New Zealand Statistical Association

NZSA 2009

Victoria University of Wellington

Tilman Davies

Massey University

On adaptive kernel estimates of spatially dependent disease risk

Kernel smoothing is a well known technique for the estimation of relative risk based on point locations of disease cases and sampled population controls contained within a defined geographical region. Most applications of this methodology have made use of the fixed-bandwidth version of the kernel estimator in order to obtain estimates of the requisite densities. A more intuitive approach is to utilize a variable smoothing parameter with which we are able to reduce the bandwidth in areas of high point clustering to provide more detail and increase it to 'smooth over' isolated observations in regional areas, a technique shown to yield certain theoretical benefits for the individual densities. Despite these potential benefits, the increased complexity involved with the adaptive estimator has left a number of technical issues such as bandwidth selection and edge-correction that warrant additional attention. Problems also present themselves should we wish to make use of the adaptive risk surface for detection of significant 'hotspots' of disease risk due to excessive computation time. The technical issues to do with the implementation of the adaptive surface are addressed and we develop a computationally inexpensive approach for highlighting anomalous sub-regions of risk on the adaptive surface. The performance of both fixed and adaptive surfaces in terms of integrated square error is then examined based on results from simulation experiments.
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