Taking advantage of sampling designs in spatial small-area survey studies

Spatial small area estimation models have become very popular in some contexts, such as disease mapping. Data in disease mapping studies are exhaustive, that is, the available data are supposed to be a complete register of all the observable events. In contrast, some other small area studies do not use exhaustive data, such as survey based studies, where a particular sampling design is typically followed and inferences are later extrapolated to the entire population. In this article we propose a spatial model for small area survey studies, taking advantage of spatial dependence between units, which is the key assumption used for yielding reliable estimates in exhaustive data based studies. In addition, and in contrast to most survey-based spatial studies, we also take into account information on the sampling design and additional supplementary variables to obtain estimates in small areas. This makes it possible to merge spatial and sampling models into a common proposal.