Penalized likelihood and multi-objective spatial scans for the detection and inference of irregular clusters

Area of Science:

• Spatial analysis
• Geographic information systems
• Epidemiology

Background:

• Delineating irregularly shaped spatial clusters is challenging.
• Existing methods like penalized likelihoods aim to control cluster shape freedom.
• Novel approaches use multi-objective algorithms to balance scan statistics with geometric constraints.

Purpose of the Study:

• To develop and evaluate a novel scan statistic algorithm for identifying geographically meaningful clusters.
• To introduce a graph topology-based function (disconnection nodes cohesion function) to penalize disconnected cluster components.
• To compare the performance of multi-objective scans with different penalty functions against single-objective methods.

Main Methods:

• Developed a novel scan statistic algorithm incorporating a disconnection nodes cohesion function.
• Employed multi-objective optimization to maximize spatial scan statistics and geometric penalty functions.
• Compared penalized likelihood methods using geometric, non-connectivity, and cohesion functions.
• Evaluated statistical significance using an attainment function approach.
• Applied the methods to Chagas' disease data in Minas Gerais, Brazil.

Main Results:

• Multi-objective scans demonstrated superior performance in power, sensitivity, and positive predicted value compared to single-objective algorithms.
• The multi-objective non-connectivity scan is efficient for moderately irregular clusters.
• The multi-objective cohesion scan excels at detecting highly irregular clusters.

Conclusions:

• Multi-objective spatial scan statistics offer improved cluster detection capabilities.
• The novel disconnection nodes cohesion function effectively refines cluster identification.
• The choice of penalty function (non-connectivity vs. cohesion) depends on the degree of cluster irregularity.