A CUSUM PROCEDURE FOR DETECTION OF OUTBREAKS IN POISSON DISTRIBUTED MEDICAL HEALTH EVENTS

Abstract

CUSUM procedures which are based on standardized statistics are often supposed to have expectation zero and being normally distributed. If these conditions are not satisfied it can have serious consequences on the determination of proper alarming bounds and on the frequency of false alarms. Here a CUSUM method for detecting outbreaks in health events is presented when the latter are Poisson distributed. It is based on a standardized statistic with a bias from zero that can be neglected. The alarming boundaries are determined from the actual distribution of the statistic rather than on normality assumptions. The boundaries are also determined from requirements on the probability of false alarms instead of the common practice to focus on average run lengths (ARLs). The new method is compared with other CUSUM methods in Monte Carlo simulations. It is found that the new method has about the same expected time to first motivated alarm and the same sensitivity. However, the new method has expected times to first false alarm that are 9 % – 90 % longer. The new method is applied to outbreaks of sick-listening and to outbreaks of Chlamydial infection.