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Spatial smoothing models play an important role in the field of small area estimation. In the context of complex survey designs, the use of design weights is indispensable in the estimation process. Recently, efforts have been made in these spatial smoothing models, in order to obtain reliable estimates of the spatial trend. However, the concept of missing data remains a prevalent problem in the context of spatial trend estimation as estimates are potentially subject to bias. In this paper, we focus on spatial health surveys where the available information consists of a binary response and its associated design weight. Furthermore, we investigate the impact of nonresponse as missing data on a range of spatial models for different missingness mechanisms and different degrees of missingness by means of an extensive simulation study. The computations were performed in R, using INLA and other existing packages. The results show that weight adjustment to correct for missingness has a beneficial effect on the bias in the missing at random setting for all models. Furthermore, we estimate the geographical distribution of perceived health at the district level based on the Belgian Health Interview Survey (2001). Copyright (c) 2017 John Wiley & Sons, Ltd. Support from the National Institutes of Health is acknowledged [award number R01CA172805]. Support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy) is gratefully acknowledged. For the simulation study, we used the infrastructure of the VSC - Flemish Supercomputer Center, funded by the Hercules Foundation and the Flemish Government - department EWI.