Survival analysis is a hotspot in statistical research for modeling time-to-event information with data censorship handling, which has been widely used in many applications such as clinical research, information system and other fields with survivorship bias. Many works have been proposed for survival analysis ranging from traditional statistic methods to machine learning models. However, the existing methodologies either utilize counting-based statistics on the segmented data, or have a pre-assumption on the event probability distribution w.r.t. time. Moreover, few works consider sequential patterns within the feature space. In this paper, we propose a Deep Recurrent Survival Analysis model which combines deep learning for conditional probability prediction at fine-grained level of the data, and survival analysis for tackling the censorship. By capturing the time dependency through modeling the conditional probability of the event for each sample, our method predicts the likelihood of the true event occurrence and estimates the survival rate over time, i.e., the probability of the non-occurrence of the event, for the censored data. Meanwhile, without assuming any specific form of the event probability distribution, our model shows great advantages over the previous works on fitting various sophisticated data distributions. In the experiments on the three real-world tasks from different fields, our model significantly outperforms the state-of-the-art solutions under various metrics.
Georgia Institute of Technology（佐治亚理工学院）；Emory University School of Medicine（埃默里大学医学院）；University of California San Diego Health（加州大学圣地亚哥分校健康中心）
Sepsis, a dysregulated immune system response to infection, is among the leading causes of morbidity, mortality, and cost overruns in the Intensive Care Unit (ICU). Early prediction of sepsis can improve situational awareness amongst clinicians and facilitate timely, protective interventions. While the application of predictive analytics in ICU patients has shown early promising results, much of the work has been encumbered by high false-alarm rates. Efforts to improve specificity have been limited by several factors, most notably the difficulty of labeling sepsis onset time and the low preval…
Imperial College London（帝国理工学院）；Vodafone Research（沃达丰研究院）；ISR, IST, Universidade de Lisboa（里斯本大学高等技术学院系统与机器人研究所）
The size of a website's active user base directly affects its value. Thus, it is important to monitor and influence a user's likelihood to return to a site. Essential to this is predicting when a user will return. Current state of the art approaches to solve this problem come in two flavors: (1) Recurrent Neural Network (RNN) based solutions and (2) survival analysis methods. We observe that both techniques are severely limited when applied to this problem. Survival models can only incorporate aggregate representations of users instead of automatically learning a representation directly from a…
We use recurrent-events survival analysis techniques and methods to analyze the duration of Olympic records. The Kaplan-Meier estimator is used to perform preliminary tests and recurrent event survivor function estimators proposed by Wang & Chang (1999) and Pena et al. (2001) are used to estimate survival curves. Extensions of the Cox Proportional Hazards model are employed as well as a discrete-time logistic model for repeated events to estimate models and quantify parameter significance. The logistic model was the best fit to the data according to the Akaike Information Criterion (AIC). We d…
University of Michigan（密歇根大学）；Merck Research Laboratories（默克研究实验室）
There has been increasing interest in modelling survival data using deep learning methods in medical research. Current approaches have focused on designing special cost functions to handle censored survival data. We propose a very different method with two steps. In the first step, we transform each subject's survival time into a series of jackknife pseudo conditional survival probabilities and then use these pseudo probabilities as a quantitative response variable in the deep neural network model. By using the pseudo values, we reduce a complex survival analysis to a standard regression probl…
University Paris Descartes（巴黎笛卡尔大学）；Institut Hypercube（超立方体研究所）；Montreal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；École Polytechnique de Montréal（蒙特利尔理工学院）
An accurate model of patient-specific kidney graft survival distributions can help to improve shared-decision making in the treatment and care of patients. In this paper, we propose a deep learning method that directly models the survival function instead of estimating the hazard function to predict survival times for graft patients based on the principle of multi-task learning. By learning to jointly predict the time of the event, and its rank in the cox partial log likelihood framework, our deep learning approach outperforms, in terms of survival time prediction quality and concordance index…
