Borrowing-dependent estimands in external-control trials: Identification, efficiency, and sensitivity in survival analysis.

Authors

Atanu Bhattacharjee, Ayon Mukherjee

Published in

Journal of biopharmaceutical statistics. Pages 1-28. Oct 11, 2026. Epub Oct 11, 2026.

Abstract

Augmenting randomised trials with external controls is increasingly common in oncology and rare diseases. This paper reviews the methodology of externally controlled trials - estimands, identification assumptions, estimation, efficiency and sensitivity analysis - for right-censored survival outcomes, and organises it around a single question: what quantity does a borrowing analysis actually deliver? We distinguish the intended estimand, fixed in advance by the clinical question and the target population, from the borrowing-dependent estimand, the quantity to which a given borrowing rule is consistent. The two coincide under source-conditional exchangeability and separate otherwise, so that the borrowing-dependent estimand names, and makes estimable, a discrepancy that is otherwise reported only as unquantified bias. Within a nonparametric potential-outcomes framework we (i) define borrowing-weighted causal contrasts indexed by a weighting kernel and set out when such a contrast is, and is not, a scientifically meaningful target in its own right; (ii) establish nonparametric identification and derive the efficient influence function; (iii) construct a doubly robust, locally efficient estimator with $\sqrt{n}$-consistency; (iv) introduce a sensitivity-analysis framework yielding closed-form bias bounds, E-values, and tipping points; and (v) characterise the sensitivity of the delivered estimand to the pre-specified borrowing rule via Fréchet differentiability. Simulations across 12 factorial scenarios confirm up to 49% RMSE reduction under compatibility, show that the estimators remain unbiased for the borrowing-dependent estimand when compatibility fails, and validate the sensitivity bounds. A worked example in metastatic colorectal cancer illustrates the complete analytical workflow.

PMID:
42860000
Bibliographic data and abstract were imported from PubMed on 12 Oct 2026.

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