The spatial autocorrelation and co-expression of genes can inflate the false-positive rate when annotating the results of correlations between brain phenotypes and brain-specific gene expression [40]. Therefore, we adopted the following strategies to assess the significance of the spatial correlation between gene expression and Combined-PC1. Similar to the spatial permutation test, the 66 loadings of Combined-PC1 were shuffled while preserving their spatial contiguity [36]. Next, the spined loadings were correlated with each of the 6,513 genes using Pearson’s correlation. The largest positive and negative correlation coefficients from among the 6,513 correlations were retained. This procedure was repeated 10,000 times, which resulted in two null distributions for positive and negative coefficients respectively. The empirical (original) coefficients greater than the 95th percentile in the positive null distribution or smaller than the 5th percentile in the negative null distribution were accepted as significant. Genes that showed significant spatial correlation with the Combined-PC1 (i.e., a set of PC1-related genes) were reported.
