Dynamic Modeling of Conditional Quantile Trajectories, With Application to Longitudinal Snippet Data
Dynamic Modeling of Conditional Quantile Trajectories, With Application to Longitudinal Snippet Data
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DOI：
10.1080/01621459.2017.1356321
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发表时间：
2018-01-01
影响因子：
3.7
通讯作者：
Mueller, Hans-Georg
中科院分区：
文献类型：
--
作者：
Dawson, Matthew;Mueller, Hans-Georg
纵向数据经常被稀疏的时间点所困扰，在这些时间点上，可以进行测量。功能数据分析的观点已经被证明提供了一种有效和灵活的方法来解决这个问题，在这种情况下，测量是稀疏的，但它们的时间在一个间隔内随机分布。在这里，我们关注一种不同的场景，在这种场景中，可用的数据可以被描述为片段，这是非常短的纵向测量范围。对于每个受试者，可用数据的范围比感兴趣的时间范围要短得多，这在加速纵向研究中是常见的。如果对于通常的纵向建模来说基本的时间代理不可用，则会引入额外的挑战。这种情况出现在阿尔茨海默病和类似的场景中，其中一个人对性能下降的时间动力学感兴趣，但疾病开始的时间未知，并且按时间顺序的年龄不能为纵向建模提供有意义的时间参考。我们解决这些挑战的主要方法论贡献是为作为动态系统解出现的单调过程引入条件分位数轨迹。我们对这些轨迹的拟议估计被证明是一致一致的。条件分位轨迹是量化随时间恶化的过程的有用描述符，例如阿尔茨海默病患者的海马体体积。我们演示了如何将所提出的方法应用于从这样的过程中采样的纵向片段数据。这篇文章的补充材料可以在网上找到。
Longitudinal data are often plagued with sparsity of time points where measurements are available. The functional data analysis perspective has been shown to provide an effective and flexible approach to address this problem for the case where measurements are sparse but their times are randomly distributed over an interval. Here, we focus on a different scenario where available data can be characterized as snippets, which are very short stretches of longitudinal measurements. For each subject, the stretch of available data is much shorter than the time frame of interest, a common occurrence in accelerated longitudinal studies. An added challenge is introduced if a time proxy that is basic for usual longitudinal modeling is not available. This situation arises in the case of Alzheimer's disease and comparable scenarios, where one is interested in time dynamics of declining performance, but the time of disease onset is unknown and chronological age does not provide a meaningful time reference for longitudinal modeling. Our main methodological contribution to address these challenges is to introduce conditional quantile trajectories for monotonic processes that emerge as solutions of a dynamic system. Our proposed estimates for these trajectories are shown to be uniformly consistent. Conditional quantile trajectories are useful descriptors of processes that quantify deterioration over time, such as hippocampal volumes in Alzheimer's patients. We demonstrate how the proposed approach can be applied to longitudinal snippets data sampled from such processes. Supplementary materials for this article are available online.