Large-scale modelling and forecasting of ambulance calls in northern Sweden using spatio-temporal log-Gaussian Cox processes

To optimally utilise the resources of a country's prehospital care system, it is crucial to spatiotemporally forecast spatial regions and periods with an increased risk of seeing a call to the emergency number 112. Such forecasts allow the dispatcher to make strategic decisions to direct unoccupied ambulances. In addition, simulations based on forecasts may serve as the starting point for different optimal routing strategies. In this paper, we study a unique set of Swedish spatiotemporal ambulance call data. The spatial study region is the four northernmost regions of Sweden and the study period is January 1, 2014, to December 31, 2018. The non-infectious disease nature of the data motivated us to employ log-Gaussian Cox processes (LGCPs) for the spatiotemporal modelling and forecasting of the calls. To this end, we propose a K-means based bandwidth selection method for the kernel estimation of the spatial component of the separable spatiotemporal intensity function. The temporal component of the intensity function is modelled by Poisson regression and the spatiotemporal random field component of the random intensity of the LGCP is fitted using Metropolis-adjusted Langevin algorithm. A study of the spatiotemporal dynamics of the data shows that a hot-spot can be found in the southeastern part of the study region, where most people in the region live and our fitted model captured this behaviour quite well. The fitted temporal component of the intensity functions reveals that there is a significant association between the expected number of calls and the day of the week as well as the season of the year. In addition, non-parametric second-order spatiotemporal summary statistic estimates indicate that LGCPs seem to be reasonable models for the data. Finally, we find that the fitted forecasts generate simulated future spatial event patterns which quite well resemble the actual future data.