  When analyzing data from randomized clinical trials, covariate adjustment can
be used to account for chance imbalance in baseline covariates and to increase
precision of the treatment effect estimate. A practical barrier to covariate
adjustment is the presence of missing data. In this paper, in the light of
recent theoretical advancement, we first review several covariate adjustment
methods with incomplete covariate data. We investigate the implications of the
missing data mechanism on estimating the average treatment effect in randomized
clinical trials with continuous or binary outcomes. In parallel, we consider
settings where the outcome data are fully observed or are missing at random; in
the latter setting, we propose a full weighting approach that combines inverse
probability weighting for adjusting missing outcomes and overlap weighting for
covariate adjustment. We highlight the importance of including the interaction
terms between the missingness indicators and covariates as predictors in the
models. We conduct comprehensive simulation studies to examine the
finite-sample performance of the proposed methods and compare with a range of
common alternatives. We find that conducting the proposed adjustment methods
generally improves the precision of treatment effect estimates regardless of
the imputation methods when the adjusted covariate is associated with the
outcome. We apply the methods to the Childhood Adenotonsillectomy Trial to
assess the effect of adenotonsillectomy on neurocognitive functioning scores.
