Approaches to modelling spatial data using skewed distributions with an application to disease mapping

In disease mapping, estimating spatial patterns is typically done by fitting Gaussian spatial models. However, this assumption may not always be correct, as there is a possibility that the spatial random component could follow a skewed and non-symmetric distribution. We propose two spatial statistics methods based on the skew-normal and skew-Laplace spatial distributions to model the spatial random effects. These approaches leverage the unique properties of skewed distributions to capture the inherent asymmetry in spatial data, providing a more accurate representation of complex disease risk. We compared the performance of our proposed non-normal spatial models with existing methodologies through simulation studies. To demonstrate the applicability of our approach, we analysed adult HIV and infant mortality in South Africa. This demonstration highlights our models' effectiveness and provides valuable insights into their practical relevance in public health research.