This work aims to expand on a previous study [1] that compares the survival predictions of 13 different supervised multi-omics methods on datasets from 18 cancer types from The Cancer Genome Atlas (TCGA). This comparison is based on the analysis of 4 types of molecular data (mRNA, miRNA, CNV, Mutations) and clinical data. Methods are divided into 3 groups: reference models (Kaplan-Meier and a Cox regression on clinical data only), "naive" models, unable to distinguish between each omics data, and "structured" models.

• Building on the conclusion in [1] that structured methods perform better than naive ones, we include methods not only capable of exploiting the group structure of omics data but also of extracting links between them: Joint Dimension Reduction (JDR) methods. We test these methods in unsupervised and supervised settings whenever possible.

• Then, to go further on the evaluation of the importance of clinical data we compare all of these methods (naive/structured/JDR) without clinical data to see if molecular data only can lead to similar prediction performance as with the addition of clinical data.

• JDR methods (supervised and unsupervised) improve both C-Index and IBS.

• IntNMF has the best median performance across datasets.

• C-index and IBS are inferior across all methods.

• JDR are the best performing non reference methods.

• Supervised RGCCA and SGCCA have the highest performance.

• Supervising JIVE does not seem to improve performance, as is the case with RGCCA/SGCCA.

• Add more JDR methods in the benchmark (MCIA, iCluster, Scikit-Fusion).

• Use an automatic procedure to select the best performing parameters for each method.

• Include methods capable of extracting Common, Local and Distinct (CLD) components, in line with the good performance of JIVE.

• Design a new method based on the best performing ones of the benchmark to exploit biological a priori information.