  The spatial composition and cellular heterogeneity of the tumor
microenvironment plays a critical role in cancer development and progression.
High-definition pathology imaging of tumor biopsies provide a high-resolution
view of the spatial organization of different types of cells. This allows for
systematic assessment of intra- and inter-patient spatial cellular interactions
and heterogeneity by integrating accompanying patient-level genomics data.
However, joint modeling across tumor biopsies presents unique challenges due to
non-conformability (lack of a common spatial domain across biopsies) as well as
high-dimensionality. To address this problem, we propose the Dual random effect
and main effect selection model for Spatially structured regression model
(DreameSpase). DreameSpase employs a Bayesian variable selection framework that
facilitates the assessment of spatial heterogeneity with respect to covariates
both within (through fixed effects) and between spaces (through spatial random
effects) for non-conformable spatial domains. We demonstrate the efficacy of
DreameSpase via simulations and integrative analyses of pathology imaging and
gene expression data obtained from $335$ melanoma biopsies. Our findings
confirm several existing relationships, e.g. neutrophil genes being associated
with both inter- and intra-patient spatial heterogeneity, as well as
discovering novel associations. We also provide freely available and
computationally efficient software for implementing DreameSpase.