Kernel survival analysis methods predict subject-specific survival curves and times using information about which training subjects are most similar to a test subject. These most similar training subjects could serve as forecast evidence. How similar any two subjects are is given by the kernel function. In this paper, we present the first neural network framework that learns which kernel functions to use in kernel survival analysis. We also show how to use kernel functions to construct prediction intervals of survival time estimates that are statistically valid for individuals similar to a tes…
Survival analysis/time-to-event models are extremely useful as they can help companies predict when a customer will buy a product, churn or default on a loan, and therefore help them improve their ROI. In this paper, we introduce a new method to calculate survival functions using the Multi-Task Logistic Regression (MTLR) model as its base and a deep learning architecture as its core. Based on the Concordance index (C-index) and Brier score, this method outperforms the MTLR in all the experiments disclosed in this paper as well as the Cox Proportional Hazard (CoxPH) model when nonlinear depende…
Many online platforms have deployed anti-fraud systems to detect and prevent fraudulent activities. However, there is usually a gap between the time that a user commits a fraudulent action and the time that the user is suspended by the platform. How to detect fraudsters in time is a challenging problem. Most of the existing approaches adopt classifiers to predict fraudsters given their activity sequences along time. The main drawback of classification models is that the prediction results between consecutive timestamps are often inconsistent. In this paper, we propose a survival analysis based…
University of Oxford（牛津大学）；University of California Los Angeles（加利福尼亚大学洛杉矶分校）
Deep learning models for survival analysis have gained significant attention in the literature, but they suffer from severe performance deficits when the dataset contains many irrelevant features. We give empirical evidence for this problem in real-world medical settings using the state-of-the-art model DeepHit. Furthermore, we develop methods to improve the deep learning model through novel approaches to feature selection in survival analysis. We propose filter methods for hard feature selection and a neural network architecture that weights features for soft feature selection. Our experiment…
Causal structures for observational survival data provide crucial information regarding the relationships between covariates and time-to-event. We derive motivation from the information theoretic source coding argument, and show that incorporating the knowledge of the directed acyclic graph (DAG) can be beneficial if suitable source encoders are employed. As a possible source encoder in this context, we derive a variational inference based conditional variational autoencoder for causal structured survival prediction, which we refer to as DAGSurv. We illustrate the performance of DAGSurv on low…
Ortho Biomed Inc.（奥索生物医学公司）；University of Toronto（多伦多大学）；Worcester Polytechnic Institute (WPI)（伍斯特理工学院（WPI））；University Health Network（大学健康网络）
The aim of survival analysis in healthcare is to estimate the probability of occurrence of an event, such as a patient's death in an intensive care unit (ICU). Recent developments in deep neural networks (DNNs) for survival analysis show the superiority of these models in comparison with other well-known models in survival analysis applications. Ensuring the reliability and explainability of deep survival models deployed in healthcare is a necessity. Since DNN models often behave like a black box, their predictions might not be easily trusted by clinicians, especially when predictions are cont…
Deep Learning-Based Survival Analysis with Copula-Based Activation Functions for Multivariate Response Prediction
Statistics Discipline, Division of Science and Mathematics, University of Minnesota-Morris（明尼苏达州立大学莫里斯分校统计学系）；EGADE Business School, Tecnológico de Monterrey（墨西哥蒙特雷技术学院EGADE商学院）；Department of Statistics and Data Science, Pukyong National University（浦项国立大学统计学与数据科学系）；Department of Management Information Systems, Dong-A University（东阿大学管理信息系）
Survival analysis (SA) is an active field of research that is concerned with time-to-event outcomes and is prevalent in many domains, particularly biomedical applications. Despite its importance, SA remains challenging due to small-scale data sets and complex outcome distributions, concealed by truncation and censoring processes. The piecewise exponential additive mixed model (PAMM) is a model class addressing many of these challenges, yet PAMMs are not applicable in high-dimensional feature settings or in the case of unstructured or multimodal data. We unify existing approaches by proposing D…
We describe a new approach to estimating relative risks in time-to-event prediction problems with censored data in a fully parametric manner. Our approach does not require making strong assumptions of constant proportional hazard of the underlying survival distribution, as required by the Cox-proportional hazard model. By jointly learning deep nonlinear representations of the input covariates, we demonstrate the benefits of our approach when used to estimate survival risks through extensive experimentation on multiple real world datasets with different levels of censoring. We further demonstra…
