Fig 1.
a. Early Integration: Sources are concatenated before being fed to a single model. b. Joint Integration: Sub-representations of each source are learned jointly before inputting into the model. c. Late Integration: Each source outputs its prediction using its independent model, and the predictions are then aggregated. d. Mixed Integration: Representation of the mixed integration approach. In phase 1, a specific model is trained for each source independently and embeds a sub-representation adapted to the source’s specificities. In phase 2, the specific models are trained jointly, similarly to the joint integration setup, to create the final output.
Fig 2.
a. Early Integration VAE: Variational Autoencoder architecture with early integration strategy. b. Joint Integration VAE: Variational Autoencoder architecture with joint integration strategy. c. Late Integration VAE: Variational Autoencoder architecture with late integration strategy.d. Mixed-Integration/CustOmics: This is a hierarchical architecture composed of specific per-source autoencoders that converges into a central variational autoencoder.
Fig 3.
a. pan-cancer and PAM50 classification results: Overall classification results for the pan-cancer tumor classification test case and the PAM50 subtype classification for breast cancer. b. T-SNE vizualization for each omic source separately, along with the latent representation constructed by CustOmics. We see that the constructed layer representation succeeds at separating the data into four distinct clusters that we couldn’t distinguish with each omic source alone. c. PAM50 gene importance: Computed SHAP values on the RNA-Seq data of the most relevant genes responsible for discriminating between subtypes against the others using CustOmics for both integration phases.
Table 1.
The classification performance for the pan-cancer dataset is evaluated with 5 standard metrics for UMAP, NMF, MFA, Unsupervised Customics with SVM, and supervised deep-learning methods.
We evaluate the performances on the final predicted output of the downstream classifier.
Table 2.
Classification performance for PAM50 classification on the TCGA-BRCA dataset, with 5 standard metrics.
We compare machine-learning methods like UMAP, NMF, and MFA with deep-learning methods. We evaluate the performances on the final predicted output of the downstream classifier.
Fig 4.
a. Survival Analysis Performances: We evaluate the performances of the survival model for the pan-cancer dataset using both the C-index and the Integrated Brier Score (IBS). Here again, our model outperforms the other integration strategies on both metrics. b. Log-rank test: We compute the p-value associated with the log-rank test between high and low-risk groups for every integration strategy on a validation set for the pan-cancer survival test case and compare it to mono-omic survival predictions. c. Kaplan Meier Curves: We draw the Kaplan Meier curves and display the p-value associated with the log-rank test as computed previously for each dataset using the predicted hazard from the CustOmics model and stratify the population into high and low risk on the test set for the predicted hazard ratio. This figure shows that our method successfully stratifies the patients into risk subgroups.
Table 3.
The survival analysis performance for the pan-cancer dataset is evaluated with two standard metrics, C-index and IBS.
We compare classical methods like UMAP, NMF, and MFA with deep-learning methods and evaluate the performances on the final predicted output of the downstream survival network.
Table 4.
Survival performances of state-of-the-art integration methods for survival analysis, using concordance index on 5 TCGA cohorts: Bladder Urothelial Carcinoma (BLCA), Breast Invasive Carcinoma (BRCA), Glioblastoma & Lower Grade Glioma (GBMLGG), Lung Adenocarcinoma (LUAD) and Ulterine Corpus Endometrial Carcinoma (UCEC).