For the last several decades, sequential change point problems have been studied in both the theoretical area (sequential analysis) and the application area (industrial SPC). In the conventional application, the baseline process is assumed to be stationary, and the shift pattern is a step function that is sustained after the shift. However, in biosurveillance, the underlying assumptions of problems are more complicated. This thesis investigates several issues in biosurveillance such as non-homogeneous populations, spatiotemporal surveillance methods, and correlated structures in regional data.

The first part of the thesis discusses popular surveillance methods in sequential change point problems and off-line problems based on count data. For sequential change point problems, the CUSUM and the EWMA have been used in healthcare and public health surveillance to detect increases in the rates of diseases or symptoms. On the other hand, for off-line problems, scan statistics are widely used. In this chapter, we link the method for off-line problems to those for sequential change point problems. We investigate three methods—the CUSUM, the EWMA, and the scan statistics—and compare them by conditional expected delay (CED).

The second part of the thesis pertains to the on-line monitoring problem of detecting a change in the mean of Poisson count data with non-homogeneous population sizes. The most common detection schemes are based on generalized likelihood ratio statistics, known as an optimal method for the i.i.d. models. We propose alternative detection schemes based on the weighted likelihood ratios and the adaptive threshold method, which perform better than generalized likelihood ratio statistics in an increasing population. The properties of these three detection schemes are investigated by both theoretical analysis and numerical simulation.

The third part of the thesis investigates spatiotemporal surveillance based on likelihood ratios. This chapter proposes a general framework for spatiotemporal surveillance based on likelihood ratio statistics over time windows. We show that the CUSUM and other popular likelihood ratio statistics are the special cases under such a general framework. We compare the efficiency of these surveillance methods in spatiotemporal cases for detecting clusters of incidence using both Monte Carlo simulations and a real example.

The fourth part proposes multivariate surveillance methods based on likelihood ratio tests in the presence of spatial correlations. By taking advantage of spatial correlations, the proposed methods can perform better than existing surveillance methods by providing the faster and more accurate detection. We illustrate the application of these methods with a breast cancer case in New Hampshire when observations are spatially correlated.