Dynamic Regression of Longitudinal Trajectory Features

Chronic disease studies often collect data on biological and clinical markers at follow-up visits to monitor disease progression. Viewing such longitudinal measurements governed by latent continuous trajectories, we develop a new dynamic regression framework to investigate the heterogeneity pattern of certain features of the latent individual trajectory that may carry substantive information on disease risk or status. Employing the strategy of multi-level modeling, we formulate the latent individual trajectory feature of interest through a flexible pseudo B-spline model with subject-specific random parameters, and then link it with the observed covariates through quantile regression, avoiding restrictive parametric distributional assumptions that are typically required by standard multi-level longitudinal models. We propose an estimation procedure from adapting the principle of conditional score and develop an efficient algorithm for implementation. Our proposals yield estimators with desirable asymptotic properties as well as good finite-sample performance as confirmed by extensive simulation studies. An application of the proposed method to a cohort of participants with mild cognitive impairment (MCI) in the Uniform Data Set (UDS) provides useful insights about the complex heterogeneous presentations of cognitive decline in MCI patients.

慢性病研究通常会在随访就诊时收集生物学与临床标志物数据，以监测疾病进展情况。鉴于此类纵向测量数据由潜在连续轨迹所支配，我们构建了一种全新的动态回归框架，用以探究潜在个体轨迹中特定特征的异质性模式——这些特征往往携带着与疾病风险或疾病状态相关的重要信息。我们采用多层建模（multi-level modeling）策略，通过引入个体特异性随机参数的灵活伪B样条（pseudo B-spline）模型，对所关注的潜在个体轨迹特征进行建模，并借助分位数回归（quantile regression）将其与观测协变量相关联，规避了标准多层纵向模型通常所需的严苛参数分布假设。我们基于条件得分原理提出了一种估计流程，并开发了一款高效的实现算法。经大量模拟研究验证，我们所提出的方法得到的估计量兼具优良的渐近性质与出色的有限样本表现。我们将所提方法应用于统一数据集（Uniform Data Set, UDS）中轻度认知障碍（mild cognitive impairment, MCI）参与者队列，为探究MCI患者认知衰退的复杂异质性临床表现提供了极具价值的洞见。