Geographically Weighted Linear Combination Test for Gene Set Analysis of a Continuous Spatial Phenotype as applied to Intratumor Heterogeneity

Background The impact of gene-sets on phenotype is not necessarily uniform across different locations of a cancer tissue. This study introduces a computational platform, GWLCT, for combining gene set analysis with spatial data modeling to provide a new statistical test for association of phenotypes and molecular pathways in spatial single-cell RNA-seq data collected from an input tumor sample. Methods At each location, the most significant linear combination is found using a geographically weighted shrunken covariance matrix and kernel function. Whether a fixed or adaptive bandwidth is determined based on a cross validation procedure. Our proposed method is compared to the global version of linear combination test (LCT), bulk and random-forest based gene-set enrichment analyses using data created by the Visium Spatial Gene Expression technique on an invasive breast cancer tissue sample, as well as 144 different simulation scenarios. Results In an illustrative example, the new geographically weighted linear combination test, GWLCT, identifies the cancer hallmark gene-sets that are significantly associated at each location with the five spatially continuous phenotypic contexts in the tumors defined by different well-known markers of cancer-associated fibroblasts. Scan statistics revealed clustering in the number of significant gene-sets. A spatial heatmap of combined significance over all selected gene-sets is also produced. Extensive simulation studies demonstrate that our proposed approach outperforms other methods in the considered scenarios, especially when the spatial association increases. Conclusions Our proposed approach considers the spatial covariance of gene expression to detect the most significant gene-sets affecting a continuous phenotype. It reveals spatially detailed information in tissue space and can thus play a key role in understanding contextual heterogeneity of cancer cells. ### Competing Interest Statement The authors have declared no competing interest.