  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.
