Knot selection for low-rank kriging models of spatial risk in case-control studies.

Many spatial analysis methods have been used to identify potential geographic clusters of disease in case-control studies. Low-rank kriging (LRK) models reduce the computational burden in generalized additive models by using a set of knot locations instead of the observed subject locations for estimating spatial risk. However, there is little guidance regarding selection of the number and location of the knots in case-control studies. We perform an extensive simulation study that compares a commonly-used method of knot selection in LRK models with two proposed methods and varies the number of knots. We find the commonly-used method is vastly outperformed by those that consider the locations of cases. We find that the Teitz and Bart heuristic allows the highest spatial sensitivity and power to detect zones of elevated risk, and recommend its use with a number of knots as close to the number of case locations as computation time will allow.