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

Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumption