ABSTRACT: Summary The characteristics and determinants of health and disease are often organized in space, reflecting our spatially extended nature. Understanding the influence of such factors requires models capable of capturing spatial relations. Drawing on statistical parametric mapping, a framework for topological inference well established in the realm of neuroimaging, we propose and validate an 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 readily interpretable, can be implemented with ease by non-specialists, enables flexible modeling of complex spatial relations, exhibits robustness to noise and under-sampling, offers principled criteria of statistical significance, and is through computational efficiency readily scalable to large datasets. We provide a complete, open-source software implementation. Highlights • A framework for topological inference applicable to diverse clinical data is proposed• Superior robustness to noise and under-sampling is observed compared with kriging• Application to UK Biobank data is demonstrated The bigger picture Many aspects of health and disease are distributed in space, requiring models of topological organization. The complexity of the task, however, makes spatial analysis comparatively rare in medicine. Here, we introduce GeoSPM, a platform for topological inference from clinical data based on a mature mathematical framework—statistical parametric mapping—validated by decades of use in neuroimaging. We provide comprehensive synthetic evaluation of the approach, and illustrate its application on large-scale data from UK Biobank. The interpretability, flexibility, scalability, ease of implementation, robustness to noise and under-sampling, computational efficiency, and provision of principled criteria of statistical significance, provided by our open-source platform should catalyze wider use of spatial analysis across medicine. We present GeoSPM, an approach to the spatial analysis of diverse clinical data that extends a framework for topological inference, well established in neuroimaging, based on differential geometry and random field theory. We evaluate GeoSPM with extensive synthetic simulations, and apply it to large-scale data from UK Biobank. Our approach is readily interpretable, easy to implement, enables flexible modeling of complex spatial relations, exhibits robustness to noise and under-sampling, offers principled criteria of statistical significance, and is scalable to large datasets.
