Copula-Based Deep Survival Models for Dependent Censoring

Ali Hossein Gharari Foomani, Michael Cooper, Russell Greiner, Rahul G Krishnan

Keywords: survival analysis, deep learning, neural networks

TL;DR: This paper applies copulas to model unobserved dependencies between times of event and censorship in survival analysis, reducing bias in learned survival curves.

Abstract: A survival dataset describes a set of instances (e.g., patients) and provides, for each, either the time until an event (e.g., death), or the censoring time (e.g., when lost to follow-up – which is a lower bound on the time until the event). We consider the challenge of survival prediction: learning, from such data, a predictive model that can produce an individual survival distribution for a novel instance. Many contemporary methods of survival prediction implicitly assume that the event and censoring distributions are independent conditional on the instance’s covariates – a strong assumption that is difficult to verify (as we observe only one outcome for each instance) and which can induce significant bias when it does not hold. This paper presents a parametric model of survival that extends modern non-linear survival analysis by relaxing the assumption of conditional independence. On synthetic and semi-synthetic data, our approach significantly improves estimates of survival distributions compared to the standard that assumes conditional independence in the data.