Gradient-based Explanations for Deep Learning Survival Models
Leibniz Institute for Prevention Research and Epidemiology – BIPS（莱布尼茨预防研究与流行病学研究所 – BIPS）；Faculty of Mathematics and Computer Science, University of Bremen（不来梅大学数学与计算机科学学院）；University of Copenhagen（哥本哈根大学）；Department of Public Health, University of Copenhagen（哥本哈根大学公共卫生系）
Semi-parametric survival analysis methods like the Cox Proportional Hazards (CPH) regression (Cox, 1972) are a popular approach for survival analysis. These methods involve fitting of the log-proportional hazard as a function of the covariates and are convenient as they do not require estimation of the baseline hazard rate. Recent approaches have involved learning non-linear representations of the input covariates and demonstrate improved performance. In this paper we argue against such deep parameterizations for survival analysis and experimentally demonstrate that more interpretable semi-par…
University of Toronto（多伦多大学）；Rubikloud Technologies Inc.（Rubikloud科技公司）
Access to a large variety of data across a massive population has made it possible to predict customer purchase patterns and responses to marketing campaigns. In particular, accurate demand forecasts for popular products with frequent repeat purchases are essential since these products are one of the main drivers of profits. However, buyer purchase patterns are extremely diverse and sparse on a per-product level due to population heterogeneity as well as dependence in purchase patterns across product categories. Traditional methods in survival analysis have proven effective in dealing with cen…
We introduce a wide and deep neural network for prediction of progression from patients with mild cognitive impairment to Alzheimer's disease. Information from anatomical shape and tabular clinical data (demographics, biomarkers) are fused in a single neural network. The network is invariant to shape transformations and avoids the need to identify point correspondences between shapes. To account for right censored time-to-event data, i.e., when it is only known that a patient did not develop Alzheimer's disease up to a particular time point, we employ a loss commonly used in survival analysis.…
Survival analysis has been developed and applied in the number of areas including manufacturing, finance, economics and healthcare. In healthcare domain, usually clinical data are high-dimensional, sparse and complex and sometimes there exists few amount of time-to-event (labeled) instances. Therefore building an accurate survival model from electronic health records is challenging. With this motivation, we address this issue and provide a new survival analysis framework using deep learning and active learning with a novel sampling strategy. First, our approach provides better representation w…
Gene/pathway-based methods are drawing significant attention due to their usefulness in detecting rare and common variants that affect disease susceptibility. The biological mechanism of drug responses indicates that a gene-based analysis has even greater potential in pharmacogenetics. Motivated by a study from the Vitamin Intervention for Stroke Prevention (VISP) trial, we develop a gene-trait similarity regression for survival analysis to assess the effect of a gene or pathway on time-to-event outcomes. The similarity regression has a general framework that covers a range of survival models,…
New York University（纽约大学）；Adobe Research（Adobe研究院）；Nutanix（路坦力）；Adobe Systems（Adobe系统公司）
Email communications are ubiquitous. Firms control send times of emails and thereby the instants at which emails reach recipients (it is assumed email is received instantaneously from the send time). However, they do not control the duration it takes for recipients to open emails, labeled as time-to-open. Importantly, among emails that are opened, most occur within a short window from their send times. We posit that emails are likely to be opened sooner when send times are convenient for recipients, while for other send times, emails can get ignored. Thus, to compute appropriate send times it …
Google Research（谷歌研究院）；Carnegie Mellon University（卡内基梅隆大学）
Survival analysis is a challenging variation of regression modeling because of the presence of censoring, where the outcome measurement is only partially known, due to, for example, loss to follow up. Such problems come up frequently in medical applications, making survival analysis a key endeavor in biostatistics and machine learning for healthcare, with Cox regression models being amongst the most commonly employed models. We describe a new approach for survival analysis regression models, based on learning mixtures of Cox regressions to model individual survival distributions. We propose an…
University of New South Wales（新南威尔士大学）；University of Auckland（奥克兰大学）；National Drug and Alcohol Research Centre（国家药物与酒精研究中心）
