Conformal Prediction Under Nonignorable Missingness

Existing methods for handling nonignorable missing data often rely on strong modeling assumptions, making them vulnerable to model misspecification.This paper proposes a conformal prediction framework for constructing prediction sets under nonignorable missing responses, which is model-free for the outcome regression while relying on a consistently estimated propensity score.Our framework addresses two central challenges posed by nonignorable missingness: non-identifiability and the lack of data exchangeability.The key idea is to construct the highest conditional density prediction set using a local subset near the target point, while correcting for selection bias via modeling the missingness mechanism.Within this framework, we develop a bias-adjusted semiparametric method for conditional density estimation, which fits a quantile process to the observed data and corrects for bias using propensity weights.This estimator integrates seamlessly into the conformal framework, allowing our approach to guarantee not only marginal coverage, but also local and asymptotic conditional coverage for any new subject, while achieving asymptotically optimal interval lengths.We demonstrate the validity and efficiency of our procedure through simulation studies and an application to a real HIV-CD4 dataset.