Assessing heterogeneity in spatial data using the HTA index with applications to spatial transcriptomics and imaging

Tumour heterogeneity is being increasingly recognized as an important characteristic of cancer and as a determinant of prognosis and treatment outcome. Emerging spatial transcriptomics data hold the potential to further our understanding of tumour heterogeneity and its implications. However, existing statistical tools are not sufficiently powerful to capture heterogeneity in the complex setting of spatial molecular biology.We provide a statistical solution, the HeTerogeneity Average index (HTA), specifically designed to handle the multivariate nature of spatial transcriptomics. We prove that HTA has an approximately normal distribution, therefore lending itself to efficient statistical assessment and inference. We first demonstrate that HTA accurately reflects the level of heterogeneity in simulated data. We then use HTA to analyze heterogeneity in two cancer spatial transcriptomics datasets: spatial RNA sequencing by 10x Genomics and spatial transcriptomics inferred from H&E. Finally, we demonstrate that HTA also applies to 3D spatial data using brain MRI. In spatial RNA sequencing, we use a known combination of molecular traits to assert that HTA aligns with the expected outcome for this combination. We also show that HTA captures immune-cell infiltration at multiple resolutions. In digital pathology, we show how HTA can be used in survival analysis and demonstrate that high levels of heterogeneity may be linked to poor survival. In brain MRI, we show that HTA differentiates between normal ageing, Alzheimer's disease and two tumours. HTA also extends beyond molecular biology and medical imaging, and can be applied to many domains, including GIS.Python package and source code are available at: https://github.com/alonalj/hta.Supplementary data are available at Bioinformatics online.