Multivariate Cluster Point Process Model: Parent Location Improves Inference for Complex Biofilm Image Data

A common challenge in spatial statistics is to quantify the spatial distributions of clusters of objects. Frequently used approaches treat the central object of each cluster as latent, but it is often the case that cells of one or more types cluster around cells of another type. Such arrangements are common, for example, in microbial biofilm, in which close interspecies spatial clustering is thought to reflect physical interactions among species. Because these interactions arise from or drive biofilm community structure, quantifying these spatial relationships may provide clues to disease pathogenesis or treatment effects. Even when clustering arrangements are not strictly parent-offspring relationships, treating the central object as a parent can enable use of parent-offspring clustering frameworks. We propose a novel multivariate spatial point process model to quantify multicellular arrangements with parent-offspring statistical approaches. We used the proposed model to analyze data from a human dental plaque biofilm image containing spatial locations of Streptococcus, Porphyromonas, Corynebacterium, and Pasteurellaceae, among other species. The proposed multivariate cluster point process (MCPP) model departs from commonly used approaches in that it exploits the locations of the central object in clusters. It also accounts for possibly multilayered, multivariate parent-offspring clustering. In simulated datasets, the MCPP outperforms the classical Neyman-Scott process model, a univariate model for modeling spatially clustered processes, by producing decisively more accurate and precise parameter estimates. Applied to the motivating data, we quantified the simultaneous clustering of Streptococcus and Porphyromonas around Corynebacterium and of Pasteurellaceae around Streptococcus. The proposed MCPP model successfully captured the parent-offspring structure for all the taxa involved.