Relative risk estimates from spatial and space-time scan statistics: are they biased?

The purely spatial and space-time scan statistics have been successfully used by many scientists to detect and evaluate geographical disease clusters. Although the scan statistic has high power in correctly identifying a cluster, no study has considered the estimates of the cluster relative risk in the detected cluster. In this paper, we evaluate whether there is any bias on these estimated relative risks. Intuitively, one may expect that the estimated relative risks has upward bias, because the scan statistic cherry picks high rate areas to include in the cluster. We show that this intuition is correct for clusters with low statistical power, but with medium to high power, the bias becomes negligible. The same behavior is not observed for the prospective space-time scan statistic, where there is an increasing conservative downward bias of the relative risk as the power to detect the cluster increases.