STATISTICS zyxwvutsrqpo IN MEDICINE, VOL. zyxwvutsrq 4,469488 (1985) THE CUSUM TEST OF HOMOGENEITY WITH AN APPLICATION IN SPONTANEOUS ABORTION EPIDEMIOLOGY BRUCE LEVIN zyxwvu Division zyxwvutsrqpo of Biosiatistics. Columbia University School of Public Healih and New York State Psychiatric Insiiiuie. zyx 600 W.168th Si.. New York City. New York 10032. zyxwvu U.S.A.. and Seryiecsky Center. Columbia Unicersii),Faculty of Medicine AND JENNIE KLINE New York Siaie Psychiatric Institute. 722 W.168rh zyxwvut 9.. New York Ciiy, New York 10032. U.S.A.. Seryiersky C~nier. Columbia Uniuersity Faculty of Medicine and Division of Epidemiology, Columbia University School of Public Health SUMMARY We test the hypothesis of homogeneity over time in the rate of an event with a modification of Page’s cumulative sum (cusum) procedure. The modification draws on an indifference zone approach to testing that is well suited to the epidemiologic study of retrospective data. We provide procedures for evaluating the significance level of the largest observed cusum value occurring in a sequence of fixed length. We draw inferences unconditionally with a known baseline rate of the event, and conditionally on observed margins with unknown baseline rate. Data collected over a five year period from one New York City hospital serve to illustrate the modified cusum test in a study of fluctuations in the proportions of chromosomally normal, trisomic, X-monosomic and triploid spontaneous abortions. KEY WORDS Cusum procedure Test of homogeneity Conditional inference Surveillance Spontaneous abortion 1. INTRODUCTION Temporal variations in the frequency of an event sometimes signal changes in the presence or prevalence of a causal agent in the environment. Such variations may be cyclic, may represent a shift to a changed ‘baseline’rate for the event, or may consist of spikes or pulses that appear to occur irregularly, at least until identification of a cause. At all times we wish to guard against the misinterpretation of observed fluctuations that occur entirely at random in a series that has a homogeneous baseline rate. As a case in point, Kline et zyxwvu al.’ have argued that the monitoring of fluctuations in the frequencies of different types of spontaneous abortions could provide an efficient approach to the surveillance of the environment for at least two types of exposures: those that cause the abortion of chromosomally normal conceptions, and those that cause chromosomal abnormality in the zygote. What size fluctuation should one consider non-random and worthy of intensive investigation for causes? In this paper we adapt the cumulative sum (cusum) technique to test the null hypothesis of homogeneity in a retrospective series of observations, and we apply the test to data on karyotyped spontaneous abortions. 027747 1 5/85/040469-20$02.00 zyxwvu 0 1985 by John Wiley & Sons, Ltd. Received May 1984 Revised February I985