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. Copyright © 2014 John Wiley & Sons, Ltd.