Models for predicting the time of a future event are crucial for risk assessment, across a diverse range of applications. Existing time-to-event (survival) models have focused primarily on preserving pairwise ordering of estimated event times, or relative risk. Model calibration is relatively under explored, despite its critical importance in time-to-event applications. We present a survival function estimator for probabilistic predictions in time-to-event models, based on a neural network model for draws from the distribution of event times, without explicit assumptions on the form of the distribution. This is done like in adversarial learning, but we achieve learning without a discriminator or adversarial objective. The proposed estimator can be used in practice as a means of estimating and comparing conditional survival distributions, while accounting for the predictive uncertainty of probabilistic models. Extensive experiments show that the proposed model outperforms existing approaches, trained both with and without adversarial learning, in terms of both calibration and concentration of time-to-event distributions.
Our work is related to other recently proposed time-to-event approaches, including Survival CRPS (S-CRPS) , that uses an AFT (log-normal distribution) specification; the approach [DATE,][] chapfuwa2018adversarial ; the AFT-based DRAFT model ; the Weibull-based Deep Survival Analysis (DSA) ; nonparametric DSA based on ; and Gaussian-process-based models . Interestingly, excluding approaches that address calibration with Brier-scores @cite_0 @cite_14 @cite_2 @cite_11 , only S-CRPS considers calibration as a performance metric. All the others focus on accuracy-centric performance estimates, , C-Index and relative absolute error.
@cite_0 @cite_14 @cite_11 @cite_2
2809313038 2798234853 2496251701 2147838747
Personalized probabilistic forecasts of time to event (such as mortality) can be crucial in decision making, especially in the clinical setting. Inspired by ideas from the meteorology literature, we approach this problem through the paradigm of maximizing sharpness of prediction distributions, subject to calibration. In regression problems, it has been shown that optimizing the continuous ranked probability score (CRPS) instead of maximum likelihood leads to sharper prediction distributions while maintaining calibration. We introduce the Survival-CRPS, a generalization of the CRPS to the time to event setting, and present right-censored and interval-censored variants. To holistically evaluate the quality of predicted distributions over time to event, we present the Survival-AUPRC evaluation metric, an analog to area under the precision-recall curve. We apply these ideas by building a recurrent neural network for mortality prediction, using an Electronic Health Record dataset covering millions of patients. We demonstrate significant benefits in models trained by the Survival-CRPS objective instead of maximum likelihood. Modern health data science applications leverage abundant molecular and electronic health data, providing opportunities for machine learning to build statistical models to support clinical practice. Time-to-event analysis, also called survival analysis, stands as one of the most representative examples of such statistical models. We present a novel deep-network-based approach that leverages adversarial learning to address a key challenge in modern time-to-event modeling: nonparametric estimation of event-time distributions. We also introduce a principled cost function to exploit information from censored events (events that occur subsequent to the observation window). Unlike most time-to-event models, we focus on the estimation of time-to-event distributions, rather than time ordering. We validate our model on both benchmark and real datasets, demonstrating that the proposed formulation yields significant performance gains relative to a parametric alternative, which we also propose. 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. Time-to-event outcomes based data can be modelled using survival regression methods which can predict these outcomes in different censored data applications in diverse fields such as engineering, economics and healthcare. Predictive models are built by inferring from the censored variable in time-to-event data, which differentiates them from other regression methods. Censoring is represented as a binary indicator variable and machine learning methods have been tuned to account for the censored attribute. Active learning from censored data using survival regression methods can make the model query a domain expert for the time-to-event label of the sampled instances. This offers higher advantages in the healthcare domain where a domain expert can interactively refine the model with his feedback. With this motivation, we address this problem by providing an active learning based survival model which uses a novel model discriminative gradient based sampling scheme. We evaluate this framework on electronic health records (EHR), publicly available survival and synthetic censored datasets of varying diversity. Experimental evaluation against state of the art survival regression methods indicates the higher discriminative ability of the proposed approach. We also present the sampling results for the proposed approach in an active learning setting which indicate better learning rates in comparison to other sampling strategies.