Survival analysis under label shift

2025-06-26

AI Summary

This paper addresses cross-distribution survival inference under concurrent label shift and random censoring: the source population (P) provides censored survival times (T) and covariates (Z), while the target population (Q) contains only (Z); the marginal distributions of (T) differ between (P) and (Q), but the conditional distribution (Z mid T) remains invariant. To this end, we introduce label shift modeling to survival analysis for the first time and propose a unified parametric inference framework compatible with classical models—including Cox proportional hazards and accelerated failure time models. Our method integrates parametric modeling with nonparametric estimation of censoring-adjusted importance weights, performing estimation via maximization of a weighted approximate likelihood. We establish rigorous consistency and asymptotic normality of the resulting estimator. Extensive simulations and real-data analyses demonstrate strong validity and robustness across diverse censoring rates and label shift magnitudes, offering a novel paradigm at the intersection of survival analysis and distributional shift.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Let P represent the source population with complete data, containing covariate $mathbf{Z}$ and response $T$, and Q the target population, where only the covariate $mathbf{Z}$ is available. We consider a setting with both label shift and label censoring. Label shift assumes that the marginal distribution of $T$ differs between $P$ and $Q$, while the conditional distribution of $mathbf{Z}$ given $T$ remains the same. Label censoring refers to the case where the response $T$ in $P$ is subject to random censoring. Our goal is to leverage information from the label-shifted and label-censored source population $P$ to conduct statistical inference in the target population $Q$. We propose a parametric model for $T$ given $mathbf{Z}$ in $Q$ and estimate the model parameters by maximizing an approximate likelihood. This allows for statistical inference in $Q$ and accommodates a range of classical survival models. Under the label shift assumption, the likelihood depends not only on the unknown parameters but also on the unknown distribution of $T$ in $P$ and $mathbf{Z}$ in $Q$, which we estimate nonparametrically. The asymptotic properties of the estimator are rigorously established and the effectiveness of the method is demonstrated through simulations and a real data application. This work is the first to combine survival analysis with label shift, offering a new research direction in this emerging topic.

Problem

• Survival analysis under label shift and censoring
• Infer target population Q using shifted source P
• Estimate model parameters via approximate likelihood maximization

Innovation

• Parametric model for T given Z in Q
• Maximize approximate likelihood for estimation
• Nonparametric estimation of unknown distributions