In a treatment effects framework, I have a control and treatment group with some covariates on which to match (I'm using nearest-neighbor method).
The control group has a no missing data, but some covariates are missing for some members of the treatment group.
Is it still possible to do matching in this case, or should i restrict my sample to individuals with only a complete data set?
There are a few statistical techniques that can be used to reduce the bias due to missing data, but the one that has been demonstrated to be most successful is multiple imputation. Multiple imputation involves creating several copies of the original dataset and filling in the missing values with guesses of their true values, allowing some randomness to exist across the imputed datasets to reflect the uncertaty in the missing values. Effects are estimated in each imputed dataset and then then estimates are combined in a certain way.
This topic has been covered with respect to propensity score matching in several papers, including Leyrat et al. (2019) and Cham and West (2016). Simulation stduies consistently indicate that multiple imputation is preferred and that the outcomes should be used in imputing the missing covariates. (The fact that propensity score matching was studied and not nearest neighbor matching is incidental.)
If you are using R, the MatchThem package makes it easy to perform matching and estimate effects across multiply imputed datasets. You can use the mice package to perform multiple imputation and supply the output to the matchthem() function. You can perform nearest neighbor (i.e., Mahalanobis distance) matching by setting distance = "mahalanobis" in the call to matchthem(). I'm an author of MatchThem so let me know if you have any questions.
Cham, H., & West, S. G. (2016). Propensity score analysis with missing data. Psychological Methods, 21(3), 427–445. https://doi.org/10.1037/met0000076
Leyrat, C., Seaman, S. R., White, I. R., Douglas, I., Smeeth, L., Kim, J., Resche-Rigon, M., Carpenter, J. R., & Williamson, E. J. (2019). Propensity score analysis with partially observed covariates: How should multiple imputation be used? Statistical Methods in Medical Research, 28(1), 3–19. https://doi.org/10.1177/0962280217713032
