Adjusted significance cutoffs for hypothesis tests applied with generalized additive models with bivariate smoothers

Area of Science:

• Spatial epidemiology
• Biostatistics
• Geographic Information Systems (GIS)

Background:

• Generalized additive models (GAMs) with bivariate locally weighted regression smoothing (LOESS) are used to detect spatial variation in disease risk.
• Existing hypothesis testing methods, the approximate chi-square test (ACST) and conditional permutation test (CPT), exhibit inflated type I error rates in this context.
• This inflation leads to inaccurate conclusions regarding the significance of spatial disease patterns.

Purpose of the Study:

• To determine empirical adjustments to significance cutoffs for ACST and CPT in GAMs with bivariate LOESS.
• To evaluate the performance of these adjusted tests across various simulation parameters.

Main Methods:

• Utilized simulated data to assess type I error rates of ACST and CPT.
• Calculated empirical adjustments to significance cutoffs for nominal type I error rates (0.01, 0.05, 0.10).
• Tested the appropriately sized ACST and CPT across diverse region shapes, population densities, sample sizes, and disease probabilities.

Main Results:

• Empirical adjustments to significance cutoffs were determined for ACST and CPT.
• When applied with these adjusted cutoffs, both ACST and CPT demonstrated appropriately controlled type I error rates.
• The adjusted tests performed reliably across a range of simulation conditions.

Conclusions:

• Adjusted significance cutoffs effectively correct the inflated type I error rates of ACST and CPT in GAMs with bivariate LOESS.
• These validated hypothesis testing methods provide accurate assessments of spatial disease risk variation.
• The findings support the reliable application of these statistical approaches in spatial epidemiology research.