A Model-Based Hierarchical Bayesian Approach to Sholl Analysis

Due to the link between microglial morphology and function, morphological changes in microglia are frequently used to identify pathological immune responses in the central nervous system. In the absence of pathology, microglia are responsible for maintaining homeostasis, and their morphology can be indicative of how the healthy brain behaves in the presence of external stimuli and genetic differences. Despite recent interest in high throughput methods for morphological analysis, Sholl analysis is still the gold standard for quantifying microglia morphology via imaging data. Often, the raw data are naturally hierarchical, minimally including many cells per image and many images per animal. However, existing methods for performing downstream inference on Sholl data rely on truncating this hierarchy so rudimentary statistical testing procedures can be used. To fill this longstanding gap, we introduce a fully parametric model-based approach for analyzing Sholl data. We generalize our model to a hierarchical Bayesian framework so that inference can be performed without aggressive reduction of otherwise very rich data. We apply our model to three real data examples and perform simulation studies comparing the proposed method with a popular alternative.