AIMS. This study compared the performance of deep learning extensions of survival analysis models with traditional Cox proportional hazards (CPH) models for deriving cardiovascular disease (CVD) risk prediction equations in national health administrative datasets. METHODS. Using individual person linkage of multiple administrative datasets, we constructed a cohort of all New Zealand residents aged 30-74 years who interacted with publicly funded health services during 2012, and identified hospitalisations and deaths from CVD over five years of follow-up. After excluding people with prior CVD or…
There has been increasing interest in modeling survival data using deep learning methods in medical research. In this paper, we proposed a Bayesian hierarchical deep neural networks model for modeling and prediction of survival data. Compared with previously studied methods, the new proposal can provide not only point estimate of survival probability but also quantification of the corresponding uncertainty, which can be of crucial importance in predictive modeling and subsequent decision making. The favorable statistical properties of point and uncertainty estimates were demonstrated by simula…
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 a…
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
Survival analysis, time-to-event analysis, is an important problem in healthcare since it has a wide-ranging impact on patients and palliative care. Many survival analysis methods have assumed that the survival data is centrally available either from one medical center or by data sharing from multi-centers. However, the sensitivity of the patient attributes and the strict privacy laws have increasingly forbidden sharing of healthcare data. To address this challenge, the research community has looked at the solution of decentralized training and sharing of model parameters using the Federated L…
Medical 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 system…
Modelling customer churn for the retail industry in a deep learning based sequential framework
University of Essex（埃塞克斯大学）；Profusion Media Ltd.（Profusion传媒有限公司）；Essex Business School（埃塞克斯商学院）；Friedrich-Alexander University Erlangen-Nuremberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）
Stanford University School of Medicine（斯坦福大学医学院）；Stanford University（斯坦福大学）
There is currently great interest in applying neural networks to prediction tasks in medicine. It is important for predictive models to be able to use survival data, where each patient has a known follow-up time and event/censoring indicator. This avoids information loss when training the model and enables generation of predicted survival curves. In this paper, we describe a discrete-time survival model that is designed to be used with neural networks, which we refer to as Nnet-survival. The model is trained with the maximum likelihood method using minibatch stochastic gradient descent (SGD). …
The University of Iowa（爱荷华大学）；Worcester Polytechnic Institute（伍斯特理工学院）
Urban dispersal events are processes where an unusually large number of people leave the same area in a short period. Early prediction of dispersal events is important in mitigating congestion and safety risks and making better dispatching decisions for taxi and ride-sharing fleets. Existing work mostly focuses on predicting taxi demand in the near future by learning patterns from historical data. However, they fail in case of abnormality because dispersal events with abnormally high demand are non-repetitive and violate common assumptions such as smoothness in demand change over time. Instead…
In this article, I present the user written stmixed command for the fitting of multilevel survival models, which serves as both an alternative to Stata's official mestreg, and a complimentary program with substantial extensions. stmixed can fit multilevel survival models with any number of levels and random effects at each level, including flexible spline-based approaches (such as Royston-Parmar and the log hazard equivalent) or user-defined hazard models. Simple or complex time-dependent effects can be included, as well as the addition of expected mortality for a relative survival model. Left…
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
Multi-state survival analysis (MSA) uses multi-state models for the analysis of time-to-event data. In medical applications, MSA can provide insights about the complex disease progression in patients. A key challenge in MSA is the accurate subject-specific prediction of multi-state model quantities such as transition probability and state occupation probability in the presence of censoring. Traditional multi-state methods such as Aalen-Johansen (AJ) estimators and Cox-based methods are respectively limited by Markov and proportional hazards assumptions and are infeasible for making subject-spe…
merlin can do a lot of things. From simple stuff, like fitting a linear regression or a Weibull survival model, to a three-level logistic mixed effects model, or a multivariate joint model of multiple longitudinal outcomes (of different types) and a recurrent event and survival with non-linear effects...the list is rather endless. merlin can do things I haven't even thought of yet. I'll take a single dataset, and attempt to show you the full range of capabilities of merlin, and discuss some future directions for the implementation in Stata.
