• Department of Clinical Sciences, UT Southwestern Medical Center, Dallas, TX, USA.
• Department of Statistics, Southern Methodist University, Dallas, TX, USA.
• Department of Statistics, Purdue University, West Lafayette, IN, USA.
• Department of Pathology, UT Southwestern Medical Center, Dallas, TX, USA and Hamon Center for Therapeutic Oncology Research, UT Southwestern Medical Center, Dallas, TX, USA.

Digital pathology imaging of tumor tissues, which captures histological details in high resolution, is fast becoming a routine clinical procedure. Recent developments in deep-learning methods have enabled the identification, characterization, and classification of individual cells from pathology images analysis at a large scale. This creates new opportunities to study the spatial patterns of and interactions among different types of cells. Reliable statistical approaches to modeling such spatial patterns and interactions can provide insight into tumor progression and shed light on the biological mechanisms of cancer. In this article, we consider the problem of modeling a pathology image with irregular locations of three different types of cells: lymphocyte, stromal, and tumor cells. We propose a novel Bayesian hierarchical model, which incorporates a hidden Potts model to project the irregularly distributed cells to a square lattice and a Markov random field prior model to identify regions in a heterogeneous pathology image. The model allows us to quantify the interactions between different types of cells, some of which are clinically meaningful. We use Markov chain Monte Carlo sampling techniques, combined with a double Metropolis-Hastings algorithm, in order to simulate samples approximately from a distribution with an intractable normalizing constant. The proposed model was applied to the pathology images of $205$ lung cancer patients from the National Lung Screening trial, and the results show that the interaction strength between tumor and stromal cells predicts patient prognosis (P = $0.005$). This statistical methodology provides a new perspective for understanding the role of cell-cell interactions in cancer progression.