  The characteristics and determinants of health and disease are often
organised in space, reflecting our spatially extended nature. Understanding the
influence of such factors requires models capable of capturing spatial
relations. Though a mature discipline, spatial analysis is comparatively rare
in medicine, arguably a consequence of the complexity of the domain and the
inclemency of the data regimes that govern it. Drawing on statistical
parametric mapping, a framework for topological inference well-established in
the realm of neuroimaging, we propose and validate a novel approach to the
spatial analysis of diverse clinical data - GeoSPM - based on differential
geometry and random field theory. We evaluate GeoSPM across an extensive array
of synthetic simulations encompassing diverse spatial relationships, sampling,
and corruption by noise, and demonstrate its application on large-scale data
from UK Biobank. GeoSPM is transparently interpretable, can be implemented with
ease by non-specialists, enables flexible modelling of complex spatial
relations, exhibits robustness to noise and under-sampling, offers well-founded
criteria of statistical significance, and is through computational efficiency
readily scalable to large datasets. We provide a complete, open-source software
implementation of GeoSPM, and suggest that its adoption could catalyse the
wider use of spatial analysis across the many aspects of medicine that urgently
demand it.
