The cumulative q interval curve as a starting point in disease cluster investigation

Statistical analyses aimed at detection and investigation of clustering are associated with inherent difficulties. Both types of statistical errors are large in these analyses. The results of the analyses should indicate whether or not at least some of the cases are clustered, and if they are, whether or not the cluster is related to an exposure. The temporal changes in the incidence rate of the disease may alleviate the difficulties associated with the large statistical errors. Because of the sparse data, estimates of the incidence rates over time are not reliable. In this study we present the q interval statistic that has the uniform (0,1) distribution. It can be viewed as a standardized time interval between consecutive diagnoses of the disease. As such, it reflects the reciprocal of the incidence rates. Since it is measured for each diagnosis, it is sensitive to gradual change in the incidence rate, and in general to a true clustering that is due to exposure, even when the test result is not significant. When clustering is detected, it may indicate which of the possible reasons leading to a cluster has a sound basis. As a result, the epidemiological search for exposure is limited to situations indicated by the q intervals. In addition, the q interval presents a useful survival statistic in a follow-up study when no control group is available. Software programs in SAS and in SYSTAT are available.