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Clusters of similar or dissimilar objects are encountered in many fields.Frequently used approaches treat the central object of each cluster as latent.Yet, often objects of one or more types cluster around objects of another type.Such arrangements are common in biomedical images of cells, in which nearbycell types likely interact. Quantifying spatial relationships may elucidatebiological mechanisms. Parent-offspring statistical frameworks can be usefullyapplied even when central objects (parents) differ from peripheral ones(offspring). We propose the novel multivariate cluster point process (MCPP) toquantify multi-object (e.g., multi-cellular) arrangements. Unlike commonly usedapproaches, the MCPP exploits locations of the central parent object inclusters. It accounts for possibly multilayered, multivariate clustering. Themodel formulation requires specification of which object types function ascluster centers and which reside peripherally. If such information is unknown,the relative roles of object types may be explored by comparing fit ofdifferent models via the deviance information criterion (DIC). In simulateddata, we compared DIC of a series of models; the MCPP correctly identifiedsimulated relationships. It also produced more accurate and precise parameterestimates than the classical univariate Neyman-Scott process model. We alsoused the MCPP to quantify proposed configurations and explore new ones in humandental plaque biofilm image data. MCPP models quantified simultaneousclustering of Streptococcus and Porphyromonas around Corynebacterium and ofPasteurellaceae around Streptococcus and successfully captured hypothesizedstructures for all taxa. Further exploration suggested the presence ofclustering between Fusobacterium and Leptotrichia, a previously unreportedrelationship.

Multivariate cluster point process to quantify and explore multi-entity configurations: Application to biofilm image data