New Methods for Sequential Monitoring of Longitudinal Patterns

在许多应用中，从疾病的早期检测和预防，飞机、汽车等耐用品和产品的维护，到污染控制和环境监测，我们都需要监测一个主体的某些性能变量的纵向模式。如果某一特定对象的表现变量的观察值明显低于同年龄的典型功能良好的对象的值，那么通过统计方法发出的信号将非常有帮助，以便及时进行适当的调整或干预，以避免任何不愉快的后果。本项目旨在开发一种新的统计方法来有效地处理这一问题。如果成功，该项目的研究成果将对上述应用产生深远的影响。在统计文献中，与上述纵向模式序列监测（SMLP）问题相关的研究领域有两个：纵向数据分析（LDA）和统计过程控制（SPC）。通过LDA方法，我们可以将新被试与一组功能良好的被试进行比较，以判断新被试在给定时间间隔内的纵向模式是否与规则模式一致。LDA方法的一个限制是，即使在当前时间点的所有可用观察都提供了足够的证据来支持该决定时，它们也不能连续快速地对受试者的纵向模式做出决定。然而，为了有效地解决SMLP问题，这种动态决策特征至关重要。通过SPC方法，我们可以按顺序跟踪每个受试者，并通过将其当前时间点的观察结果与所有历史数据进行比较来决定其性能。SPC方法的一个主要限制是，当对给定主题做出决定时，它们不能比较不同的主题。因此，目前还没有能够有效解决SMLP问题的统计方法。本项目提出了一种新的方法，通过将一个主题与其他主题进行横断面比较，并使用其所有历史数据以及顺序监测方案，来决定一个主题的纵向模式。该方法结合了LDA和SPC两种方法的主要优点，可以有效地解决SMLP问题。

In many applications, ranging from disease early detection and prevention, maintenance of airplanes, cars and other durable goods and products, to pollution control and environment monitoring, we need to monitor the longitudinal pattern of certain performance variables of a subject. If the observed values of the performance variables of a given subject are significantly worse than the values of a typical well-functioning subject of the same age, then a signal by a statistical method would be extremely helpful so that some proper adjustments or interventions can be made in a timely manner to avoid any unpleasant consequences. This project aims to develop a new statistical method to handle this problem effectively. If successful, research results from this project will have a profound impact on the applications mentioned above.In the statistical literature, there are two research areas relevant to the above sequential monitoring of longitudinal pattern (SMLP) problem: longitudinal data analysis (LDA) and statistical process control (SPC). By an LDA method, we can compare a new subject with a group of well-functioning subjects to judge whether the new subject's longitudinal pattern is consistent with the regular pattern in a given time interval. One limitation of the LDA methods is that they cannot make a decision about a subject's longitudinal pattern sequentially and quickly even when all available observations up to the current time point have provided enough evidence to support the decision. For solving the SMLP problem effectively, however, this dynamic decision-making feature is crucial. By a SPC method, we can follow each subject sequentially, and make a decision about its performance by comparing its observations at the current time point with all of its history data. One major limitation of the SPC methods is that they cannot compare different subjects when making decisions about a given subject. Therefore, there are no existing statistical methods that can solve the SMLP problem effectively yet. This project proposes a new method that makes decisions about the longitudinal pattern of a subject by comparing it with other subjects cross-sectionally and by using all its history data as well with a sequential monitoring scheme. The new method combines the major strengths of the LDA and SPC methods and should provide an effective solution to the SMLP problem.