  How to deal with missing data in observational studies is a common concern
for causal inference. When the covariates are missing at random (MAR), multiple
approaches have been provided to help solve the issue. However, if the exposure
is MAR, few approaches are available and careful adjustments on both
missingness and confounding issues are required to ensure a consistent estimate
of the true causal effect on the response. In this article, a new inverse
probability weighting (IPW) estimator based on weighted estimating equations
(WEE) is proposed to incorporate weights from both the missingness and
propensity score (PS) models, which can reduce the joint effect of extreme
weights in finite samples. Additionally, we develop a triple robust (TR)
estimator via WEE to further protect against the misspecification of the
missingness model. The asymptotic properties of WEE estimators are proved using
properties of estimating equations. Based on the simulation studies, WEE
methods outperform others including imputation-based approaches in terms of
bias and variability. Finally, an application study is conducted to identify
the causal effect of the presence of cardiovascular disease on mortality for
COVID-19 patients.
