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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.

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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.

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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.

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