Solved – Propensity score matching with multiple treatments
logisticmatchingpropensity-scores
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:
A
B
A and B
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.
Best Answer
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.
The first thing to say is that, for me, method 1 (sampling) seems to be without much merit - it is discarding the benefits of multiple imputation, and reduces to single imputation for each observation, as mentioned by Stas. I can't see any advantage in using it.
There is an excellent discussion of the issues surrounding propensity score analysis with missing data in Hill (2004):
Hill, J. "Reducing Bias in Treatment Effect Estimation in Observational Studies Suffering from Missing Data"
ISERP Working Papers, 2004.
It is downloadable from here.
The paper considers two approaches to using multiple imputation (and also other methods of dealing with missing data) and propensity scores :
averaging of propensity scores after multiple imputation, followed by causal inference (method 2 in your post above)
causal inference using each set of propensity scores from the multiple imputations followed by averaging of the causal estimates.
Additionally, the paper considers whether the outcome should be included as a predictor in the imputation model.
Hill asserts that while multiple imputation is preferred to other methods of dealing with missing data, in general, there is no a priori reason to prefer one of these techniques over the other. However, there may be reasons to prefer averaging the propensity scores, particularly when using certain matching algorithms. Hill did a a simulation study in the same paper and found that averaging the propensity scores prior to causal inference, when including the outcome in the imputation model produced the best results in terms of mean squared error, and averaging the scores first, but without the outcome in the imputation model, produced the best results in terms of average bias (absolute difference between estimated and true treatment effect). Generally, it is advisable to include the outcome in the imputation model (for example see here).
So it would seem that your method 2 is the way to go.
Best Answer
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.