Conformal prediction regions for dependent censored lifetimes

Abstract

Joint-life insurance often involves several lifetimes subject to censoring at known dates. We construct prediction regions by reducing the lifetime vector to a suitable scalar outcome. We first characterise the reduction maps for which arbitrary componentwise censoring becomes ordinary right censoring. These maps are minima of coordinatewise nondecreasing transformations, with upper orthants as prediction regions. Under a common censoring date, the admissible class also includes the first-death and last-survivor times. Applying univariate weighted split-conformal calibration to the reduced outcomes then gives finite-sample marginal coverage with known retention probabilities under conditionally independent censoring. With estimated probabilities, asymptotic validity follows from consistent weight or outcome-quantile estimation under the respective regularity conditions. We then quantify retention through the censoring copula, compare joint calibration with coordinatewise bounds and study path selection and estimation. Simulations examine several aspects of the proposed method. Finally, an application to a Canadian joint-life annuity portfolio illustrates one-sided lower prediction bounds for reported first- and second-death times. The five-year observation period puts a limit to the attainable lower bounds, with different limits for different paths; the bounds seem most informative for older annuitants.