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This paper describes geographically weighted Poisson regression (GWPR) and its semi‐parametric variant as a new statistical tool for analysing disease maps arising from spatially non‐stationary processes. The method is a type of conditional kernel regression which uses a spatial weighting function to estimate spatial variations in Poisson regression parameters. It enables us to draw surfaces of local parameter estimates which depict spatial variations in the relationships between disease rates and socio‐economic characteristics. The method therefore can be used to test the general assumption made, often without question, in the global modelling of spatial data that the processes being modelled are stationary over space. Equally, it can be used to identify parts of the study region in which ‘interesting’ relationships might be occurring and where further investigation might be warranted. Such exceptions can easily …