Mondrian Predictive Systems for Censored Data

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.