Supervisor: Dr. Adam Spannaus (Research Scientist; Oak Ridge National Laboratory, USA)

Additional Resources: Paper (Draft) · Git Repository · Presentation · Poster

Bayesian spatial models are widely used in disease mapping to estimate area-level overdose risk from socioeconomic covariates such as poverty and unemployment. These models work well at small spatial units, where they stabilize risk estimates in data-sparse areas by smoothing toward local neighborhood averages. But at the regional level, large spatial units like counties, where risk can shift sharply between neighbors, that same smoothing becomes a drawback: standard models impose a uniform level of smoothness across the whole region, masking sharp transitions in risk and producing overly uncertain estimates.

My research addresses this by introducing topological data analysis (TDA) into the disease-mapping pipeline. Using persistent homology, I extract topological summaries, statistics describing the shape of the data, such as how prominent and long-lived a cluster of high-poverty census tracts is, from finer-grained, subregional covariate data. I then integrate these summaries as a third component of the spatial random effect in a Bayesian hierarchical model (which I call BYM-T), alongside the usual structured (neighbor-dependent) and unstructured (localized noise) components. This gives the model region-specific structural information it previously had no way to access.

I validated the approach on synthetic data and on real opioid-overdose mortality and social vulnerability data from West Virginia and Tennessee, using Bayesian inference via PyMC. The topology-integrated model matches the predictive accuracy of the standard approach while substantially reducing uncertainty in regional risk estimates and correctly identifying sharp risk transitions between neighboring counties that the standard model smooths away.