  Complementary features of randomized controlled trials (RCTs) and
observational studies (OSs) can be used jointly to estimate the average
treatment effect of a target population. We propose a calibration weighting
estimator that enforces the covariate balance between the RCT and OS, therefore
improving the trial-based estimator's generalizability. Exploiting
semiparametric efficiency theory, we propose a doubly robust augmented
calibration weighting estimator that achieves the efficiency bound derived
under the identification assumptions. A nonparametric sieve method is provided
as an alternative to the parametric approach, which enables the robust
approximation of the nuisance functions and data-adaptive selection of outcome
predictors for calibration. We establish asymptotic results and confirm the
finite sample performances of the proposed estimators by simulation experiments
and an application on the estimation of the treatment effect of adjuvant
chemotherapy for early-stage non-small cell lung patients after surgery.
