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

In spatial epidemiology, generalized additive models (GAMs) can be applied with bivariate locally weighted regression smoothing terms (LOESS), smoothing over longitude and latitude, to evaluate whether there is spatial variation in disease risk across a study region. Two hypothesis testing methods applicable with GAMs with bivariate LOESS smoothes, an approximate chi-square test (ACST) and the conditional permutation test (CPT), have inflated type I error rates. Using simulated data we determined empirical adjustments to significance cutoffs for nominal type I error rates of 0.01, 0.05, and 0.10. When applied with adjusted significance cutoffs, both ACST and CPT were appropriately sized across region shapes, population densities, sample sizes, and probabilities of disease.