  Traditional statistical and machine learning methods assume identical
distribution for the training and test data sets. This assumption, however, is
often violated in real applications, particularly in health care research,
where the training data~(source) may underrepresent specific subpopulations in
the testing or target domain. Such disparities, coupled with censored
observations, present significant challenges for investigators aiming to make
predictions for those minority groups. This paper focuses on target-independent
learning under covariate shift, where we study multicalibration for survival
probability and restricted mean survival time, and propose a black-box
post-processing boosting algorithm designed for censored survival data. Our
algorithm, leveraging the pseudo observations, yields a multicalibrated
predictor competitive with propensity scoring regarding predictions on the
unlabeled target domain, not just overall but across diverse subpopulations.
Our theoretical analysis for pseudo observations relies on functional delta
method and $p$-variational norm. We further investigate the algorithm's sample
complexity and convergence properties, as well as the multicalibration
guarantee for post-processed predictors. Our theoretical insights reveal the
link between multicalibration and universal adaptability, suggesting that our
calibrated function performs comparably to, if not better than, the inverse
propensity score weighting estimator. The performance of our proposed methods
is corroborated through extensive numerical simulations and a real-world case
study focusing on prediction of cardiovascular disease risk in two large
prospective cohort studies. These empirical results confirm its potential as a
powerful tool for predictive analysis with censored outcomes in diverse and
shifting populations.
