation to outcomes of interest. Intensive longitudinal biomarker data, such as those obtained from wearable devices, are often obtained at a high frequency typically resulting in several hundred to thousand observations per individual measured over minutes, hours, or days. Often in longitudinal studies, the primary focus is on relating the means of biomarker trajectories to an outcome, and the variances are treated as nuisance parameters, although they may also be informative for the outcomes. In this paper, we propose a Bayesian hierarchical model to jointly model a cross-sectional outcome and the intensive longitudinal biomarkers. To model the variability of biomarkers and deal with the high intensity of data, we develop subject-level cubic B-splines and allow the sharing of information across individuals for both the residual variability and the random effects variability. Then different levels of variability are extracted and incorporated into an outcome submodel for inferential and predictive purposes. We demonstrate the utility of the proposed model via an application involving bio-monitoring of hertz-level heart rate information from a study on social stress.

翻译：密集纵向生物标志物数据在旨在从时间粒度上理解行为与生理因素对感兴趣结局影响的科学研究中日益普遍。这类数据（如可穿戴设备获取的）通常以高频采集，每名个体在数分钟、数小时乃至数天内可获得数百至数千次观测值。在纵向研究中，主要关注点常是生物标志物轨迹均值与结局的关联，而方差则被视作 nuisance 参数，尽管其对结局可能同样具有信息价值。本文提出一种贝叶斯层次模型，用于联合建模横截面结局与密集纵向生物标志物。为刻画生物标志物的变异性并应对高频数据特性，我们构建了基于个体层面的三次B样条，并允许残差变异与随机效应变异在个体间共享信息。随后提取不同层次的变异性，并将其纳入结局子模型以实现推断与预测。通过一项纳入社交压力研究中基于赫兹级心率生物监测的应用案例，我们论证了所提模型的有效性。