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.
