Estimating the Relative Risks of Spatial Clusters Using a Predictor-Corrector Method

Spatial, temporal, and space-time scan statistics can be used for geographical surveillance, identifying temporal and spatial patterns, and detecting outliers. While statistical cluster analysis is a valuable tool for identifying patterns, optimizing resource allocation, and supporting decision-making, accurately predicting future spatial clusters remains a significant challenge. Given the known relative risks of spatial clusters over the past $k$ time intervals, the main objective of the present study is to predict the relative risks for the subsequent interval, $k+1$ . Building on our prior research, we propose a predictive Markov chain model with an embedded corrector component. This corrector utilizes either multiple linear regression or exponential smoothing method, selecting the one that minimizes the relative distance between observed and predicted values in the $k$ -th interval. To test the proposed method, we first calculated the relative risks of statistically significant spatial clusters of COVID-19 mortality in the U.S. over seven time intervals from May 2020 to March 2023. Then, for each time interval, we selected the top 25 clusters with the highest relative risks and iteratively predicted the relative risks of clusters from intervals three to seven. The predictive accuracies ranged from moderate to high, indicating the potential applicability of this method for predictive disease analytics and future pandemic preparedness.