  Chance imbalance in baseline characteristics is common in randomized clinical
trials. Regression adjustment such as the analysis of covariance (ANCOVA) is
often used to account for imbalance and increase precision of the treatment
effect estimate. An objective alternative is through inverse probability
weighting (IPW) of the propensity scores. Although IPW and ANCOVA are
asymptotically equivalent, the former may demonstrate inferior performance in
finite samples. In this article, we point out that IPW is a special case of the
general class of balancing weights, and advocate to use overlap weighting (OW)
for covariate adjustment. The OW method has a unique advantage of completely
removing chance imbalance when the propensity score is estimated by logistic
regression. We show that the OW estimator attains the same semiparametric
variance lower bound as the most efficient ANCOVA estimator and the IPW
estimator for a continuous outcome, and derive closed-form variance estimators
for OW when estimating additive and ratio estimands. Through extensive
simulations, we demonstrate OW consistently outperforms IPW in finite samples
and improves the efficiency over ANCOVA and augmented IPW when the degree of
treatment effect heterogeneity is moderate or when the outcome model is
incorrectly specified. We apply the proposed OW estimator to the Best Apnea
Interventions for Research (BestAIR) randomized trial to evaluate the effect of
continuous positive airway pressure on patient health outcomes. All the
discussed propensity score weighting methods are implemented in the R package
PSweight.
