Spatial Scan Statistics Adjusted for Multiple Clusters

Abstract

The spatial scan statistic is one of the main epidemiological tools to test for the presence of disease clusters in a geographical region. While the statistical significance of the most likely cluster is correctly assessed using the model assumptions, secondary clusters tend to have conservatively highP-values. In this paper, we propose a sequential version of the spatial scan statistic to adjust for the presence of other clusters in the study region. The procedure removes the effect due to the more likely clusters on less significant clusters by sequential deletion of the previously detected clusters. Using the Northeastern United States geography and population in a simulation study, we calculated the type I error probability and the power of this sequential test under different alternative models concerning the locations and sizes of the true clusters. The results show that the type I error probability of our method is close to the nominalαlevel and that for secondary clusters its power is higher than the standard unadjusted scan statistic.

A Bayesian Method for Cluster Detection with Application to Brain and Breast Cancer in Puget Sound

“…We present results of the multiple cluster Kulldorff method 14 using both income unadjusted and adjusted expected counts. We set the highest proportion of the population a zone can contain at 15%, the α -cutoff to declare significance at α = 0.05 and simulate 9,999 Monte Carlo realizations under the null hypothesis of no clusters.…”

“…This approach is therefore not using the correct reference distribution. The most recent multiple cluster version of the Kulldorff method 14 removes the significant zone, and then repeats the procedure now using a new reference distribution, until no more significant zones are found. A deficiency of this approach is that the p -values are not directly comparable since they are based on different sample sizes and hence have different power.…”

“…Furthermore, one should also consider the multiple testing aspect of the multiple comparisons that are being made but it would be very difficult to determine the appropriate error rate of the overall sequential procedure just described. 14 …”

Disease cluster detection methods: recent developments and public health implications

“…Improvements to wellestablished methods such as SatScan have been developed (Zhang, Assunção, and Kulldorf 2010). However, much effort has focused on innovative Bayesian methods.…”

Stepwise and stagewise approaches for spatial cluster detection

“…Some recent methods more rigorously account for multiple clusters in the detection process. Zhang et al (2010) propose assessing secondary clusters after sequential deletion of observed data inside the previously detected clusters, essentially a variant of more traditional forward stepwise variable selection. Li et al (2011) propose a modified scan statistic that evaluates the most likely two (or more) clusters rather than the single most likely cluster.…”