Fig. 2

Simulated examples of associations more easily detected by GSDA than by other methods. a A scatterplot of the expression of two genes colored cyan or gold by the value of a categorical variable. b Boxplots for each of these two genes by category level with the Wilcoxon rank-sum test p value for each gene (p = 0.13 and 0.24 for genes 1 and 2, respectively). c A dendrogram for hierarchical clustering of these two genes on Euclidean distance on the expression data by Ward’s criteria with a color bar for the categorical variable value (GSDA t-test p = \(1.41 \times 10^{-33}\), permutation \(p< 10^{-6}\)). Five branches of the dendrogram are numerically indexed and the means of those five branches are shown by the positions of the numeric indices in a. d A scatterplot of a numeric variable Y and the expression of gene 1 (Spearman \(p = 0.36\)). The numeric variable Y is also indicated by a blue–purple–red color scale. e A scatterplot of a numeric variable Y and the expression of gene 2 (Spearman \(p = 0.00052\)). f Dendrogram for hierarhical clustering on genes 1 and 2 by Ward’s criteria with a blue–purple–red color bar for the numeric variable Y (GSDA \(p = 5.28 \times 10^{-41}\), permutation \(p < 10^{-6}\)). g A scatterplot of the expression of genes 1 and 2 with plotting character showing event status (red x = event, blue o = censored). h A scatterplot of gene 1 expression versus observation time with the same plotting characters showing event status (Cox regression \(p = 0.87\)). i A dendrogram for hierarchical clustering of the expression of genes 1 and 2 by Ward’s criteria with a color bar indicating event status (blue indicates event before year 4, gray indicates censor before year 4, red indicates event after year 4; GSDA t-test \(p = 6.1 \times 10^{-13}\), permutation \(p = 0.000111\))