Disease mapping via negative binomial regression M-quantiles.

We introduce a semi-parametric approach to ecological regression for disease mapping, based on modelling the regression M-quantiles of a negative binomial variable. The proposed method is robust to outliers in the model covariates, including those due to measurement error, and can account for both spatial heterogeneity and spatial clustering. A simulation experiment based on the well-known Scottish lip cancer data set is used to compare the M-quantile modelling approach with a disease mapping approach based on a random effects model. This suggests that the M-quantile approach leads to predicted relative risks with smaller root mean square error. The paper concludes with an illustrative application of the M-quantile approach, mapping low birth weight incidence data for English Local Authority Districts for the years 2005-2010.