Researches On Dynamic Screening System

In our daily life, we often need to identify individuals whose longitudinal behavior is different from the behavior of those well-functioning individuals, so that some unpleasant consequences can be avoided. In many such applications, observations of a given individual are obtained sequentially, and it is desirable to have a screening system to give a signal of irregular behavior as soon as possible after that individual’s longitudinal behavior starts to deviate from the regular behavior, so that some adjustments or interventions can be made in a timely manner.In the statistical literature, there are two relevant methods. One is to construct confi-dence intervals of the mean performance variables, using longitudinal data analysis (LDA), and the subject’s longitudinal pattern can be identified as abnormal if its observations fall outside the intervals. The second method is to monitor each subject sequentially using a statistical process control (SPC) chart. By this method, a signal will be given after the chart detects a significant shift in the longitudinal pattern of the subject over time. These two methods, however, are ineffective to handle the dynamic screening (DS) problem, because the LDA method cannot sequentially monitor a subject in question while the SPC method cannot compare the subject cross-sectionally with other subjects. In this paper, we propose a new method to handle the DS problem effectively by combining the major strengths of the LDA and SPC methods.For the LDA method, the univariate longitudinal data has been widely studied in the literature. Besides, multivariate longitudinal data are common in medical, industrial, and social science research (e.g., the data from the SHARe Framingham Heart Study). Thus, in this paper we focus on the study of multivariate longitudinal data. Statistical analysis of such data in the current literature is restricted to linear or parametric modeling, which may well be inappropriate in applications. However, in most cases this two assumptions are invalid. Thus, it is desirable to develop a nonparametric method to handle multivariate longitudinal data. When longitudinal data are multivariate, nonparametric modeling becomes challenging, as one needs to properly handle the association among the observed data across different time points and across different components of the multivariate response. Motivated by data from the National Heart, Lung and Blood Institute, this paper proposes a nonparametric modeling approach for analyzing multivariate longitudinal data in Chapter2. Our method is based on multivariate local polynomial smoothing. Both theoretical and numerical results show that it is useful in various settings.In Chapter3, we consider cases when the longitudinal behavior is univariate. Sev-eral different cases, including those with regularly spaced observation times, irregularly s-paced observation times, and correlated observations, are discussed. Our proposed method is demonstrated using a real-data example about the SHARe Framingham Heart Study of the National Heart, Lung and Blood Institute.In Chapter4, we consider cases when the longitudinal behavior is multivariate. Our proposed multivariate dynamic screening system makes decisions about the longitudinal pat-tern of a subject by comparing it with other subjects cross-sectionally and by sequentially monitoring it as well. Related results show that it provides good performance in various cases.