Doubly robust augmented weighting estimators for the analysis of externally controlled single-arm trials and unanchored indirect treatment comparisons

Externally controlled single-arm trials are critical to assess treatment efficacy across therapeutic indications for which randomized controlled trials are not feasible. A closely-related research design, the unanchored indirect treatment comparison, is often required for disconnected treatment networks in health technology assessment. We present a unified causal inference framework for both research designs. We develop a novel estimator that augments a popular weighting approach based on entropy balancing – matching-adjusted indirect comparison (MAIC) – by fitting a model for the conditional outcome expectation. The predictions of the outcome model are combined with the entropy balancing MAIC weights. While the standard MAIC estimator is singly robust where the outcome model is non-linear, our augmented MAIC approach is doubly robust, providing increased robustness against model misspecification. This is demonstrated in a simulation study with binary outcomes and a logistic outcome model, where the augmented estimator demonstrates its doubly robust property, while exhibiting higher precision than all non-augmented weighting estimators and near-identical precision to G-computation. We describe the extension of our estimator to the setting with unavailable individual participant data for the external control, illustrating it through an applied example. Our findings reinforce the understanding that entropy balancing-based approaches have desirable properties compared to standard ``modeling’’ approaches to weighting, but should be augmented to improve protection against bias and guarantee double robustness.

💡 Research Summary

The paper addresses the growing need for robust causal inference methods in externally controlled single‑arm trials (SATs) and unanchored indirect treatment comparisons (ITCs), both of which involve treatment and control groups drawn from different data sources. Traditional approaches include propensity‑score weighting and the matching‑adjusted indirect comparison (MAIC), which uses entropy‑balancing to directly match covariate means without explicitly modeling the propensity score. While MAIC is attractive for its stability and applicability when only aggregate data are available for the external control, its double‑robustness holds only when the true outcome model is linear in the balanced covariates—a condition rarely met in practice.

The authors propose an augmented MAIC estimator that combines the entropy‑balancing weights with predictions from a conditional outcome model (e.g., logistic regression for binary outcomes). The procedure consists of three steps: (1) compute MAIC weights by solving an entropy‑balancing optimization problem; (2) fit an outcome regression model using the same covariates; (3) obtain the treatment‑effect estimate by averaging the model‑based predictions weighted by the MAIC weights. This “double‑robust” construction guarantees consistent estimation if either the weighting model or the outcome model is correctly specified, regardless of the linearity of the outcome‑covariate relationship.

The authors formalize the target estimands using potential‑outcome notation, focusing on the average treatment effect in the external control population (A_TC) because, in unanchored ITCs, only aggregate data are typically available for that group. They assume strong ignorability (no unmeasured confounding after adjusting for baseline covariates) and no trial‑participation effect (no Hawthorne effect). Under these assumptions, the mean outcome under control is trivially estimated by the external sample mean, while the mean outcome under treatment in the external population must be inferred via the augmented estimator.

A comprehensive simulation study with binary outcomes generated from a logistic true model demonstrates the properties of the proposed method. When the outcome model is correctly specified but the weighting model is misspecified, the augmented MAIC remains unbiased, and vice‑versa. Compared with standard (non‑augmented) MAIC, inverse‑probability weighting, and G‑computation, the augmented estimator exhibits substantially lower bias and variance, achieving precision comparable to G‑computation while retaining double‑robustness.

The paper also extends the methodology to the common “IPD‑AD” scenario where individual‑level data are unavailable for the external control. By treating published covariate means as constraints in the entropy‑balancing problem, the authors obtain feasible weights and apply the same augmentation, showing in an applied example that the method yields narrower confidence intervals than conventional MAIC.

Limitations discussed include potential instability when MAIC weights become extreme, which can be mitigated by trimming or weight‑capping, and the need for careful model selection in high‑dimensional settings. The authors suggest future work on regularized entropy‑balancing, machine‑learning outcome models, and sensitivity analyses for violations of ignorability.

In conclusion, the augmented, doubly robust MAIC provides a principled and efficient tool for causal effect estimation in externally controlled trials and unanchored indirect comparisons, offering protection against misspecification of either the weighting or outcome model while maintaining the practical advantages of entropy‑balancing in settings with limited individual‑level data.