Hi, Luca:

Here is an article which discusses propensity score weighting to estimate causal effects in multivalued treatments, which may be of interest:

• Linden, A., & Yarnold, P.R. (2016). Combining machine learning and propensity score weighting to estimate causal effects in multivalued treatments. Journal of Evaluation in Clinical Practice, 22, 875-885. DOI: 10.1111/jep.12610

And here is an article discussing how to compute maximum-accuracy propensity score weights, which may be of interest:

• Linden, A., & Yarnold, P.R. (2017). Using classification tree analysis to generate propensity score weights. Journal of Evaluation in Clinical Practice, 23, 703-712. DOI: 10.1111/jep.12744

A Stata interface to the maximum-accuracy software needed to conduct these analyses is available:

• https://odajournal.com/2020/02/27/implementing-oda-from-within-stata-assessing-covariate-balance-in-observational-studies-invited/
• https://odajournal.com/2020/02/02/implementing-oda-from-within-stata-an-application-to-estimating-treatment-effects-using-observational-data-invited/