I refer to this paper: Hayes JR, Groner JI. "Using multiple imputation and propensity scores to test the effect of car seats and seat belt usage on injury severity from trauma registry data." J Pediatr Surg. 2008 May;43(5):924-7.
In this study, multiple imputation was performed to obtain 15 complete datasets. Propensity scores were then computed for each dataset. Then, for each observational unit, a record was chosen randomly from one of the completed 15 datasets (including the related propensity score) thereby creating a single final dataset for which was then analysed by propensity score matching.
My questions are: Is this valid way to perform propensity score matching following multiple imputation ? Are there alternative ways to do it ?
For context: In my new project, I aim to compare the effects of 2 treatment methods using propensity score matching. There is missing data and I intend to use the
MICE package in R to impute missing values, then
twang to do the propensity score matching, and then
lme4 to analyse the matched data.
I have found this paper which takes a different approach: Mitra, Robin and Reiter, Jerome P. (2011) Propensity score matching with missing covariates via iterated, sequential multiple imputation [Working Paper]
In this paper the authors compute propensity scores on all the imputed datasets and then pool them by averaging, which is in the spirit of multiple imputation using Rubin's rule's for a point estimate - but is it really applicable for a propensity score ?
It would be really nice if anyone on CV could provide an answer with commentary on these 2 different approaches, and/or any others....