Enhancing Treatment Effect Estimation: A Model Robust Approach Integrating Randomized Experiments and External Controls using the Double Penalty Integration Estimator

TL;DR

This paper proposes a robust statistical method that combines randomized experiments with external controls to improve treatment effect estimation, ensuring consistency and efficiency even under model misspecification.

Contribution

It introduces a novel bias function and a double penalty integration estimator (DPIE) that enhance treatment effect estimation by effectively integrating external controls with randomized experiments.

Findings

DPIE achieves consistency and asymptotic normality.

DPIE outperforms traditional estimators in efficiency.

The method is validated through theoretical proofs and experiments.

Abstract

Randomized experiments (REs) are the cornerstone for treatment effect evaluation. However, due to practical considerations, REs may encounter difficulty recruiting sufficient patients. External controls (ECs) can supplement REs to boost estimation efficiency. Yet, there may be incomparability between ECs and concurrent controls (CCs), resulting in misleading treatment effect evaluation. We introduce a novel bias function to measure the difference in the outcome mean functions between ECs and CCs. We show that the ANCOVA model augmented by the bias function for ECs renders a consistent estimator of the average treatment effect, regardless of whether or not the ANCOVA model is correct. To accommodate possibly different structures of the ANCOVA model and the bias function, we propose a double penalty integration estimator (DPIE) with different penalization terms for the two functions. With an appropriate choice of penalty parameters, our DPIE ensures consistency, oracle property, and asymptotic normality even in the presence of model misspecification. DPIE is more efficient than the estimator derived from REs alone, validated through theoretical and experimental results.