Loglinear Residual Tests of Moran's I Autocorrelation and their Applications to Kentucky Breast Cancer Data

This article bridges the permutation test of Moran's I to the residuals of a loglinear model under the asymptotic normality assumption. It provides the versions of Moran's I based on Pearson residuals ( I _PR) and deviance residuals ( I _DR) so that they can be used to test for spatial clustering while at the same time account for potential covariates and heterogeneous population sizes. Our simulations showed that both I _PR and I _DR are effective to account for heterogeneous population sizes. The tests based on I _PR and I _DR are applied to a set of log-rate models for early-stage and late-stage breast cancer with socioeconomic and access-to-care data in Kentucky. The results showed that socioeconomic and access-to-care variables can sufficiently explain spatial clustering of early-stage breast carcinomas, but these factors cannot explain that for the late stage. For this reason, we used local spatial association terms and located four late-stage breast cancer clusters that could not be explained. The results also confirmed our expectation that a high screening level would be associated with a high incidence rate of early-stage disease, which in turn would reduce late-stage incidence rates.