The integration of high-dimensional genomic data and clinical data into time-to-event prediction models has gained significant attention due to the growing availability of these datasets. Traditionally, a Cox regression model is employed, concatenating various covariate types linearly. Given that much of the data may be redundant or irrelevant, feature selection through penalization is often desirable. A notable characteristic of these datasets is their organization into blocks of distinct data types, such as methylation and clinical predictors, which requires selecting a subset of covariates from each group due to high intra-group correlations. For this reason, we propose utilizing Exclusive Lasso regularization in place of standard Lasso penalization. We apply our methodology to a real-life cancer dataset, demonstrating enhanced survival prediction performance compared to the conventional Cox regression model.
Massive Open Online Courses (MOOCs) are emerging as a popular alternative to traditional education, offering learners the flexibility to access a wide range of courses from various disciplines, anytime and anywhere. Despite this accessibility, a significant number of enrollments in MOOCs result in dropouts. To enhance learner engagement, it is crucial to recommend courses that align with their preferences and needs. Course Recommender Systems (RSs) can play an important role in this by modeling learners' preferences based on their previous interactions within the MOOC platform. Time-to-dropout and time-to-completion in MOOCs, like other time-to-event prediction tasks, can be effectively modeled using survival analysis (SA) methods. In this study, we apply SA methods to improve collaborative filtering recommendation performance by considering time-to-event in the context of MOOCs. Our proposed approach demonstrates superior performance compared to collaborative filtering methods trained based on learners' interactions with MOOCs, as evidenced by two performance measures on three publicly available datasets. The findings underscore the potential of integrating SA methods with RSs to enhance personalization in MOOCs.
Time-to-event analysis provides insights into clinical prognosis and treatment recommendations. However, this task is more challenging than standard regression problems due to the presence of censored observations. Additionally, the lack of confidence assessment, model robustness, and prediction calibration raises concerns about the reliability of predictions. To address these challenges, we propose an evidential regression model specifically designed for time-to-event prediction. The proposed model quantifies both epistemic and aleatory uncertainties using Gaussian Random Fuzzy Numbers and belief functions, providing clinicians with uncertainty-aware survival time predictions. The model is trained by minimizing a generalized negative log-likelihood function accounting for data censoring. Experimental evaluations using simulated datasets with different data distributions and censoring conditions, as well as real-world datasets across diverse clinical applications, demonstrate that our model delivers both accurate and reliable performance, outperforming state-of-the-art methods. These results highlight the potential of our approach for enhancing clinical decision-making in survival analysis.
Many applications involve reasoning about time durations before a critical event happens--also called time-to-event outcomes. When will a customer cancel a subscription, a coma patient wake up, or a convicted criminal reoffend? Time-to-event outcomes have been studied extensively within the field of survival analysis primarily by the statistical, medical, and reliability engineering communities, with textbooks already available in the 1970s and '80s. This monograph aims to provide a reasonably self-contained modern introduction to survival analysis. We focus on predicting time-to-event outcomes at the individual data point level with the help of neural networks. Our goal is to provide the reader with a working understanding of precisely what the basic time-to-event prediction problem is, how it differs from standard regression and classification, and how key "design patterns" have been used time after time to derive new time-to-event prediction models, from classical methods like the Cox proportional hazards model to modern deep learning approaches such as deep kernel Kaplan-Meier estimators and neural ordinary differential equation models. We further delve into two extensions of the basic time-to-event prediction setup: predicting which of several critical events will happen first along with the time until this earliest event happens (the competing risks setting), and predicting time-to-event outcomes given a time series that grows in length over time (the dynamic setting). We conclude with a discussion of a variety of topics such as fairness, causal reasoning, interpretability, and statistical guarantees. Our monograph comes with an accompanying code repository that implements every model and evaluation metric that we cover in detail.
We introduce an evidential model for time-to-event prediction with censored data. In this model, uncertainty on event time is quantified by Gaussian random fuzzy numbers, a newly introduced family of random fuzzy subsets of the real line with associated belief functions, generalizing both Gaussian random variables and Gaussian possibility distributions. Our approach makes minimal assumptions about the underlying time-to-event distribution. The model is fit by minimizing a generalized negative log-likelihood function that accounts for both normal and censored data. Comparative experiments on two real-world datasets demonstrate the very good performance of our model as compared to the state-of-the-art.
