Dynamic regularized borrowing—an approach for binary outcomes in single‑arm trials

Abstract Single-arm clinical trials with binary outcomes often face enrollment challenges, particularly in rare diseases and oncology, where limited sample sizes can reduce estimation precision. Borrowing information from historical trials can improve estimation efficiency, but naïve pooling may introduce bias and inflate false-positive rates when historical and current data are heterogeneous. We propose a data-adaptive borrowing approach, termed Regularized Borrowing (RB), based on a regularized likelihood approach with conditional Bayesian interpretation, for single-arm trials with binary outcomes. The RB method incorporates historical data through a regularization framework that calibrates the degree of borrowing by minimizing the reference-based mean squared error (MSE) of the current-study estimator. The borrowing parameter is selected using a bootstrap-based objective evaluated via repeated cross-fitting, allowing RB to adaptively balance bias and variance without requiring strong exchangeability assumptions or prior specification of borrowing strength. Through simulation studies, we show that RB down-weights incompatible historical information while improving estimation efficiency relative to independent analysis and several existing Bayesian borrowing methods. As with other data-adaptive borrowing approaches, empirical false-positive rate inflation was observed in some scenarios, with the greatest inflation occurring in smaller-sample and more discordant settings. An application to real clinical trial data illustrates the practical advantages of RB in reducing uncertainty while maintaining robust performance under heterogeneity. Although this manuscript focuses on binary outcomes in single‑arm trials, the proposed RB framework is not specific to this setting and is conceptually extendable to other outcome types and trial designs, including randomized controlled trials.