Cancer is a complex disease with significant social and economic impact. Advancements in high-throughput molecular assays and the reduced cost for performing high-quality multi-omics measurements have fuelled insights through machine learning . Previous studies have shown promise on using multiple omic layers to predict survival and stratify cancer patients. In this paper, we developed a Supervised Autoencoder (SAE) model for survival-based multi-omic integration which improves upon previous work, and report a Concrete Supervised Autoencoder model (CSAE), which uses feature selection to jointly reconstruct the input features as well as predict survival. Our experiments show that our models outperform or are on par with some of the most commonly used baselines, while either providing a better survival separation (SAE) or being more interpretable (CSAE). We also perform a feature selection stability analysis on our models and notice that there is a power-law relationship with features which are commonly associated with survival. The code for this project is available at: https://github.com/phcavelar/coxae
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