TodevelopanovelUncertaintyQuantification (UQ) framework to estimate the uncertainty of patient survival models in the absence of ground truth, we developed and evaluated our approach based on a dataset of 1383 patients treated with stereotactic radiosurgery (SRS) for brain metastases between January 2015 and December 2020. Our motivating hypothesis is that a time-to-event prediction of a test patient on inference is more certain given a higher feature-space-similarity to patients in the training set. Therefore, the uncertainty for a particular patient-of-interest is represented by the concordance index between a patient similarity rank and a prediction similarity rank. Model uncertainty was defined as the increased percentage of the max uncertainty-constrained-AUC compared to the model AUC. We evaluated our method on multiple clinically-relevant endpoints, including time to intracranial progression (ICP), progression-free survival (PFS) after SRS, overall survival (OS), and time to ICP and/or death (ICPD), on a variety of both statistical and non-statistical models, including CoxPH, conditional survival forest (CSF), and neural multi-task linear regression (NMTLR). Our results show that all models had the lowest uncertainty on ICP (2.21%) and the highest uncertainty (17.28%) on ICPD. OS models demonstrated high variation in uncertainty performance, where NMTLR had the lowest uncertainty(1.96%)and CSF had the highest uncertainty (14.29%). In conclusion, our method can estimate the uncertainty of individual patient survival modeling results. As expected, our data empirically demonstrate that as model uncertainty measured via our technique increases, the similarity between a feature-space and its predicted outcome decreases.
Machine learning applications for longitudinal electronic health records often forecast the risk of events at fixed time points, whereas survival analysis achieves dynamic risk prediction by estimating time-to-event distributions. Here, we propose a novel conditional variational autoencoder-based method, DySurv, which uses a combination of static and longitudinal measurements from electronic health records to estimate the individual risk of death dynamically. DySurv directly estimates the cumulative risk incidence function without making any parametric assumptions on the underlying stochastic process of the time-to-event. We evaluate DySurv on 6 time-to-event benchmark datasets in healthcare, as well as 2 real-world intensive care unit (ICU) electronic health records (EHR) datasets extracted from the eICU Collaborative Research (eICU) and the Medical Information Mart for Intensive Care database (MIMIC-IV). DySurv outperforms other existing statistical and deep learning approaches to time-to-event analysis across concordance and other metrics. It achieves time-dependent concordance of over 60% in the eICU case. It is also over 12% more accurate and 22% more sensitive than in-use ICU scores like Acute Physiology and Chronic Health Evaluation (APACHE) and Sequential Organ Failure Assessment (SOFA) scores. The predictive capacity of DySurv is consistent and the survival estimates remain disentangled across different datasets. Our interdisciplinary framework successfully incorporates deep learning, survival analysis, and intensive care to create a novel method for time-to-event prediction from longitudinal health records. We test our method on several held-out test sets from a variety of healthcare datasets and compare it to existing in-use clinical risk scoring benchmarks.
Time-to-event analysis, also known as survival analysis, aims to predict the time of occurrence of an event, given a set of features. One of the major challenges in this area is dealing with censored data, which can make learning algorithms more complex. Traditional methods such as Cox's proportional hazards model and the accelerated failure time (AFT) model have been popular in this field, but they often require assumptions such as proportional hazards and linearity. In particular, the AFT models often require pre-specified parametric distributional assumptions. To improve predictive performance and alleviate strict assumptions, there have been many deep learning approaches for hazard-based models in recent years. However, representation learning for AFT has not been widely explored in the neural network literature, despite its simplicity and interpretability in comparison to hazard-focused methods. In this work, we introduce the Deep AFT Rank-regression model for Time-to-event prediction (DART). This model uses an objective function based on Gehan's rank statistic, which is efficient and reliable for representation learning. On top of eliminating the requirement to establish a baseline event time distribution, DART retains the advantages of directly predicting event time in standard AFT models. The proposed method is a semiparametric approach to AFT modeling that does not impose any distributional assumptions on the survival time distribution. This also eliminates the need for additional hyperparameters or complex model architectures, unlike existing neural network-based AFT models. Through quantitative analysis on various benchmark datasets, we have shown that DART has significant potential for modeling high-throughput censored time-to-event data.
Deep-learning techniques, particularly the transformer model, have shown great potential in enhancing the prediction performance of longitudinal health records. While previous methods have mainly focused on fixed-time risk prediction, time-to-event prediction (also known as survival analysis) is often more appropriate for clinical scenarios. Here, we present a novel deep-learning architecture we named STRAFE, a generalizable survival analysis transformer-based architecture for electronic health records. The performance of STRAFE was evaluated using a real-world claim dataset of over 130,000 individuals with stage 3 chronic kidney disease (CKD) and was found to outperform other time-to-event prediction algorithms in predicting the exact time of deterioration to stage 5. Additionally, STRAFE was found to outperform binary outcome algorithms in predicting fixed-time risk, possibly due to its ability to train on censored data. We show that STRAFE predictions can improve the positive predictive value of high-risk patients by 3-fold, demonstrating possible usage to improve targeting for intervention programs. Finally, we suggest a novel visualization approach to predictions on a per-patient basis. In conclusion, STRAFE is a cutting-edge time-to-event prediction algorithm that has the potential to enhance risk predictions in large claims datasets.
