The objective of this thesis is to examine the relationship between CAIX (a biomarker for insufficient oxygen in tumor microenvironment) and CD8+ T cells (the immune cells for killing cancer cells) for ovarian cancer. We approach the problem from two perspectives. The first approach is to set up count models such as Poisson, negative binomial, and zero-inflated Poisson models to examine the cell counts between CAIX and CD8+ T cells in the tumor microenvironment. The second approach is to apply the cross-K function, which is a second-order property of the point pattern process. We find that the tissue microarray (TMA), which is a technique to assemble hundreds of tissue samples on one TMA block, has a fixed effect on the CD8+ T cell counts. There are two TMA blocks A2 and B1. The relationship between CAIX and CD8+ T cells highly depends on TMAs. On TMA B1 stroma, a negative relationship between CAIX and CD8+ T cell counts is observed in the negative binomial models. When taking the spatial domain into account and comparing the estimated cross-K function of CAIX and CD8+ T cells to the simulated envelopes generated by a homogeneous Poisson process, we find that CAIX and CD8+ T cells are regulated and repel each other on TMA B1. Tissue category also plays an influential role in analyzing the relationship. The estimated cross-K function of CAIX and CD8 + T cells is more dispersed on tumors than on stroma. / Graduate