Analysis of aberrations in public health surveillance data: estimating variances on correlated samples

The detection of unusual patterns in health data presents an important challenge to health workers interested in early identification of epidemics or important risk factors. A useful procedure for detection of aberrations is the ratio of a current report to some historic baseline. This work addresses the problem of finding the variance of such a ratio when the surveillance reports are correlated. Results show that, when estimating this variance or the variance of the sample mean from a series of observations with an estimated correlation structure, bootstrap and jackknife estimates may be overly optimistic. The delta method or a classical method may be more useful when such model dependence is inappropriate.