Machine Learning for Survival Analysis: A Survey <s> Artificial Neural Networks <s> We consider feed-forward neural nets and their relation to regression models for survival data. We show how the back-propagation algorithm may be used to obtain maximum likelihood estimates in certain standard regression models for survival data, as well as in various generalizations of these. Examples concerning malignant melanoma and post-partum amenorrhoea during lactation are used as illustration. We conclude that although problems with the substantial number of parameters and their interpretation remain, the feed-forward neural network models are flexible extensions to the standard regression models and thereby candidates for use in prediction and exploratory analyses in larger data sets. <s> BIB001 </s> Machine Learning for Survival Analysis: A Survey <s> Artificial Neural Networks <s> Neural networks have received considerable attention recently, mostly by non-statisticians. They are considered by many to be very promising tools for classification and prediction. In this paper we present an approach to modelling censored survival data using the input—output relationship associated with a simple feed-forward neural network as the basis for a non-linear proportional hazards model. This approach can be extended to other models used with censored survival data. The proportional hazards neural network parameters are estimated using the method of maximum likelihood. These maximum likelihood based models can be compared, using readily available techniques such as the likelihood ratio test and the Akaike criterion. The neural network models are illustrated using data on the survival of men with prostatic carcinoma. A method of interpreting the neural network predictions based on the factorial contrasts is presented. <s> BIB002 </s> Machine Learning for Survival Analysis: A Survey <s> Artificial Neural Networks <s> Flexible modelling in survival analysis can be useful both for exploratory and predictive purposes. Feed forward neural networks were recently considered for flexible non-linear modelling of censored survival data through the generalization of both discrete and continuous time models. We show that by treating the time interval as an input variable in a standard feed forward network with logistic activation and entropy error function, it is possible to estimate smoothed discrete hazards as conditional probabilities of failure. We considered an easily implementable approach with a fast selection criteria of the best configurations. Examples on data sets from two clinical trials are provided. The proposed artificial neural network (ANN) approach can be applied for the estimation of the functional relationships between covariates and time in survival data to improve model predictivity in the presence of complex prognostic relationships. <s> BIB003 </s> Machine Learning for Survival Analysis: A Survey <s> Artificial Neural Networks <s> A Bayesian framework is introduced to carry out Automatic Relevance Determination (ARD) in feedforward neural networks to model censored data. A procedure to identify and interpret the prognostic group allocation is also described. These methodologies are applied to 1616 records routinely collected at Christie Hospital, in a monthly cohort study with 5-year follow-up. Two cohort studies are presented, for low- and high-risk patients allocated by standard clinical staging. The results of contrasting the Partial Logistic Artificial Neural Network (PLANN)-ARD model with the proportional hazards model are that the two are consistent, but the neural network may be more specific in the allocation of patients into prognostic groups. With automatic model selection, the regularised neural network is more conservative than the default stepwise forward selection procedure implemented by SPSS with the Akaike Information Criterion. <s> BIB004 </s> Machine Learning for Survival Analysis: A Survey <s> Artificial Neural Networks <s> The purpose of the present study was toassess prognostic factors for metachronous contralateral recurrence ofbreast cancer (CBC). Two factors were of particularinterest, namely estrogen (ER) and progesterone (PgR) receptorsassayed with the biochemical method in primary tumortissue. Information was obtained from a prospective clinicaldatabase for 1763 axillary node-negative women who hadreceived curative surgery, mostly of the conservative type,and followed-up for a median of 82 months.The analysis was performed based on both astandard (linear) Cox model and an artificial neuralnetwork (ANN) extension of this model proposed byFaraggi and Simon [9]. Furthermore, to assess theprognostic importance of the factors considered, model predictiveability was computed. <s> BIB005 </s> Machine Learning for Survival Analysis: A Survey <s> Artificial Neural Networks <s> Previous research has shown that neural networks can model survival data in situations in which some patients' death times are unknown, e.g. right-censored. However, neural networks have rarely been shown to outperform their linear counterparts such as the Cox proportional hazards model. In this paper, we run simulated experiments and use real survival data to build upon the risk-regression architecture proposed by Faraggi and Simon. We demonstrate that our model, DeepSurv, not only works as well as the standard linear Cox proportional hazards model but actually outperforms it in predictive ability on survival data with linear and nonlinear risk functions. We then show that the neural network can also serve as a recommender system by including a categorical variable representing a treatment group. This can be used to provide personalized treatment recommendations based on an individual's calculated risk. We provide an open source Python module that implements these methods in order to advance research on deep learning and survival analysis. <s> BIB006 </s> Machine Learning for Survival Analysis: A Survey <s> Artificial Neural Networks <s> The electronic