Confidence Set for the Cluster of a Spatial Scan Statistic

Area of Science:

• Spatial statistics
• Geographic Information Science
• Epidemiology

Background:

• Spatial cluster detection identifies unusual patterns in geographic data, crucial for epidemiology and environmental science.
• Traditional methods like spatial scan statistics lack robust uncertainty quantification and visualization tools.
• Existing techniques struggle with non-circular or multiple spatial clusters, limiting their practical application.

Purpose of the Study:

• To develop a novel framework for constructing confidence sets for spatial clusters, addressing uncertainty in detection.
• To provide tools for quantifying and visualizing the uncertainty associated with identified spatial clusters.
• To offer a principled alternative to traditional significance-based methods in spatial cluster analysis.

Main Methods:

• Developed a likelihood-based framework for constructing confidence sets applicable to Poisson and Normal models.
• Utilized the p-value of the likelihood ratio test statistic to ensure empirical coverage near nominal levels.
• Implemented a binary search algorithm for efficient determination of significance thresholds and introduced confidence heatmaps and envelopes for visualization.

Main Results:

• The proposed framework successfully constructs confidence sets for spatial clusters with empirical coverage close to nominal levels.
• Simulation studies and real-world cancer mortality data analysis demonstrated the method's interpretability and robustness.
• The confidence heatmap and envelopes effectively visualized cluster uncertainty, enhancing practical utility.

Conclusions:

• The novel framework provides a principled and effective approach to spatial cluster detection with uncertainty quantification.
• The method is robust to various cluster shapes and numbers, offering practical advantages over traditional techniques.
• This approach opens new possibilities for extensions in spatio-temporal analysis and spatially varying regression models.