  Causal inference methods based on electronic health record (EHR) databases
must simultaneously handle confounding and missing data. Vast scholarship
exists aimed at addressing these two issues separately, but surprisingly few
papers attempt to address them simultaneously. In practice, when faced with
simultaneous missing data and confounding, analysts may proceed by first
imputing missing data and subsequently using outcome regression or
inverse-probability weighting (IPW) to address confounding. However, little is
known about the theoretical performance of such $\textit{ad hoc}$ methods. In a
recent paper Levis $\textit{et al.}$ outline a robust framework for tackling
these problems together under certain identifying conditions, and introduce a
pair of estimators for the average treatment effect (ATE), one of which is
non-parametric efficient. In this work we present a series of simulations,
motivated by a published EHR based study of the long-term effects of bariatric
surgery on weight outcomes, to investigate these new estimators and compare
them to existing $\textit{ad hoc}$ methods. While the latter perform well in
certain scenarios, no single estimator is uniformly best. As such, the work of
Levis $\textit{et al.}$ may serve as a reasonable default for causal inference
when handling confounding and missing data together.