health record (EHR) provides an unprecedented opportunity to build actionable tools to support physicians at the point of care. In this paper, we investigate survival analysis in the context of EHR data. We introduce deep survival analysis, a hierarchical generative approach to survival analysis. It departs from previous approaches in two primary ways: (1) all observations, including covariates, are modeled jointly conditioned on a rich latent structure; and (2) the observations are aligned by their failure time, rather than by an arbitrary time zero as in traditional survival analysis. Further, it (3) scalably handles heterogeneous (continuous and discrete) data types that occur in the EHR. We validate deep survival analysis model by stratifying patients according to risk of developing coronary heart disease (CHD). Specifically, we study a dataset of 313,000 patients corresponding to 5.5 million months of observations. When compared to the clinically validated Framingham CHD risk score, deep survival analysis is significantly superior in stratifying patients according to their risk. <s> BIB007 </s> Machine Learning for Survival Analysis: A Survey <s> Artificial Neural Networks <s> Technological advances have created a great opportunity to provide multi-view data for patients. However, due to the large discrepancy between different heterogeneous views, traditional survival models are unable to efficiently handle multiple modalities data as well as learn very complex interactions that can affect survival outcomes in various ways. In this paper, we develop a Deep Correlational Survival Model (DeepCorrSurv) for the integration of multi-view data. The proposed network consists of two sub-networks, view-specific and common sub-network. To remove the view discrepancy, the proposed DeepCorrSurv first explicitly maximizes the correlation among the views. Then it transfers feature hierarchies from view commonality and specifically fine-tunes on the survival regression task. Extensive experiments on real lung and brain tumor data sets demonstrated the effectiveness of the proposed DeepCorrSurv model using multiple modalities data across different tumor types. <s> BIB008 </s> Machine Learning for Survival Analysis: A Survey <s> Artificial Neural Networks <s> The ability to predict future user activity is invaluable when it comes to content recommendation and personalization. For instance, knowing when users will return to an online music service and what they will listen to increases user satisfaction and therefore user retention. We present a model based on Long-Short Term Memory to estimate when a user will return to a site and what their future listening behavior will be. In doing so, we aim to solve the problem of Just-In-Time recommendation, that is, to recommend the right items at the right time. We use tools from survival analysis for return time prediction and exponential families for future activity analysis. We show that the resulting multitask problem can be solved accurately, when applied to two real-world datasets. <s> BIB009
Inspired by biological neural systems, Frank Rosenblatt published the first paper  on Artificial Neural Networks (ANN) in 1958. Here, the simple artificial nodes that he dubbed "neurons" are connected based on a weighted link to form a network which simulates a biological neural network. A neuron in this context is a computing element that consists of sets of adaptive weights and generates the output based on a certain kind of activation function. ANNs have been widely used in survival analysis. Three main methods are proposed in the literature for applying neural network methods to address survival analysis problems. (1) Neural network survival analysis has been employed to predict the survival time of a subject directly from the inputs provided. (2) BIB002 extended the Cox PH model to the nonlinear ANN predictor and suggested using this to fit a neural network with a linear output layer and a single logistic hidden layer. BIB005 used both the standard Cox model and the neural network method proposed in BIB002 to assess prognostic factors for the recurrence of breast cancer. Although these extensions of the Cox model preserved most of the advantages of a typical PH model, they were still not optimal for modeling the baseline variation  ). (3) Many approaches BIB001 BIB003  BIB004 ) take the survival status of a subject, which can be represented by the survival or hazard probability, as the output of the neural network. For example, BIB003 applied the Partial Logistic ANN (PLANN) method to analyze the relationship between features and survival times in order to boost the prediction ability of the model. The same group used feed-forward neural networks to obtain a more flexible nonlinear model by considering the censored information in the data using a generalization of both continuous and discrete time models BIB003 . BIB004 extended PLANN to a Bayesian neural framework with covariate-specific regularization to perform model selection using automatic relevance determination (MacKay 1995). These approaches indicate that neural networks have an excellent ability to handle the censored data in survival analysis. Recently, deep learning methods have gained considerable attention to tackle the survival analysis problems in various application domains. For example, in the healthcare domain, deep correlational survival models and Convolutional Neural Networks (CNNs) are used BIB008 to efficiently learn the complex interactions for multiple modalities of patient data. Several deep survival analysis approaches BIB006 BIB007 ) are also proposed to assist physicians with their clinical decisions on patients by estimating their risk of diseases and providing personalized treatment recommendations. In addition, Recurrent Neural Network (RNN)-based approaches have been successfully combined with survival analysis for studying recurring events, particularly in the context of user behavior modeling applications BIB009  ).