Distributionally Robust Survival Models under Subpopulation Shift and Outlier Contamination

Abstract

Learning robust survival models under distribution shift is an important but challenging problem in many applications. In heterogeneous populations, a model that performs well on average may still perform poorly on certain subpopulations, and this issue becomes even more severe when the training data are contaminated by outliers. In this paper, we propose a novel distributionally robust framework for survival analysis that jointly addresses latent subpopulation shift and outlier contamination. The proposed method combines an outer minimization that selects a refined nominal distribution by reducing the influence of contaminated samples and an inner maximization that focuses on the most challenging subpopulation. This formulation directly accommodates non-decomposable survival losses while preserving interactions across samples, including the risk-set structure of the Cox negative partial log-likelihood. We develop an alternating gradient-based algorithm with outer updates derived from the KKT conditions of the inner maximization. Experiments on simulated data and two survival benchmarks demonstrate that the proposed method remains robust when subpopulation shift and outlier contamination occur simultaneously. It stabilizes training in contaminated settings and substantially improves worst-group performance across both linear and nonlinear survival models, while maintaining competitive and sometimes superior overall performance.