Testing for a pulse in seasonal event data

Most tests for seasonal clustering are sensitive to the peak in incidence in some season (90-day interval) followed by a trough 6 months later. We present two statistics sensitive to a relatively sharp increase in disease incidence for a season superimposed on a constant incidence over the entire year: the ratchet scan, based on the maximum number of events in k consecutive months, and the continuous circular scan, the maximum number of events in d consecutive days. We tabulate the tail distribution of the ratchet scan for N less than or equal to 35 and k = 2 and 3, and find the asymptotic distribution which is applicable for N greater than or equal to 50 when k = 2 or 3. We evaluate an approximation for the distribution of the continuous scan. The statistics are applied to investigate seasonal clustering of adolescent suicide in the United States. An illustration is given of the application of the circular scan, and a small simulation study and the example are used to compare the statistics with others proposed in the literature.