Effect of relative risk and cluster configuration on the power of the one-dimensional scan statistic

The scan test for clustering in time is based on the maximum number of events in an interval (window) of width w as the window moves across the entire time frame. Power estimates of the scan statistic are simulated for a variety of epidemiologically motivated situations. Two cluster configurations are used: a rectangular pulse, and a triangular pulse designed to emulate environmental contamination. For a rectangular pulse, the relative risk R of disease in the cluster region is R-fold as high as it is for the background region. The power is strongly influenced by the sample size, the relative risk, and the width or duration of the cluster region, whereas the effect of the cluster configuration is small. Using a 5 per cent significance level, a relative risk of 4, a standardized cluster duration of 0.10, a relative window width of 1.5, and a (non-random) sample size of 50, the simulated power is approximately 80 per cent, indicating that the minimum sample size in the cluster region for adequate power is in the 12-32 range for values of the parameters used in this study.