It is often important to detect an increase in the frequency of some event. Particular attention is given to medical events such as mortality or the incidence of a given disease, infection or birth defect. Observations are regularly taken in which either an incidence occurs or one does not. This dissertation contains the result of an investigation of prospective monitoring techniques in two distinct surveillance situations. In the first situation, the observations are assumed to be the results of independent Bernoulli trials. Some have suggested adapting the scan statistic to monitor such rates and detect a rate increase as soon as possible after it occurs. Other methods could be used in prospective surveillance, such as the Bernoulli cumulative sum (CUSUM) technique. Issues involved in selecting parameters for the scan statistic and CUSUM methods are discussed, and a method for computing the expected number of observations needed for the scan statistic method to signal a rate increase is given. A comparison of these methods shows that the Bernoulli CUSUM method tends to be more effective in detecting increases in the rate. In the second situation, the incidence information is available at multiple locations. In this case the individual sites often report a count of incidences on a regularly scheduled basis. It is assumed that the counts are Poisson random variables which are independent over time, but the counts at any given time are possibly correlated between regions. Multivariate techniques have been suggested for this situation, but many of these approaches have shortcomings which have been demonstrated in the quality control literature. In an attempt to remedy some of these shortcomings, a new control chart is recommended based on a multivariate exponentially weighted moving average. The average run-length performance of this chart is compared with that of the existing methods. / Ph. D.

In epidemiology it is often useful to monitor disease occurrences prospectively to determine the location and time when clusters of disease are forming. This aids in the prevention of illness and injury of the public and is the reason spatio-temporal disease surveillance methods are implemented. Care must be taken in the design and implementation of these types of surveillance methods so that the methods provide accurate information on the development of clusters. Here two spatio-temporal methods for prospective disease surveillance are considered. These include the local Knox monitoring method and a new wavelet-based prospective monitoring method. The local Knox surveillance method uses a cumulative sum (CUSUM) control chart for monitoring the local Knox statistic, which tests for space-time clustering each time there is an incoming observation. The detection of clusters of events occurring close together both temporally and spatially is important in finding outbreaks of disease within a specified geographic region. The local Knox surveillance method is based on the Knox statistic, which is often used in epidemiology to test for space-time clustering retrospectively. In this method, a local Knox statistic is developed for use with the CUSUM chart for prospective monitoring so that epidemics can be detected more quickly. The design of the CUSUM chart used in this method is considered by determining the in-control average run length (ARL) performance for different space and time closeness thresholds as well as for different control limit values. The effect of nonuniform population density and region shape on the in-control ARL is explained and some issues that should be considered when implementing this method are also discussed. In the wavelet-based prospective monitoring method, a surface of incidence counts is modeled over time in the geographical region of interest. This surface is modeled using Poisson regression where the regressors are wavelet functions from the Haar wavelet basis. The surface is estimated each time new incidence data is obtained using both past and current observations, weighing current observations more heavily. The flexibility of this method allows for the detection of changes in the incidence surface, increases in the overall mean incidence count, and clusters of disease occurrences within individual areas of the region, through the use of control charts. This method is also able to incorporate information on population size and other covariates as they change in the geographical region over time. The control charts developed for use in this method are evaluated based on their in-control and out-of-control ARL performance and recommendations on the most appropriate control chart to use for different monitoring scenarios is provided. / Ph. D.