Functional Data Analysis of Spatial Clustering Identifies Prognostic T Cell Patterns in Ovarian Cancer

Spatial proteomic imaging technologies enable the simultaneous assessment of immune cell abundance and spatial organization within the tumor microenvironment. Spatial clustering is commonly summarized using measures such as Ripley's K or nearest neighbor G-functions at a fixed radius. However, these approaches depend on scale selection and may obscure biologically relevant patterns occurring across spatial ranges. We propose a functional data analysis (FDA) framework to model spatial clustering trajectories derived across a continuum of radii. Functional principal component analysis (FPCA) was used to summarize dominant modes of spatial variation, and resulting scores were incorporated into Cox proportional hazards models as both main effects and interaction with immune cell abundance. The approach was applied to multiplex immunofluorescence data from five ovarian cancer studies, comprising 773 high grade ovarian serous tumors. Analyses focused on CD3+ and CD8+ T cell populations within the tumor compartment of the tissue, adjusting for age at diagnosis and cancer stage, with study-specific estimates combined using random-effects meta-analysis. Higher abundance of both T cells and CD8+ T cells was consistently associated with improved overall survival. Beyond abundance, spatial features captured by the leading functional principal component were independently associated with survival, particularly for CD8+ T cells. Interaction models further showed that the prognostic effect of immune infiltration depended on spatial clustering, with tumors characterized by high abundance and low spatial clustering exhibiting the most favorable outcomes. These findings indicate that spatial organization provides complementary prognostic information beyond abundance alone and suggests that more diffuse immune infiltration may reflect more effective anti-tumor activity in ovarian cancer. Overall, FDA offers a flexible and interpretable framework for modeling spatial clustering across scales and identifying prognostic spatial features not captured by fixed-radius or distance analyses.