Fig 1.
Summary of the SHADE (Spatial Hierarchical Asymmetry via Directional Estimation) framework.
A) Multiplexed imaging data is structured hierarchically across cohorts, patients, and images. Multiplex images were adapted from [21] and are used under a Creative Commons CC BY 4.0 license. B) Images are processed into spatial point patterns with cell type annotations. C) SHADE estimates Spatial Interaction Curves (SICs) that capture directional associations between cell types across spatial scales. D) SICs are estimated at cohort, patient, and image levels, enabling multilevel analysis of spatial heterogeneity. E) Posterior distributions provide uncertainty quantification. F) SICs can be compared across cohorts to assess differences in spatial organization.
Fig 2.
An example spatial interaction curve showing the effect of a source cell type Ak on a target cell type B.
At each distance s, the curve value represents the change in log-intensity of type B associated with the presence of a type Ak cell at distance s.
Fig 3.
Simulation study comparing spatial analysis methods.
(a) Simulated pattern showing T cells, B cells, and tumor cells in a region with known spatial clustering. (b) G-cross analysis with the observed curve (black), CSR expectation (dashed red), and 95% global envelope (gray ribbon) from 99 CSR simulations. (c) L-cross analysis, which counts all tumor cells within distance r of a typical T cell rather than measuring nearest-neighbor distances. (d) SIC estimates from SHADE Hierarchical (red), SHADE Flat (blue), and the ground truth (black dashed), with simultaneous 95% credible bands.
Fig 4.
Detection power comparison across simulation conditions.
Boxplots show the proportion of all images in which methods correctly identify non-zero spatial interactions by testing whether simultaneous credible bands (SHADE) or global envelopes (G-cross, K-cross) exclude zero anywhere in the 0–75 μm range. Results are stratified by source cell density (rows: the conditioning cell type) and target cell density (columns: the cell type being modeled), with number of images per patient (1, 2, or 3) shown on the x-axis. SHADE Hierarchical achieves highest power when source density is high, with performance when source density is low depending critically on having multiple images per patient available for hierarchical pooling (see main text).
Fig 5.
Robustness to spatial confounding via compartments.
A: Compartment structure showing log-intensity effect on target density (3 compartments with moderate effect strength). B: Example simulated pattern with tumor cells (red) and T cells (blue). C: Detection power stratified by compartment effect strength (weak/moderate/strong), source density (T cells, rows), and target density (tumor cells, columns). Despite unmeasured compartments, all methods maintain high power in favorable scenarios. However, elevated Type I error rates (see Sect D.10 in S1 Text) indicate that SHADE incorrectly attributes compartment effects to source-target interactions when both cell types are abundant, demonstrating regime-dependent confounding bias.
Fig 6.
SIC showing the directional association of CAFs (source) with CTLs (target), stratified by patient group.
Solid lines show cohort-level estimates for CLR and DII; dashed lines show patient-level SICs, illustrating hierarchical variability across patients within each cohort. CTLs in CLR patients exhibit avoidance of CAFs, while DII patients show neutral to clustering patterns, indicating group-specific spatial organization.
Fig 7.
Examples of patient- and image-level SICs for high-heterogeneity cell type pairs.
Solid lines: patient-level SICs; dotted lines: image-level SICs, illustrating variability within patients.
Fig 8.
Cohort-level SICs () estimated for all source–target cell type pairs in the CRC dataset, stratified by CLR and DII patient groups, with simultaneous 95% credible bands.