We published a recent paper that compares matching, weighting, and regression adjustment methods with a single covariate in unconfounded studies using extensive simulations. We showed that regression adjustment using spline/penalized spline resulted in statistically invalid method in many configurations. (Estimation of causal effects of binary treatments in unconfounded studies with one continuous covariate. Stat Methods Med Res) Generally, matching with replacement (with appropriate weighting) will allow researchers to discard less observations than commonly use matching. It also results in smaller bias, and relatively decent variance. In a different paper (currently in review), we have proposed a different method using multiple imputation with regression splines on the propensity score to obtain estimates which are more efficient and generally statistically valid. However, we do show that all methods (including the proposed one), may perform badly in areas where there is no overlap in the propensity score, which requires to drop those cases that are in non-overlapping areas. I would be happy to share our results, if you are interested. -------------------------------------------
Roee Gutman
Assistant Professor of Biostatistics
Brown University
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