Unlike standard prediction tasks, survival analysis requires modeling right censored data, which must be treated with care. While deep neural networks excel in traditional supervised learning, it remains unclear how to best utilize these models in survival analysis. A key question asks which data-generating assumptions of traditional survival models should be retained and which should be made more flexible via the function-approximating capabilities of neural networks. Rather than estimating the survival function targeted by most existing methods, we introduce a Deep Extended Hazard (DeepEH) model to provide a flexible and general framework for deep survival analysis. The extended hazard model includes the conventional Cox proportional hazards and accelerated failure time models as special cases, so DeepEH subsumes the popular Deep Cox proportional hazard (DeepSurv) and Deep Accelerated Failure Time (DeepAFT) models. We additionally provide theoretical support for the proposed DeepEH model by establishing consistency and convergence rate of the survival function estimator, which underscore the attractive feature that deep learning is able to detect low-dimensional structure of data in high-dimensional space. Numerical experiments also provide evidence that the proposed methods outperform existing statistical and deep learning approaches to survival analysis.

Unlike standard prediction tasks, survival analysis requires modeling right censored data, which must be treated with care. While deep neural networks excel in traditional supervised learning, it remains unclear how to best utilize these models in survival analysis. A key question asks which data-generating assumptions of traditional survival models should be retained and which should be made more flexible via the function-approximating capabilities of neural networks. Rather than estimating the survival function targeted by most existing methods, we introduce a Deep Extended Hazard (DeepEH) model to provide a flexible and general framework for deep survival analysis. The extended hazard model includes the conventional Cox proportional hazards and accelerated failure time models as special cases, so DeepEH subsumes the popular Deep Cox proportional hazard (DeepSurv) and Deep Accelerated Failure Time (DeepAFT) models.

Unlike standard prediction tasks, survival analysis requires modeling right censored data, which must be treated with care. While deep neural networks excel in traditional supervised learning, it remains unclear how to best utilize these models in survival analysis. A key question asks which data-generating assumptions of traditional survival models should be retained and which should be made more flexible via the function-approximating capabilities of neural networks. Rather than estimating the survival function targeted by most existing methods, we introduce a Deep Extended Hazard (DeepEH) model to provide a flexible and general framework for deep survival analysis. The extended hazard model includes the conventional Cox proportional hazards and accelerated failure time models as special cases, so DeepEH subsumes the popular Deep Cox proportional hazard (DeepSurv) and Deep Accelerated Failure Time (DeepAFT) models.

Survival prediction is an important branch of cancer prognosis analysis. The model that predicts survival risk through TCGA genomics data can discover genes related to cancer and provide diagnosis and treatment recommendations based on patient characteristics. We found that deep learning models based on Cox proportional hazards often suffer from overfitting when dealing with high-throughput data. Moreover, we found that as the number of network layers increases, the experimental results will not get better, and network degradation will occur. Based on this problem, we propose a new framework based on Deep Residual Learning. Combine the ideas of Cox proportional hazards and Residual. And name it ResSurv. First, ResSurv is a feed-forward deep learning network stacked by multiple basic ResNet Blocks. In each ResNet Block, we add a Normalization Layer to prevent gradient disappearance and gradient explosion. Secondly, for the loss function of the neural network, we inherited the Cox proportional hazards methods, applied the semi-parametric of the CPH model to the neural network, combined with the partial likelihood model, established the loss function, and performed backpropagation and gradient update. Finally, we compared ResSurv networks of different depths and found that we can effectively extract high-dimensional features. Ablation experiments and comparative experiments prove that our model has reached SOTA(state of the art) in the field of deep learning, and our network can effectively extract deep information.

Time-to-event analysis is a branch of statistics that has increased in popularity during the last decades due to its many application fields, such as predictive maintenance, customer churn prediction and population lifetime estimation. In this paper, we review and compare the performance of several prediction models for time-to-event analysis. These consist of semi-parametric and parametric statistical models, in addition to machine learning approaches. Our study is carried out on three datasets and evaluated in two different scores (the integrated Brier score and concordance index). Moreover, we show how ensemble methods, which surprisingly have not yet been much studied in time-to-event analysis, can improve the prediction accuracy and enhance the robustness of the prediction performance. We conclude the analysis with a simulation experiment in which we evaluate the factors influencing the performance ranking of the methods using both scores. Keywords: Ensemble methods, time-to-event analysis, integrated Brier score, concordance index.

The Concordance Index (C-index) is a commonly used metric in Survival Analysis to evaluate how good a prediction model is. This paper proposes a decomposition of the C-Index into a weighted harmonic mean of two quantities: one for ranking observed events versus other observed events, and the other for ranking observed events versus censored cases. This decomposition allows a more fine-grained analysis of the pros and cons of survival prediction methods. The utility of the decomposition is demonstrated using three benchmark survival analysis models (Cox Proportional Hazard, Random Survival Forest, and Deep Adversarial Time-to-Event Network) together with a new variational generative neural-network-based method (SurVED), which is also proposed in this paper. The demonstration is done on four publicly available datasets with varying censoring levels. The analysis with the C-index decomposition shows that all methods essentially perform equally well when the censoring level is high because of the dominance of the term measuring the ranking of events versus censored cases. In contrast, some methods deteriorate when the censoring level decreases because they do not rank the events versus other events well.

In time-to-event prediction problems, a standard approach to estimating an interpretable model is to use Cox proportional hazards, where features are selected based on lasso regularization or stepwise regression. However, these Cox-based models do not learn how different features relate. As an alternative, we present an interpretable neural network approach to jointly learn a survival model to predict time-to-event outcomes while simultaneously learning how features relate in terms of a topic model. In particular, we model each subject as a distribution over "topics", which are learned from clinical features as to help predict a time-to-event outcome. From a technical standpoint, we extend existing neural topic modeling approaches to also minimize a survival analysis loss function. We study the effectiveness of this approach on seven healthcare datasets on predicting time until death as well as hospital ICU length of stay, where we find that neural survival-supervised topic models achieves competitive accuracy with existing approaches while yielding interpretable clinical "topics" that explain feature relationships.