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、汽车和其他耐用品和产品的维护，到污染控制和环境监测，我们需要监测对象的某些性能变量的纵向模式。如果给定受试者的表现变量的观察值显著差于相同年龄的典型功能良好受试者的值，则通过统计方法的信号将是非常有帮助的，使得可以及时地进行一些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。在统计学文献中，有两个研究领域与上述纵向模式的顺序监测（SMLP）问题相关：纵向数据分析（LDA）和统计过程控制（SPC）。通过LDA方法，我们可以将一个新的被试与一组功能良好的被试进行比较，以判断新的被试在给定的时间间隔内的纵向模式是否与规则模式一致。LDA方法的一个局限性是，即使到当前时间点为止的所有可用观察结果都提供了足够的证据来支持决策，它们也不能顺序地和快速地做出关于受试者的纵向模式的决策。然而，为了有效地解决SMLP问题，这种动态决策功能是至关重要的。通过SPC方法，我们可以按顺序跟踪每个受试者，并通过将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表现。SPC方法的一个主要局限性是，当对给定的主题做出决定时，它们不能比较不同的主题。因此，还没有现有的统计方法可以有效地解决SMLP问题。该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截面比较，并使用其所有历史数据以及顺序监测方案，来确定该主题的纵向模式。新方法结合了LDA和SPC方法的主要优点，应该提供一个有效的解决方案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.