Testing for changes in spatial relative risk.

The spatial relative risk function is a useful tool for describing geographical variation in disease incidence. We consider the problem of comparing relative risk functions between two time periods, with the idea of detecting alterations in the spatial pattern of disease risk irrespective of whether there has been a change in the overall incidence rate. Using case-control datasets for each period, we use kernel smoothing methods to derive a test statistic based on the difference between the log-relative risk functions, which we term the log-relative risk ratio. For testing a null hypothesis of an unchanging spatial pattern of risk, we show how p-values can be computed using both randomization methods and an asymptotic normal approximation. The methodology is applied to data on campylobacteriosis from 2006 to 2013 in a region of New Zealand. We find clear evidence of a change in the spatial pattern of risk between those years, which can be explained in differences by response to a public health initiative between urban and rural communities.