Causal inference for multi-level treatments with machine-learned propensity scores

Propensity score-based methods have been widely developed to adjust for confounders in observational studies to estimate causal treatment effect for binary treatments. We generalize these causal inference methods to the multi-level treatment case. We review the generalized causal inference framework and several propensity score estimation methods. We conduct a comprehensive simulation study to evaluate the performance of multinomial logistic regression, generalized boosted models, random forest and data adaptive matching score for estimating propensity scores based on inverse probability of treatment weighting. From our findings, multinomial logistic regression is susceptible to yielding extreme weights while a mis-specified model is assumed, which results in poor performance of the inverse probability weighted estimator. On the other hand, machine-learned propensity scores tend to have less biased and more stable performance, and the data adaptive matching score tends to perform the best overall. The above-mentioned propensity score based methods are applied to the Taobao dataset to evaluate the causal effect of reputation on sales.