Statistical analysis of multiple regions-of-interest in multiplexed spatial proteomics data

Multiplexed spatial proteomics reveals the spatial organization of cells in tumors, which is associated with important clinical outcomes such as survival and treatment response. This spatial organization is often summarized using spatial summary statistics, including Ripley's K and Besag's L. However, if multiple regions of the same tumor are imaged, it is unclear how to synthesize the relationship with a single patient-level endpoint. We evaluate extant approaches for accommodating multiple images within the context of associating summary statistics with outcomes. First, we consider averaging-based approaches wherein multiple summaries for a single sample are combined in a weighted mean. We then propose a novel class of ensemble testing approaches in which we simulate random weights used to aggregate summaries, test for an association with outcomes, and combine the $P$-values. We systematically evaluate the performance of these approaches via simulation and application to data from non-small cell lung cancer, colorectal cancer, and triple negative breast cancer. We find that the optimal strategy varies, but a simple weighted average of the summary statistics based on the number of cells in each image often offers the highest power and controls type I error effectively. When the size of the imaged regions varies, incorporating this variation into the weighted aggregation may yield additional power in cases where the varying size is informative. Ensemble testing (but not resampling) offered high power and type I error control across conditions in our simulated data sets.