  The problem of missingness in observational data is ubiquitous. When the
confounders are missing at random, multiple imputation is commonly used;
however, the method requires congeniality conditions for valid inferences,
which may not be satisfied when estimating average causal treatment effects.
Alternatively, fractional imputation, proposed by Kim 2011, has been
implemented to handling missing values in regression context. In this article,
we develop fractional imputation methods for estimating the average treatment
effects with confounders missing at random. We show that the fractional
imputation estimator of the average treatment effect is asymptotically normal,
which permits a consistent variance estimate. Via simulation study, we compare
fractional imputation's accuracy and precision with that of multiple
imputation.
