This study examines three applications of control charts used for monitoring syndromic data with different characteristics. The first part develops a seasonal autoregressive integrated moving average (SARIMA) based surveillance chart, and compares it with the CDC Early Aberration Reporting System (EARS) W2c method using both authentic and simulated data. After successfully removing the long-term trend and the seasonality involved in syndromic data, the performance of the SARIMA approach is shown to be better than the performance of the EARS method in terms of two key surveillance characteristics, the false alarm rate and the average time to detect the outbreaks.
In the second part, we propose a generalized likelihood ratio (GLR) control chart to detect a wide range of shifts in the mean of Poisson distributed biosurveillance data. The application of a sign function on the original GLR chart statistics leads to downward-sided, upward-sided, and two-sided GLR chart statistics in an unified framework. To facilitate the use of such charts in practice, we provide detailed guidance on developing and implementing the GLR chart. Under the steady-state framework, this study indicates that the overall GLR chart performance in detecting a range of shifts of interest is superior to the performance of traditional control charts including the EARS method, Shewhart charts, EWMA charts, and CUSUM charts.
There is often an excessive number of zeros involved in health care related data. Zero-inflated Poisson (ZIP) models are more appropriate than Poisson models to describe such data. The last part of the dissertation considers the GLR chart for ZIP data under a research framework similar to the second part. Because small sample sizes may influence the estimation of ZIP parameters, the efficiency of MLEs is investigated in depth, followed by suggestions for improvement. Numerical approaches to solving for the MLEs are discussed as well. Statistics for a set of GLR charts are derived, followed by modifications changing them from two-sided statistics to one-sided statistics. Although not a complete study of GLR charts for ZIP processes, due to limited time and resources, suggestions for future work are proposed at the end of this dissertation. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/77128 |
| Date | 09 August 2011 |
| Creators | Zheng, Hongzhang |
| Contributors | Statistics, Woodall, William H., Reynolds, Marion R. Jr., Birch, Jeffrey B., DeLisle, Sylvain S. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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