A Spatial Scan Statistic on Trends
Spatial scan statistics have been widely researched for detecting geographic clusters of heterogeneous rates. This article explores a relevant field of detecting clusters of different relationships of quantities, for instance, trends of logarithmic values of age-adjusted rates over a period of time. The proposed method distinguishes itself by detecting geographic clusters with higher trends of rates. A typical problem is whether the curves of logarithmic values of age-adjusted rates of geographic units are parallel (i.e., have the same slopes or trends). If not, then where are the clusters with higher trends? A likelihood ratio is employed for deriving a spatial scan statistic that is proposed for (1) evaluation of global geographic heterogeneity of trends and (2) detecting clusters of high trends. The method is illustrated on trends of cancer mortality rates of states in the United States. The data used in this article are publicly available at https://doi.org/seer.cancer.gov/seerstat/.
KeywordsSpatial scan statistic Trend Linear regression model Likelihood ratio Heterogeneity Geographic unit Cluster detection
AMS Classification62H11 62H30 65C60
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