The discovery of patterns of molecular signatures in genomic profiles is one of the most essential data-driven research approaches in cancer biology. Gene expression data, measured by estimates of mRNA levels, contain tens of thousands of features, making dimensionality reduction a critical step in data analysis. This data-driven selection of genes and markers can be greatly improved by incorporating domain knowledge. For example, autoencoder-based approaches that incorporate the gene set hierarchy into the neural network architecture design can improve both accuracy and interpretability. Alternatively, domain knowledge could be incorporated into the loss functions used to train models. To this end, we propose a novel, biologically inspired loss function for autoencoders based on the first-order dynamics of mRNA expression. By decomposing the steady state of expression into transcription and mRNA decay rates, we model mRNA lifetime as a survival problem. Our approach borrows from Cox proportional hazard partial likelihood to model transcription rates and the risk of decay of individual genes. We show that the resulting autoencoders can improve the clustering of cancer patients and cell lines and drug response prediction.