Fig. 2: Results of DLVPM analysis applied to TCGA breast cancer data.

a, Illustration of DLVPM in a Siamese/twin network configuration. b, Plots comparing the performance of DLVPM-Twins against VicReg, Barlow twins and several pretrained foundation models (n = 152). The error bars represent the mean-centred 95% bootstrapped confidence intervals. c, Illustration of the DLVPM method showing a graph representation of the path model, and the associated adjacency matrix. d, Comparison of the mean Pearson’s correlation across dimensions and data modalities for DLVPM and PLS-PM (n = 152). The error bars represent the mean-centred 95% bootstrapped confidence intervals. e, Plots show the mean Pearson’s correlation of each DLV, with DLVs from the data types connected by the path model. The error bars represent the mean-centred 95% bootstrapped confidence intervals (n = 152). f, Association matrices for all the five DLVs. The entries in the top triangular part of the matrix indicate the Pearson’s correlation values between the different data types. The entries in the bottom part of the matrix are significance values for these correlations, obtained using permutation testing (n = 152). g, Path model linking the omics and imaging data types included in this analysis. This graph represents the first orthogonal mode of variation between DLVs. The edges connecting the network nodes are labelled with Pearson’s pairwise correlation coefficient (n = 152). h, Results of mediation analyses carried out using the first DLV. The numbers on the network graph are beta values. The significance of the mediated effect is shown on the right of the graph (n = 152). i, Results of additional analyses to localize effects to particular genetic loci. The plot shows the Pearson’s correlation values between the genetic loci and DLVs connected to the data view under analysis by the path model. The plots on the left show the ten most positively and negatively associated genetic loci for each data type. The error bars represent the mean-centred 95% bootstrapped confidence intervals. The bar plots show the Pearson’s correlation values for all the loci under analysis, along with the family-wise error-corrected (FWER) significance threshold (n = 152). Panels a and c created with BioRender.com.