A Real Data-Driven, Robust Survival Analysis on Patients who Underwent Deep Brain Stimulation for Parkinson's Disease by Utilizing Parametric, Non-Parametric, and Semi-Parametric Approaches
Illness-death models are a class of stochastic models inside the multi-state framework. In those models, individuals are allowed to move over time between different states related to illness and death. They are of special interest when working with non-terminal diseases, as they not only consider the competing risk of death but also allow to study progression from illness to death. The intensity of each transition can be modelled including both fixed and random effects of covariates. In particular, spatially structured random effects or their multivariate versions can be used to assess spatial…
Survival competing risks models are very useful for studying the incidence of diseases whose occurrence competes with other possible diseases or health conditions. These models perform properly when working with terminal events, such as death, that imply the conclusion of the corresponding study. But they do not allow the treatment of scenarios with non-terminal competing events that may occur sequentially. Multi-state models are complex survival models. They focus on pathways defined by the temporal and sequential occurrence of numerous events of interest and thus they are suitable for connec…
Ortho Biomed Inc.（Ortho Biomed公司）；University Health Network（大学健康网络）；Toronto Rehabilitation Institute, University Health Network（大学健康网络多伦多康复研究所）
This paper introduces a novel non-parametric deep model for estimating time-to-event (survival analysis) in presence of censored data and competing risks. The model is designed based on the sequence-to-sequence (Seq2Seq) architecture, therefore we name it Survival Seq2Seq. The first recurrent neural network (RNN) layer of the encoder of our model is made up of Gated Recurrent Unit with Decay (GRU-D) cells. These cells have the ability to effectively impute not-missing-at-random values of longitudinal datasets with very high missing rates, such as electronic health records (EHRs). The decoder o…
In the following short article we adapt a new and popular machine learning model for inference on medical data sets. Our method is based on the Variational AutoEncoder (VAE) framework that we adapt to survival analysis on small data sets with missing values. In our model, the true health status appears as a set of latent variables that affects the observed covariates and the survival chances. We show that this flexible model allows insightful decision-making using a predicted distribution and outperforms a classic survival analysis model.
ETH Zürich（苏黎世联邦理工学院）；Human Technopole（人类技术园）；University Hospital Basel（巴塞尔大学医院）；University Children’s Hospital Basel（巴塞尔大学儿童医院）；University of Zürich（苏黎世大学）；Politecnico di Milano（米兰理工大学）；St. Gallen Cantonal Hospital（圣加仑州立医院）
In this work, we study the problem of clustering survival data $-$ a challenging and so far under-explored task. We introduce a novel semi-supervised probabilistic approach to cluster survival data by leveraging recent advances in stochastic gradient variational inference. In contrast to previous work, our proposed method employs a deep generative model to uncover the underlying distribution of both the explanatory variables and censored survival times. We compare our model to the related work on clustering and mixture models for survival data in comprehensive experiments on a wide range of sy…
Technische Universität Darmstadt（达姆施塔特工业大学）；Concordia University（康考迪亚大学）
A regression problem with dependent data is considered. Regularity assumptions on the dependency of the data are introduced, and it is shown that under suitable structural assumptions on the regression function a deep recurrent neural network estimate is able to circumvent the curse of dimensionality.
TorchSurv: A Lightweight Package for Deep Survival Analysis
Novartis Pharma AG（诺华制药公司）；Center for Devices and Radiological Health, Food and Drug Administration（美国食品药品监督管理局器械和放射卫生中心）；Novartis Pharmaceuticals Corporation（诺华制药公司）
Deep learning has shown remarkable results for image analysis and is expected to aid individual treatment decisions in health care. To achieve this, deep learning methods need to be promoted from the level of mere associations to being able to answer causal questions. We present a scenario with real-world medical images (CT-scans of lung cancers) and simulated outcome data. Through the sampling scheme, the images contain two distinct factors of variation that represent a collider and a prognostic factor. We show that when this collider can be quantified, unbiased individual prognosis predictio…
