Non‐Parametric Ecological Regression and Spatial Variation

Ecological studies aim to analyse the variation of disease risk in relation to exposure variables that are measured at an area unit level. In practice it is rarely possible to use the exposure variables themselves, either because the corresponding data are not available or because the causes of the disease are not fully understood. It is therefore quite common to use crude proxies of the real exposure to the disease in question. These proxies are rarely able to explain the disease variation and hence additional area level random effects are introduced to account for the residual variation. In this paper we investigate the possibility to model the effect of ecological covariates non‐parametrically, with and without additional random effects for the residual spatial variation. We illustrate the issues arising through analyses of simulated and real data on larynx cancer mortality in Germany, during the years of 1986 to 1990, where we use the corresponding lung cancer rates as a proxy for smoking consumption.