Scalable inference for spatial generalized mixed models for use in multiplexed imaging analysis.

Understanding how cells interact to coordinate tissue function and respond to disease remains a central challenge in biology. Recently developed multiplex bioimaging technologies [multiplex immunofluorescence (MxIF)] can quantify multiple protein markers at a single-cell resolution in spatially preserved tissue, offering the opportunity to understand how cellular organization relates to disease mechanisms and treatment response. Spatial generalized linear mixed models for cell co-localization offer a flexible framework for these analyses, accommodating cell-, image-, or subject-level predictors while accounting for correlation arising from repeated cells per image, repeated images per subject, and spatial dependence among nearby cells. However, as MxIF data typically have hundreds of thousands to millions of cells per study, fitting the full spatial model is computationally infeasible due to the large, dense, spatial covariance matrix. We present a scalable inference strategy that uses parallelizable eigen-decomposition of an empirically estimated spatial correlation matrix to approximate the full spatial model. This approach enables fast estimation of fixed effects of interest without requiring formal estimation of spatial parameters or surface prediction. In simulations, our proposed method could be fitted to large datasets ($ \sim $ 285,000 observations) in under a minute, with runtime linearly increasing by only $ \sim $ 7 s per 50,000 additional observations. This scalability makes cell-level modeling in the presence of spatial correlation feasible for real-world MxIF datasets, as we demonstrate through applications to metastatic melanoma and high-grade serous ovarian carcinoma.