Auxiliary-survival-probabilities-informed survival analysis under Cox model

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Abstract

Transferring summary-level auxiliary information from source domains to enhance statistical analysis in target domains is increasingly important, yet settings involving right-censored survival data remain underexplored. To address this gap, we developed a general methodology for incorporating subgroup Kaplan–Meier survival probabilities at multiple time points, a widely reported form of auxiliary information. Our framework handles both estimation of an abstractly defined target parameter, such as a regression coefficient or a causal estimand, and hypothesis testing for it. We first constructed a target-only estimator that possesses a unified structure applicable to a broad class of target parameters. This estimator was then linked, via a leveraging factor, to a transitional element computed from the target dataset in a manner analogous to the available auxiliary information. We proposed and compared two versions of this element. The model-free version is universally applicable and robust, whereas the model-based version delivers improved efficiency under a partly independent censoring assumption that has often been overlooked in existing literature. Our method requires no individual-level source data and maintains low computational complexity. Theoretical derivations and numerical experiments together demonstrated gains in estimation efficiency and testing power. In addition, Python implementations of the proposed approaches were provided.

Keywords

Cox model / partly independent censoring / summary-level auxiliary information / transfer learning / transitional element

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