Multiscale Statistical Models for Understanding Tumor Microenvironment Heterogeneity

The tumor microenvironment (TME) is a complex and spatially structured system of immune, stromal, and tumor cells whose interactions play a central role in cancer progression and treatment response. Advances in multiplexed imaging have enabled detailed spatial profiling of the TME at single-cell resolution, but extracting interpretable, reproducible insights from these data remains a major challenge. This dissertation develops and applies a set of spatial statistical models for analyzing spatial tissue data in a way that reflects biological complexity while remaining statistically coherent and computationally tractable. The first part of the dissertation focuses on applied spatial analysis, characterizing immune architecture in metastatic melanoma and colorectal cancer using both descriptive and model-based approaches. These studies reveal spatial patterns associated with disease stage, immune suppression, and patient survival. The second part introduces new multilevel spatial models, including SHADE, a hierarchical extension of the Gibbs point process that captures directional cell–cell interactions across multiple spatial and biological scales, and BIPPS, a latent spatial factor model that estimates shared patterns of cellular organization across subjects. Chapter 6 develops a Bayesian survival model that integrates functional spatial covariates while accounting for sampling uncertainty and hierarchical data structure. Finally, Chapter 7 explores simulation-based inference in mechanistic models of tumor–immune dynamics, demonstrating the feasibility of applying amortized neural inference methods to recover parameters from dynamic biological systems. Together, these contributions offer a flexible statistical framework for studying spatial organization in cancer tissues and connecting it to clinical outcomes. By combining spatial statistics, hierarchical modeling, and Bayesian inference, the dissertation provides tools for more principled and interpretable analysis of high-dimensional tissue imaging data.