Adaptive Data-Borrowing for Improving Treatment Effect Estimation using External Controls

TL;DR

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

Contribution

It proposes a novel influence function-based adaptive borrowing approach with a data-driven selection process, addressing bias issues when external controls are not fully comparable.

Findings

Significantly improves treatment effect estimation efficiency.

Outperforms existing methods in simulations and real data.

Effectively balances bias and variance in external control borrowing.

Abstract

Randomized controlled trials (RCTs) often exhibit limited inferential efficiency in estimating treatment effects due to small sample sizes. In recent years, the combination of external controls has gained increasing attention as a means of improving the efficiency of RCTs. However, external controls are not always comparable to RCTs, and direct borrowing without careful evaluation can introduce substantial bias and reduce the efficiency of treatment effect estimation. In this paper, we propose a novel influence-based adaptive sample borrowing approach that effectively quantifies the comparability of each sample in the external controls using influence function theory. Given a selected set of borrowed external controls, we further derive a semiparametric efficient estimator under an exchangeability assumption. Recognizing that the exchangeability assumption may not hold for all possible borrowing sets, we conduct a detailed analysis of the asymptotic bias and variance of the proposed estimator under violations of exchangeability. Building on this bias-variance trade-off, we further develop a data-driven approach to select the optimal subset of external controls for borrowing. Extensive simulations and real-world applications demonstrate that the proposed approach significantly enhances treatment effect estimation efficiency in RCTs, outperforming existing approaches.