Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumption

TL;DR

This paper introduces a method to construct synthetic treatment groups without relying on the mean exchangeability assumption, enabling better transfer of trial data to target populations.

Contribution

It proposes a weighted mixture approach inspired by synthetic control methods, estimating weights via minimizing maximum mean discrepancy, and establishes its asymptotic properties.

Findings

Effective in synthetic and real datasets

Performs well when mean exchangeability is violated

Provides a new tool for causal inference in complex settings

Abstract

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.