Sufficient reduction methods for multivariate health surveillance

Surveillance systems aim to detect sudden changes or aberrations in data series which might signal the possibility of disease outbreaks. Early detection with a low false alarm rate (FAR) is the main aim of outbreak detection as used in health surveillance or in regard to bioterrorism. Multivariate surveillance is preferable to univariate surveillance since correlation between series (CBS) is recognized and incorporated and so small but consistent shifts are more likely to be detected. In this thesis, sufficient reduction (SR) methods are considered. These are dimensionality reduction tools for multivariate surveillance which have proved promising for handling CBS, and lag between change points (LCP), but have not previously been used when correlation within series (CWS) is present. We develop SR methods for reducing a p-dimensional multivariate series to a univariate series of statistics shown to be sufficient for monitoring a sudden, but persistent, shift in a multivariate process of normal or Poisson data. CBS, CWS and LCP are all taken into account, as health data typically exhibit these forms of association. Different types of change point and shift sizes are investigated. A standard one-sided EWMA chart is used as a detection tool. Due to the nature of health data, the one-sided EWMA chart is modified for independent Poisson data and to allow for CWS in normal and Poisson processes. The performance of the proposed method is compared with existing SR and parallel methods. A simulation study shows that the proposed method is superior, giving a shorter delay and a lower FAR than other methods which have high FARs when CWS is clearly present. Although their high FAR can be improved by using a suitably modified EWMA chart, the proposed method still gives shorter delays than the others. The implementation of the proposed methods is illustrated with four real data sets.