The space-time scan statistic is a powerful statistical tool for prospective disease surveillance. It searches over a set of spatio-temporal regions (each representing some spatial area S for the last k days), finding the most significant regions (S, k) by maximizing a likelihood ratio statistic, and computing p-values of these potential clusters by randomization.
The standard, "population-based" method assumes that, for each spatial location si on each day t, we have a population pti and a count (observed number of cases) cti. Then, under the null hypothesis of no clusters, we expect each count cti to be proportional to its population pti. We then search for regions (S, k) with disease rate (cases per unit population) significantly higher inside the region than outside. In the original space-time scan statistic, the populations are assumed to be given, and in, populations are estimated assuming independence of space and time.
Here we propose an alternative, "expectation-based" method, in which we infer the expected number of cases bti in each spatial location, based on the time series of previous counts. In this case, under the null hypothesis of no clusters, we expect each count cti to be equal to bti, rather than proportional to population. We then search for regions (S, k) with counts that are significantly higher than expected.
Objective
This paper describes a new class of space-time scan statistics designed for rapid detection of emerging disease clusters. We evaluate these methods on the task of prospective disease surveillance, and show that our methods consistently outperform the standard space-time scan statistic approach.