Fig 1.
H&E-stained images and spatial clusters for breast and prostate cancer.
(a) H&E-stained image with pathology labels for breast cancer (10× Genomics). (b) H&E-stained image with pathology labels for prostate cancer (10× Genomics; [24]). (c) Spatial clusters (n = 100) for breast cancer. (d) Spatial clusters (n = 100) for prostate cancer.
Table 1.
Type I error comparison of GEE with robust Wald test, GEE with GST, Independent GEE with robust Wald test, Wilcoxon rank-sum test, and z-test across different spatial scenarios and spatial cluster numbers. Type I error was evaluated at significance levels of α = 0.01, 0.001, and 0.0001 across 100,000 simulation replications. Inflated or deflated empirical Type I error rates (larger or smaller than the nominal α by 50% or more) are in boldface.
Fig 2.
Power comparison of GEE with robust Wald test, GEE with GST, Independent GEE with robust Wald test and Wilcoxon test across different spatial scenarios and spatial cluster numbers.
Panels (a–f) represent power curves for three spatial scenarios with 25 and 100 clusters: (a) Scenario 1 (25 clusters), (b) Scenario 1 (100 clusters), (c) Scenario 2 (25 clusters), (d) Scenario 2 (100 clusters), (e) Scenario 3 (25 clusters), and (f) Scenario 3 (100 clusters). Scenarios represent varying spatial correlation and spatial variance: Scenario 1 (weak), Scenario 2 (moderate), and Scenario 3 (strong). Type I error and power were evaluated at a significance level of α = 0.001.
Fig 3.
QQ plots of GEE with robust Wald test, GEE with GST, Independent GEE with robust Wald test, Wilcoxon rank-sum test and z-test for breast cancer comparisons: tumor-controls (DCIS vs. FT:(a), (d), (g), (j), (m); IC vs. FT: (b), (e), (h), (k), (n)) and control-control (FT1 vs. FT2: (c), (f), (i), (l), (o)).
The red line represents the expected distribution under the null hypothesis. DCIS: ductal carcinoma in situ; IC: invasive carcinoma; FT: fibrous tissue.
Fig 4.
Dot plots of enriched KEGG pathways identified in breast and prostate cancer.
Pathways identified by (a) the Wilcoxon rank-sum test, (b) GEE with GST test, and (c) Independent GEE test in the breast cancer dataset, and by the three tests ((d), (e), (f)) in the prostate cancer dataset. IC: invasive carcinoma; FT: fibrous tissue; FT1 vs FT2 (control-vs-control) comparison.
Table 2.
Runtime comparison in real ST datasets and simulated ST data.
Table 3.
Comparative performance of various statistical tests for detecting DE genes in ST data.