Multicalibration for Modeling Censored Survival Data with Universal Adaptability

Abstract: Traditional statistical and machine learning methods typically assume that the training and test data follow the same distribution. However, this assumption is frequently violated in real-world applications, where the training data in the source domain may under-represent specific subpopulations in the test data of the target domain. This paper addresses target-independent learning under covariate shift, focusing on multicalibration for survival probability and restricted mean survival time. A black-box post-processing boosting algorithm specifically designed for censored survival data is introduced. By leveraging pseudo-observations, our method produces a multicalibrated predictor that is competitive with inverse propensity score weighting in predicting the survival outcome in an unlabeled target domain, ensuring not only overall accuracy but also fairness across diverse subpopulations. Our theoretical analysis of pseudo-observations builds upon the functional delta method and the $p$-variational norm. The algorithm's sample complexity, convergence properties, and multicalibration guarantees for post-processed predictors are provided. Our results establish a fundamental connection between multicalibration and universal adaptability, demonstrating that our calibrated function is comparable to, or outperforms, the inverse propensity score weighting estimator. Extensive numerical simulations and a real-world case study on cardiovascular disease risk prediction using two large prospective cohort studies validate the effectiveness of our approach.