# Propensity score matching with multiple treatments

Is anyone aware of propensity score matching methods for when there are more than 2 treatment groups? I am working on a project with 4 treatment groups:

1. A
2. B
3. A and B
4. Neither A nor B

Calculating propensity scores using multinomial logistic regression might work, but then I'd get multiple scores for each observation so I'm not sure how I'd match/analyze the matched data.

It is not hard to do simultaneous covariate adjustment for multiple propensity scores. I recommend always using the logit propensity scale, and expanding those into restricted cubic splines. An example paper is Mark et al (1994) Circulation 89:2015-2025 where we analyzed three treatments.

Have a look at the mnps function in the twang package, described in this primer from the RAND Corporation. The package optimizes the tuning parameters of gradient-boosted tree models (highly flexible, non-linear, regularized) to user-specified sample-balance criteria. Then you can estimate the sample weights based on the optimized model.