The impact of spatial scales on discretised spatial point patterns

Spatial data are common in health sciences and are available at various spatial scales such as the point, grid or area level. This research considers modelling of point level data, which in practice could resemble disease data with exact residential locations, by discretizing the study region into regular grid cells. Modelling of health data at the grid level is desirable as it is geographically more accurate than using area level data and yet protects patient confidentiality. The challenge is to specify an appropriate spatial scale for discretization of point patterns. We investigate how changes in grid cell size affect model outcomes for various structures of spatial point patterns. A Bayesian spatial model is used to evaluate the impact of varying spatial scales on model outcomes. Estimation is based on a Bayesian spatial smoothness prior to model spatial dependence of neighboring grid cells, namely an intrinsic Gaussian Markov random field (IGMRF). Bayesian computation is carried out using integrated nested Laplace approximation (INLA). The impact of varying spatial scales is studied in a simulation study. The simulated data consist of various spatial patterns that resemble different patterns of point level health data in realistic settings, including inhomogeneous point patterns, patterns with local repulsion, patterns with local clustering, and patterns with local clustering in the presence of a largerscale inhomogeneity. The evaluation criteria used in this study include the spatial correlation coefficient, the coefficient of variation of the spatially structured effect, and the mean squared error between the observed counts and the estimated counts. Based on the results, we note that complicated spatial patterns such as inhomogeneous point patterns and spatially clustered patterns tend to be more sensitive to the changing spatial scales, compared to homogeneous point patterns. It is therefore recommended to repeat the spatial analyses at multiple spatial scales in order to determine the best scale to analyze the data in order to address the inferential aims of interest. In particular, it is noted that fine grid cell sizes do not necessarily improve inferential outcomes as there has to be sufficient information in the grid cells.