Spatially aligned random partition models on spatially resolved transcriptomics data

We propose spatially aligned random partition (SARP) models for clustering multiple types of experimental units, incorporating dependence in a subvector of the cluster-specific parameters, e.g., a subvector of spatial information, as in the motivating application. The approach is developed for inference about co-localization of immune, stromal, and tumor cell sub-populations. The aim is to understand the recruitment of immune and stromal cell subtypes by tumor cells, formalized as spatial dependence of the corresponding homogeneous cell subpopulations. This is achieved by constructing Bayesian nonparametric random partition models for the different types of cells, with a hierarchically structured prior introducing the desired dependence. Specifically, we use Pitman-Yor priors and add dependence in the base measure for spatial features, while leaving the base measure corresponding to gene expression features a priori independent across different types of cells. Details of the model construction are designed to lead to a convenient MCMC algorithm for posterior inference. Simulation studies show favorable performance in identifying co-localization between types of cells. We apply the proposed approach with colorectal cancer (CRC) data and discover subtypes of immune and stromal cells that are spatially aligned with specific tumor regions.