Fig. 4

Visualization of sample pair frequencies of image-based metrics compared to survival outcome metric; results on the a first-order, b second-order, c third-order, and d fourth-order HOCUS. For this visualization only, data was restricted to patients with a death event, then sample–based pairwise correlations were calculated using 1st-, 2nd-, 3rd-, 4th-order HOCUS metrics as well as difference in the length of survival, in days, between each pair of patients. In each plot, the conditional density is shown in which the distribution of all sample pairs are depicted as density maps. On the left-hand side of each plot, a series of plots are shown in which the feature-based measure is divided into five bands of equal size, and differences in survival time (the outcome metric) are plotted in histograms for those samples restricted to each band. The kernel similarity between the HOCUS metric and the co-survival metric is shown in the top right corner of each plot