MoSAIC: Multi-Resolution Spatial Regression Analysis of Cellular Colocalizations in Cancer Imaging

Technical Summary: MoSAIC – Multi-Resolution Spatial Regression Analysis of Cellular Colocalizations in Cancer Imaging

Problem Statement
Hierarchical multiplex imaging (HMI) technologies generate spatially resolved single-cell measurements across multiple fields of view (FOVs) within patient tumor specimens. This data structure presents unique analytical challenges: (1) complex spatial relationships among cells within a single FOV; (2) non-ignorable spatial dependencies between FOVs within the same tumor tissue; and (3) high degrees of both within-patient and between-patient heterogeneity. Existing methods fail to jointly address this multi-resolution structure. Summary-based approaches (e.g., Ripley's K-cross, DIMPLE) characterize colocalization within single FOVs but ignore inter-FOV spatial dependencies, limiting scalability. Conversely, standard model-based approaches (e.g., mixed-effects models, Conditional Autoregressive models) either ignore spatial dependencies among FOVs or rely on assumptions (e.g., conformable grid spaces) that do not hold for irregular tumor geometries. Consequently, there is a lack of methods capable of disentangling global tumor-gradient effects, patient-specific variability, and spatial dependence to recover true biological signals in HMI data.

Methodology: The MoSAIC Model
The authors propose MoSAIC (Multi-Resolution Spatial regression Analysis of cell colocalizations), a hierarchical Bayesian spatial regression model designed specifically for HMI data. The model decomposes the joint variation of cellular colocalization outcomes into three components:

1. Global Tumor-Gradient Effects ($g(X)$): Modeled using penalized spline-based basis functions to capture potentially non-linear relationships between covariates (e.g., biomarker expression levels representing an Epithelial-to-Mesenchymal Transition (EMT) gradient) and the outcome. This allows for flexible estimation of population-level trends.
2. Patient-Specific Effects ($\mu_i$): Random intercepts for each patient to account for inter-patient variability that might obscure global gradient effects.
3. Spatial Random Effects ($\psi$): Modeled using Gaussian Processes (GP) to capture spatial dependence between FOVs within a single patient. The GP utilizes a squared exponential kernel with a spatial decay parameter ($\phi$) to define correlation as a function of distance, ensuring independence across different patients.

The model is formulated as:
$$y(s_{j(i)}) = g(x(s_{j(i)})) + \mu_i + \psi(s_{j(i)}) + \epsilon_{j(i)}$$
where $y$ represents the colocalization metric, $x$ represents the tumor gradient covariates, and $\epsilon$ is measurement error.

Estimation and Inference
MoSAIC employs a robust adaptive Metropolis algorithm to sample variance parameters from the marginal posterior distribution. To address multiple testing issues inherent in estimating smoothed covariate functions, the authors utilize joint credible bands to assess global significance. Furthermore, the model facilitates variance decomposition, calculating the Percentage of Variance Explained (PVE) for tumor gradients, patient differences, spatial relationships, and measurement error.

Key Results

• Simulation Studies: Across three scenarios (low spatial dependence, high spatial dependence, and non-linear effects), MoSAIC demonstrated superior performance compared to non-spatial models, Generalized Additive Models (GAM), and spatial models using Conditional Autoregressive (CAR) effects. MoSAIC consistently achieved lower WAIC (better model fit), lower Mean Squared Predictive Error (MSPE), and more accurate predictive coverage (approaching nominal 95%). The performance gains were most pronounced in settings with strong spatial dependence and complex covariate effects.
• Renal Cell Carcinoma (RCC) Application: Applied to a cohort of 21 patients with sarcomatoid RCC (sRCC) and 354 FOVs, MoSAIC investigated cellular colocalization patterns across the EMT gradient (defined by PD-L1 and N-cadherin expression).
  • PD-L1: Increased PD-L1 expression was associated with increased macrophage–tumor colocalization and a non-monotonic relationship with cytotoxic T–tumor colocalization (initially increasing then decreasing).
  • N-cadherin (NCAD): Higher NCAD expression (indicating a more mesenchymal phenotype) was associated with decreased cytotoxic T–tumor colocalization, suggesting reduced immune targeting in aggressive sRCC regions.
  • Variance Decomposition: The model explained 75–90% of the total outcome variability. Patient-specific effects accounted for the largest share (29–54%), followed by spatial random effects (11–30%), with PD-L1 and NCAD explaining smaller but significant portions (8–13% and <1–5%, respectively).

Significance and Claims
The paper claims that MoSAIC provides an interpretable, multi-resolution framework for quantifying spatial tumor-gradient effects in cancer imaging. By explicitly modeling the hierarchical nature of HMI data, the method successfully disentangles global biological trends from patient-specific and spatial noise. The authors assert that MoSAIC offers a methodologically principled choice for analyzing multi-resolution spatial data, filling a critical gap where existing methods either ignore spatial dependencies or fail to accommodate the irregular geometry of tumor tissues. The application to sRCC data demonstrates the model's ability to reveal biologically meaningful patterns, such as the spatially varying immune engagement associated with the EMT gradient, which may inform immunotherapy strategies. The authors note that the method is computationally efficient, fitting models in minutes on standard hardware, and is available as open-source software.