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# Mondrian Predictive Systems for Censored Data

*Proceedings of the Twelfth Symposium on Conformal and Probabilistic Prediction with Applications*, PMLR 204:399-412, 2023.

#### Abstract

Conformal predictive systems output predictions in
the form of well-calibrated cumulative distribution
functions (conformal predictive distributions). In
this paper, we apply conformal predictive systems to
the problem of time-to-event prediction, where the
conformal predictive distribution for a test object
may be used to obtain the expected time until an
event occurs, as well as p-values for an event to
take place earlier (or later) than some specified
time points. Specifically, we target right-censored
time-to-event prediction tasks, i.e., situations in
which the true time-to-event for a particular
training example may be unknown due to observation
of the example ending before any event occurs. By
leveraging the Kaplan-Meier estimator, we develop a
procedure for constructing Mondrian predictive
systems that are able to produce well-calibrated
cumulative distribution functions for right-censored
time-to-event prediction tasks. We show that the
proposed procedure is guaranteed to produce
conservatively valid predictive distributions, and
provide empirical support using simulated censoring
on benchmark data. The proposed approach is
contrasted with established techniques for survival
analysis, including random survival forests and
censored quantile regression forests, using both
synthetic and non-synthetic censoring.