Copula-Based Deep Survival Models for Dependent Censoring
Ali Hossein Gharari Foomani Michael Cooper Russell Greiner Rahul G. Krishnan
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.