BackgroundMedical practitioners use survival models to explore and understand the relationships between patients’ covariates (e.g. clinical and genetic features) and the effectiveness of various treatment options. Standard survival models like the linear Cox proportional hazards model require extensive feature engineering or prior medical knowledge to model treatment interaction at an individual level. While nonlinear survival methods, such as neural networks and survival forests, can inherently model these high-level interaction terms, they have yet to be shown as effective treatment recommender systems.MethodsWe introduce DeepSurv, a Cox proportional hazards deep neural network and state-of-the-art survival method for modeling interactions between a patient’s covariates and treatment effectiveness in order to provide personalized treatment recommendations.ResultsWe perform a number of experiments training DeepSurv on simulated and real survival data. We demonstrate that DeepSurv performs as well as or better than other state-of-the-art survival models and validate that DeepSurv successfully models increasingly complex relationships between a patient’s covariates and their risk of failure. We then show how DeepSurv models the relationship between a patient’s features and effectiveness of different treatment options to show how DeepSurv can be used to provide individual treatment recommendations. Finally, we train DeepSurv on real clinical studies to demonstrate how it’s personalized treatment recommendations would increase the survival time of a set of patients.ConclusionsThe predictive and modeling capabilities of DeepSurv will enable medical researchers to use deep neural networks as a tool in their exploration, understanding, and prediction of the effects of a patient’s characteristics on their risk of failure.

We propose a general framework for increasing local stability of Artificial Neural Nets (ANNs) using Robust Optimization (RO). We achieve this through an alternating minimization-maximization procedure, in which the loss of the network is minimized over perturbed examples that are generated at each parameter update. We show that adversarial training of ANNs is in fact robustification of the network optimization, and that our proposed framework generalizes previous approaches for increasing local stability of ANNs. Experimental results reveal that our approach increases the robustness of the network to existing adversarial examples, while making it harder to generate new ones. Furthermore, our algorithm improves the accuracy of the network also on the original test data.

We discuss approximation of functions using deep neural nets. Given a function f on a d-dimensional manifold Γ ⊂ R m , we construct a sparsely-connected depth-4 neural network and bound its error in approximating f . The size of the network depends on dimension and curvature of the manifold Γ, the complexity of f , in terms of its wavelet description, and only weakly on the ambient dimension m. Essentially, our network computes wavelet functions, which are computed from Rectified Linear Units (ReLU).