Detecting the spatial clustering of exposure–response relationships with estimation error: a novel spatial scan statistic

Detecting the spatial clustering of the exposure–response relationship (ERR) between environmental risk factors and health‐related outcomes plays important roles in disease control and prevention, such as identifying highly sensitive regions, exploring the causes of heterogeneous ERRs, and designing region‐specific health intervention measures. However, few studies have focused on this issue. A possible reason is that the commonly used cluster‐detecting tool, spatial scan statistics, cannot be used for multivariate spatial datasets with estimation error, such as the ERR, which is often defined by a vector with its covariance estimated by a regression model. Such spatial datasets have been produced in abundance in the last decade, which suggests the importance of developing a novel cluster‐detecting tool applicable for multivariate datasets with estimation error. In this work, by extending the classic scan statistic, we developed a novel spatial scan statistic called the estimation‐error‐based scan statistic (EESS), which is applicable for both univariate and multivariate datasets with estimation error. Then, a two‐stage analytic process was proposed to detect the spatial clustering of ERRs in practical studies. A published motivating example and a simulation study were used to validate the performance of EESS. The results show that the clusters detected by EESS can efficiently reflect the clustering heterogeneity and yield more accurate ERR estimates by adjusting for such heterogeneity.