Adaptive Influence-Based Borrowing Framework for Improving Treatment Effect Estimation in RCTs Using External Controls

TL;DR

This paper introduces an adaptive influence-based framework for selectively borrowing external control data in RCTs to improve treatment effect estimation, balancing bias and variance.

Contribution

It proposes a principled, individual-level compatibility metric using influence scores to guide external control borrowing, with an implementation in an R package.

Findings

The framework effectively identifies compatible external controls for bias reduction.

Influence scores guide optimal subset selection of external controls.

The method improves treatment effect estimation in underpowered RCTs.

Abstract

Randomized controlled trials (RCTs) often suffer from limited sample sizes due to high costs and lengthy recruitment periods, compromising precision in treatment effect estimation. External real-world control data offer a valuable opportunity for augmentation, but na\"ive integration may introduce bias without careful compatibility assessment. This paper presents a practical tutorial on the adaptive influence-based borrowing framework~\citep{Yang-etal2026}, which addresses this challenge through a principled, individual-level borrowing strategy. The core intuition is straightforward: rather than indiscriminately pooling all external controls (ECs), the framework first asks how much each external patient would perturb the outcome model fitted using RCT controls. External patients whose inclusion barely changes this model are deemed comparable and prioritized for borrowing, whereas those who substantially shift it are flagged as potentially incompatible. This individual-level compatibility metric, based on the influence score, is then used to construct a sequence of nested candidate subsets of ECs, from which the optimal subset is selected by minimizing the mean squared error of the treatment effect estimator, balancing the competing risks of bias from over-borrowing and imprecision from under-borrowing. When systematic differences between ECs and RCT controls are substantial, an optional outcome calibration step can align the two groups before influence-based selection proceeds. We provide a clear, step-by-step workflow with emphasis on methodological intuition, practical considerations, and visualization, thereby offering a principled, transparent, and practical method for leveraging ECs when RCTs alone are underpowered. Implementation is supported by an accompanying \texttt{R} package InfluenceBorrowing.