Leveraging random assignment to impute missing covariates in causal studies

Baseline covariates in randomized experiments are often used in the estimation of treatment effects, for example, when estimating treatment effects within covariate-defined subgroups. In practice, however, covariate values may be missing for some data subjects. To handle missing values, analysts can use imputation methods to create completed datasets, from which they can estimate treatment effects. Common imputation methods include mean imputation, single imputation via regression, and multiple imputation. For each of these methods, we investigate the benefits of leveraging randomized treatment assignment in the imputation routines, that is, making use of the fact that the true covariate distributions are the same across treatment arms. We do so using simulation studies that compare the quality of inferences when we respect or disregard the randomization. We consider this question for imputation routines implemented using covariates only, and imputation routines implemented using the outcome variable. In either case, accounting for randomization offers only small gains in accuracy for our simulation scenarios. Our results also shed light on the performances of these different procedures for imputing missing covariates in randomized experiments when one seeks to estimate heterogeneous treatment effects.