Survival Conformal Prediction Under Random Censoring

In survival analysis, existing methods for handling censored data often focus on parameter estimation based on specific model assumptions, which may result in errors from potential model misspecification. In this paper, we study a different problem: uncertainty quantification for randomly censored data without model assumptions. Specifically, we propose a survival conformal prediction framework to construct two-sided prediction intervals for the survival times of new subjects. To identify the upper bound of the interval under right censoring, we use the idea of inverse probability weighting to redistribute the weights of the observed survival time, in which the distribution of censoring time is used to compensate for the loss of information. By fitting quantile regression, we are able to capture heterogeneous and skewed error distributions present in the data. Our framework is simple and flexible and can incorporate any quantile regression algorithm while ensuring the validity of the predictions. The finite-sample performance of our procedure is demonstrated on simulation data and an acute myocardial infarction dataset.