# A Causal Inference Framework for Leveraging External Controls in Hybrid Trials

arXiv: https://arxiv.org/abs/2305.08969 · HTML: https://mlsanity.com/paper/2305.08969/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 63 references that are in the map.
- First posted on arXiv 15 May 2023.

## Builds on (most cited first, 9 of 9)

- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [A Review of Generalizability and Transportability](https://mlsanity.com/paper/2102.11904/) (2021)
- [A General Algorithm for Deciding Transportability of Experimental Results](https://mlsanity.com/paper/1312.7485/) (2013)
- [Data Integration in Causal Inference](https://mlsanity.com/paper/2110.01106/) (2021)
- [Improving efficiency of inference in clinical trials with external control data](https://mlsanity.com/paper/2011.07234/) (2020)
- [An Omnibus Nonparametric Test of Equality in Distribution for Unknown Functions](https://mlsanity.com/paper/1510.04195/) (2015)
- [Optimal transport weights for causal inference](https://mlsanity.com/paper/2109.01991/) (2021)
- [Generalizing causal inferences from randomized trials: counterfactual and graphical identification](https://mlsanity.com/paper/1906.10792/) (2019)
- [Incorporating External Data into the Analysis of Clinical Trials via Bayesian Additive Regression Trees](https://mlsanity.com/paper/2103.08754/) (2021)

## Built on by (most cited first, 1 of 1)

- [Incorporating External Controls for Estimating the Average Treatment Effect on the Treated with High-Dimensional Data: Retaining Double Robustness and Ensuring Double Safety](https://mlsanity.com/paper/2509.20586/) (2025)

## Abstract (arXiv)

We consider the challenges associated with causal inference in settings where data from a randomized trial is augmented with control data from an external source to improve efficiency in estimating the average treatment effect (ATE). Through the development of a formal causal inference framework, we outline sufficient causal assumptions about the exchangeability between the internal and external controls to identify the ATE and establish the connection to a novel graphical criteria. We propose estimators, review efficiency bounds, develop an approach for efficient doubly-robust estimation even when unknown nuisance models are estimated with flexible machine learning methods, and demonstrate finite-sample performance through a simulation study. To illustrate the ideas and methods, we apply the framework to a trial investigating the effect of risdisplam on motor function in patients with spinal muscular atrophy for which there exists an external set of control patients from a previous trial.