We develop flexible, semiparametric estimators of the average treatment effect (ATE) transported to a new population ("target population") that offer potential efficiency gains. Transport may be of value when the ATE may differ across populations. We consider the setting where differences in the ATE are due to differences in the distribution of baseline covariates that modify the treatment effect ("effect modifiers"). First, we propose a collaborative one-step semiparametric estimator that can improve efficiency. This approach does not require researchers to have knowledge about which covariates are effect modifiers and which differ in distribution between the populations, but does require all covariates to be measured in the target population. Second, we propose two one-step semiparametric estimators that assume knowledge of which covariates are effect modifiers and which are both effect modifiers and differentially distributed between the populations. These estimators can be used even when not all covariates are observed in the target population; one requires that only effect modifiers are observed, and the other requires that only those modifiers that are also differentially distributed are observed. We use simulation to compare finite sample performance across our proposed estimators and an existing semiparametric estimator of the transported ATE, including in the presence of practical violations of the positivity assumption. Lastly, we apply our proposed estimators to a large-scale housing trial.
