The main goal of biosurveillance is the early detection of disease outbreaks. Advances in technology have allowed the collection, transfer, and storage of pre-diagnostic information in addition to traditional diagnostic data. Such data carry the potential of an earlier outbreak signature. In this work we deal with monitoring multivariate time series of daily counts. Current temporal monitoring in biosurveillance is done univariately by applying control charts to each time series separately. However, monitoring via multivariate control charts has the potential of greatly reducing false alert rates and increasing true alert rates. Classical multivariate control charts are aimed at detecting shifts in the vector of means in any direction. Whereas one-side univariate control charts are easy to obtain from their two-sided counterpart, directional sensitivity in the multivariate case is non trivial. Several approaches were suggested for obtaining directionally-sensitive multivariate Shewhart chart (commonly referred to as Hotelling T2 charts). However, there has not been an extensive comparison of these methods and it is not clear which approach performs better.

In this work we compare two computational-feasible approaches suggested in the literature, namely Follmann's simple correction and Testik and Runger's (TR) quadratic programming approach. In addition to their proposed directionally sensitive Hotelling charts we derive directionally sensitive Multivariate EWMA (MEWMA) charts. We then perform an extensive analysis of the performance the four methods, where we examine model performance in terms of true and false detection, robustness to assumptions, training data length and sensitivity to data characteristics. Our results show that TR's approach performs slightly better for normally distributed data, yet Follmann's approach is more robust to normality and independence assumptions