Prediction Sets and Conformal Inference with Censored Outcomes

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Given data on a scalar random variable Y, a prediction set for Y with miscoverage level alpha is a set of values for Y that contains a randomly drawn Y with probability 1 - alpha, where alpha belongs to the interval (0,1). Among all prediction sets that satisfy this coverage property, the oracle prediction set is the one with the smallest volume. This paper provides estimation methods of such prediction sets given observed conditioning covariates when Y is censored or measured in intervals. We first characterise the oracle prediction set under interval censoring and develop consistent estimators for the oracle prediction {intervals} and prediction sets consisting of multiple disjoint intervals. We use conformal inference to construct a prediction set that achieves finite-sample validity under censoring and maintains consistency as sample size increases, using a conformity score function designed for interval data. The procedure accommodates the prediction uncertainty that is irreducible (due to the stochastic nature of outcomes), the modelling uncertainty due to partial identification and also sampling uncertainty that gets reduced as samples get larger. We conduct a set of Monte Carlo simulations and an application to data from the Current Population Survey. The results highlight the robustness and efficiency of the proposed methods.