Time elapsed till an event of interest is often modeled using the survival analysis methodology, which estimates a survival score based on the input features. There is a resurgence of interest in developing more accurate prediction models for time-to-event prediction in personalized healthcare using modern tools such as neural networks. Higher quality features and more frequent observations improve the predictions for a patient, however, the impact of including a patient's geographic location-based public health statistics on individual predictions has not been studied. This paper proposes a complementary improvement to survival analysis models by incorporating public health statistics in the input features. We show that including geographic location-based public health information results in a statistically significant improvement in the concordance index evaluated on the Surveillance, Epidemiology, and End Results (SEER) dataset containing nationwide cancer incidence data. The improvement holds for both the standard Cox proportional hazards model and the state-of-the-art Deep Survival Machines model. Our results indicate the utility of geographic location-based public health features in survival analysis.
Time-to-event prediction, e.g. cancer survival analysis or hospital length of stay, is a highly prominent machine learning task in medical and healthcare applications. However, only a few interpretable machine learning methods comply with its challenges. To facilitate a comprehensive explanatory analysis of survival models, we formally introduce time-dependent feature effects and global feature importance explanations. We show how post-hoc interpretation methods allow for finding biases in AI systems predicting length of stay using a novel multi-modal dataset created from 1235 X-ray images with textual radiology reports annotated by human experts. Moreover, we evaluate cancer survival models beyond predictive performance to include the importance of multi-omics feature groups based on a large-scale benchmark comprising 11 datasets from The Cancer Genome Atlas (TCGA). Model developers can use the proposed methods to debug and improve machine learning algorithms, while physicians can discover disease biomarkers and assess their significance. We hope the contributed open data and code resources facilitate future work in the emerging research direction of explainable survival analysis.
A characteristic feature of time-to-event data analysis is possible censoring of the event time. Most of the statistical learning methods for handling censored data are limited by the assumption of independent censoring, even if this can lead to biased predictions when the assumption does not hold. This paper introduces Clayton-boost, a boosting approach built upon the accelerated failure time model, which uses a Clayton copula to handle the dependency between the event and censoring distributions. By taking advantage of a copula, the independent censoring assumption is not needed any more. During comparisons with commonly used methods, Clayton-boost shows a strong ability to remove prediction bias at the presence of dependent censoring and outperforms the comparing methods either if the dependency strength or percentage censoring are considerable. The encouraging performance of Clayton-boost shows that there is indeed reasons to be critical about the independent censoring assumption, and that real-world data could highly benefit from modelling the potential dependency.
Machine and deep learning survival models demonstrate similar or even improved time-to-event prediction capabilities compared to classical statistical learning methods yet are too complex to be interpreted by humans. Several model-agnostic explanations are available to overcome this issue; however, none directly explain the survival function prediction. In this paper, we introduce SurvSHAP(t), the first time-dependent explanation that allows for interpreting survival black-box models. It is based on SHapley Additive exPlanations with solid theoretical foundations and a broad adoption among machine learning practitioners. The proposed methods aim to enhance precision diagnostics and support domain experts in making decisions. Experiments on synthetic and medical data confirm that SurvSHAP(t) can detect variables with a time-dependent effect, and its aggregation is a better determinant of the importance of variables for a prediction than SurvLIME. SurvSHAP(t) is model-agnostic and can be applied to all models with functional output. We provide an accessible implementation of time-dependent explanations in Python at http://github.com/MI2DataLab/survshap.
Applications of machine learning in healthcare often require working with time-to-event prediction tasks including prognostication of an adverse event, re-hospitalization or death. Such outcomes are typically subject to censoring due to loss of follow up. Standard machine learning methods cannot be applied in a straightforward manner to datasets with censored outcomes. In this paper, we present auton-survival, an open-source repository of tools to streamline working with censored time-to-event or survival data. auton-survival includes tools for survival regression, adjustment in the presence of domain shift, counterfactual estimation, phenotyping for risk stratification, evaluation, as well as estimation of treatment effects. Through real world case studies employing a large subset of the SEER oncology incidence data, we demonstrate the ability of auton-survival to rapidly support data scientists in answering complex health and epidemiological questions.
