A new proposal to adjust Moran's I for population density.

Area of Science:

• Spatial statistics
• Epidemiology
• Biostatistics

Background:

• Spatial independence tests are crucial for analyzing disease patterns.
• Prevalence rates can be influenced by population size and density.
• Existing spatial correlation indices may be sensitive to population variations.

Purpose of the Study:

• To analyze the effect of population size on spatial independence test power.
• To compare Moran's index with population density-adjusted indices.
• To propose a new spatial correlation index for morbidity risks.

Main Methods:

• Analysis of spatial independence test power using varying population sizes.
• Comparison of Moran's index with Oden's, Waldhör's, and a newly proposed index.
• Evaluation of type I error probability and statistical power.

Main Results:

• Spatially correlated populations affect the type I error of Moran's and Waldhör's indices.
• Oden's test is effective for risk heterogeneity but less so for pure spatial correlation.
• The newly proposed test shows higher power than Moran's index for spatial correlation of morbidity risks.

Conclusions:

• Population density adjustments are important for spatial independence tests.
• The proposed index offers improved power for assessing spatial correlation of morbidity risks.
• Careful selection of spatial statistics is necessary based on research objectives.