In cohort studies, a clinical outcome sometimes cannot be measured at a patient's visit when a resource-intensive measurement is skipped, and a prediction interval provides a range of values the unmeasured outcome may plausibly take, reported with the prediction level. Constructing the interval requires knowing how far the patient's disease has advanced, and a time-to-event covariate, the time until an anchoring event common to all patients, places each patient at a comparable point in the disease. For many patients, however, this event has not occurred by the end of their follow-up, so the time-to-event covariate is right-censored: its value is not observed and is known only to exceed the time to study exit. Conformal prediction methods can be adapted to this right-censored covariate setting, but these methods produce intervals whose length and coverage rate vary substantially from study to study. Such variability cannot support reliable clinical decisions, since the outcome range would overly depend on the study sample rather than on the true disease process. We develop a semiparametric prediction method that recasts the construction of the prediction interval as semiparametric estimation of its half-length, using the distributional information that conformal prediction methods discard. The method achieves the smallest possible variance in the estimated half-length and remains consistent even when the model for the time-to-event covariate or the model for the censoring time is misspecified. Simulation studies confirm substantially more stable interval lengths and coverage rates than conformal prediction methods across censoring rates. In a Huntington disease study with 77.2\% censoring, our method achieves reliable coverage with stable interval lengths, while conformal prediction methods produce either persistent undercoverage or intervals too wide to be informative.

翻译：暂无翻译