Recurrent neural network based solutions are increasingly being used in the analysis of longitudinal Electronic Health Record data. However, most works focus on prediction accuracy and neglect prediction uncertainty. We propose Deep Kernel Accelerated Failure Time models for the time-to-event prediction task, enabling uncertainty-awareness of the prediction by a pipeline of a recurrent neural network and a sparse Gaussian Process. Furthermore, a deep metric learning based pre-training step is adapted to enhance the proposed model. Our model shows better point estimate performance than recurrent neural network based baselines in experiments on two real-world datasets. More importantly, the predictive variance from our model can be used to quantify the uncertainty estimates of the time-to-event prediction: Our model delivers better performance when it is more confident in its prediction. Compared to related methods, such as Monte Carlo Dropout, our model offers better uncertainty estimates by leveraging an analytical solution and is more computationally efficient.
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 synthetic, semi-synthetic, and real-world datasets, including medical imaging data. Our method performs better at identifying clusters and is competitive at predicting survival times. Relying on novel generative assumptions, the proposed model offers a holistic perspective on clustering survival data and holds a promise of discovering subpopulations whose survival is regulated by different generative mechanisms.
Integrating methods for time-to-event prediction with diagnostic imaging modalities is of considerable interest, as accurate estimates of survival requires accounting for censoring of individuals within the observation period. New methods for time-to-event prediction have been developed by extending the cox-proportional hazards model with neural networks. In this paper, to explore the feasibility of these methods when applied to deep learning with echocardiography videos, we utilize the Stanford EchoNet-Dynamic dataset with over 10,000 echocardiograms, and generate simulated survival datasets based on the expert annotated ejection fraction readings. By training on just the simulated survival outcomes, we show that spatiotemporal convolutional neural networks yield accurate survival estimates.
Traffic accident anticipation aims to predict accidents from dashcam videos as early as possible, which is critical to safety-guaranteed self-driving systems. With cluttered traffic scenes and limited visual cues, it is of great challenge to predict how long there will be an accident from early observed frames. Most existing approaches are developed to learn features of accident-relevant agents for accident anticipation, while ignoring the features of their spatial and temporal relations. Besides, current deterministic deep neural networks could be overconfident in false predictions, leading to high risk of traffic accidents caused by self-driving systems. In this paper, we propose an uncertainty-based accident anticipation model with spatio-temporal relational learning. It sequentially predicts the probability of traffic accident occurrence with dashcam videos. Specifically, we propose to take advantage of graph convolution and recurrent networks for relational feature learning, and leverage Bayesian neural networks to address the intrinsic variability of latent relational representations. The derived uncertainty-based ranking loss is found to significantly boost model performance by improving the quality of relational features. In addition, we collect a new Car Crash Dataset (CCD) for traffic accident anticipation which contains environmental attributes and accident reasons annotations. Experimental results on both public and the newly-compiled datasets show state-of-the-art performance of our model. Our code and CCD dataset are available at https://github.com/Cogito2012/UString.
We present a neural network framework for learning a survival model to predict a time-to-event outcome while simultaneously learning a topic model that reveals feature relationships. In particular, we model each subject as a distribution over "topics", where a topic could, for instance, correspond to an age group, a disorder, or a disease. The presence of a topic in a subject means that specific clinical features are more likely to appear for the subject. Topics encode information about related features and are learned in a supervised manner to predict a time-to-event outcome. Our framework supports combining many different topic and survival models; training the resulting joint survival-topic model readily scales to large datasets using standard neural net optimizers with minibatch gradient descent. For example, a special case is to combine LDA with a Cox model, in which case a subject's distribution over topics serves as the input feature vector to the Cox model. We explain how to address practical implementation issues that arise when applying these neural survival-supervised topic models to clinical data, including how to visualize results to assist clinical interpretation. We study the effectiveness of our proposed framework on seven clinical datasets on predicting time until death as well as hospital ICU length of stay, where we find that neural survival-supervised topic models achieve competitive accuracy with existing approaches while yielding interpretable clinical topics that explain feature relationships. Our code is available at: https://github.com/georgehc/survival-topics
The abundance of modern health data provides many opportunities for the use of machine learning techniques to build better statistical models to improve clinical decision making. Predicting time-to-event distributions, also known as survival analysis, plays a key role in many clinical applications. We introduce a variational time-to-event prediction model, named Variational Survival Inference (VSI), which builds upon recent advances in distribution learning techniques and deep neural networks. VSI addresses the challenges of non-parametric distribution estimation by ($i$) relaxing the restrictive modeling assumptions made in classical models, and ($ii$) efficiently handling the censored observations, {\it i.e.}, events that occur outside the observation window, all within the variational framework. To validate the effectiveness of our approach, an extensive set of experiments on both synthetic and real-world datasets is carried out, showing improved performance relative to competing solutions.