# Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumption

arXiv: https://arxiv.org/abs/2309.16409 · HTML: https://mlsanity.com/paper/2309.16409/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 79 references that are in the map.
- First posted on arXiv 28 Sep 2023.

## Builds on (most cited first, 27 of 27)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [A Review of Generalizability and Transportability](https://mlsanity.com/paper/2102.11904/) (2021)
- [Generalizing causal inferences from individuals in randomized trials to all trial-eligible individuals](https://mlsanity.com/paper/1709.04589/) (2017)
- [Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence](https://mlsanity.com/paper/1912.05737/) (2019)
- [Conditional Generative Moment-Matching Networks](https://mlsanity.com/paper/1606.04218/) (2016)
- [Extending inferences from a randomized trial to a new target population](https://mlsanity.com/paper/1805.00550/) (2018)
- [On the Assumptions of Synthetic Control Methods](https://mlsanity.com/paper/2112.05671/) (2021)
- [Improving efficiency of inference in clinical trials with external control data](https://mlsanity.com/paper/2011.07234/) (2020)
- [Distributional synthetic controls](https://mlsanity.com/paper/2001.06118/) (2020)
- [Covariate Balancing Sensitivity Analysis for Extrapolating Randomized Trials across Locations](https://mlsanity.com/paper/2112.04723/) (2021)
- [Risk ratio, odds ratio, risk difference... Which causal measure is easier to generalize?](https://mlsanity.com/paper/2303.16008/) (2023)
- [Sensitivity analysis for an unobserved moderator in RCT-to-target-population generalization of treatment effects](https://mlsanity.com/paper/1610.06943/) (2016)
- [Sensitivity analysis using bias functions for studies extending inferences from a randomized trial to a target population](https://mlsanity.com/paper/1905.10684/) (2019)
- [Sensitivity Analysis in the Generalization of Experimental Results](https://mlsanity.com/paper/2202.03408/) (2022)
- [Nonparametric Heterogeneous Treatment Effect Estimation in Repeated Cross Sectional Designs](https://mlsanity.com/paper/1905.11622/) (2019)
- [Sensitivity analyses for effect modifiers not observed in the target population when generalizing treatment effects from a randomized controlled trial: Assumptions, models, effect scales, data scenarios, and implementation details](https://mlsanity.com/paper/2011.13058/) (2020)
- [A bracketing relationship between difference-in-differences and lagged-dependent-variable adjustment](https://mlsanity.com/paper/1903.06286/) (2019)
- [Causal Inference for Comprehensive Cohort Studies](https://mlsanity.com/paper/1910.03531/) (2019)
- [Asymptotically Unbiased Synthetic Control Methods by Moment Matching](https://mlsanity.com/paper/2307.11127/) (2023)
- [Using Multiple Samples to Learn Mixture Models](https://mlsanity.com/paper/1311.7184/) (2013)
- [Effect heterogeneity and variable selection for standardizing causal effects to a target population](https://mlsanity.com/paper/1610.00068/) (2016)
- [The choice of effect measure for binary outcomes: Introducing counterfactual outcome state transition parameters](https://mlsanity.com/paper/1610.00069/) (2016)
- [Identification and Estimation of Heterogeneous Treatment Effects under Non-compliance or Non-ignorable assignment](https://mlsanity.com/paper/1808.03750/) (2018)
- [A Semiparametric Efficient Approach To Label Shift Estimation and Quantification](https://mlsanity.com/paper/2211.04274/) (2022)

## Abstract (arXiv)

The purpose of this work is to transport the information from multiple randomized controlled trials to the target population where we only have the control group data. Previous works rely critically on the mean exchangeability assumption. However, as pointed out by many current studies, the mean exchangeability assumption might be violated. Motivated by the synthetic control method, we construct a synthetic treatment group for the target population by a weighted mixture of treatment groups of source populations. We estimate the weights by minimizing the conditional maximum mean discrepancy between the weighted control groups of source populations and the target population. We establish the asymptotic normality of the synthetic treatment group estimator based on the sieve semiparametric theory. Our method can serve as a novel complementary approach when the mean exchangeability assumption is violated. Experiments are conducted on synthetic and real-world datasets to demonstrate the effectiveness of our methods.