Statistical Methods for Anomalous Discrete Time Series Based on Minimum Cell Count

Abstract

Temporal incidence patterns of point epidemics often contain periods of unusually low or high frequencies. Identifying variations in incidence frequencies, which may be caused by changes in exposure to infectious or environmental agents, may provide important insights into the pathogenesis or etiology of a disease. We propose and formulate new statistical tests for temporal and space-time anomalies that are based on the minimum frequency in a unit of time and that are meaningful for the characteristic incidence patterns of the cases studied. Among the most widely applied methods are the Ederer–Myers–Mantel test, the Maxima test, and the scan test, which are all sensitive to the maximum frequency within a short period of time. We elucidate the importance and utility of our new tests and the existing tests and suggest a systematic statistical analysis of reported disease anomalies using these tests combined. Data on a temporal series of adolescent suicide from the US National Center for Health Statistics were analyzed using these methods.