Multiple imputation procedures for estimating causal effects with multiple treatments with application to the comparison of healthcare providers.

Choosing between multiple healthcare providers requires us to simultaneously compare the expected outcomes under each provider. This comparison is complex because the composition of patients treated by each provider may differ. Similar issues arise when simultaneously comparing the adverse effects of interventions using non-randomized data. To simultaneously estimate the effects of multiple providers/interventions we propose procedures that explicitly impute the set of potential outcomes for each subject. The procedures are based on different specifications of the generalized additive models (GAM) and the Bayesian additive regression trees (BART). We compare the performance of the proposed procedures to previously proposed matching and weighting procedures using an extensive simulation study for continuous outcomes. Our simulations show that when the distributions of the covariates across treatment groups have adequate overlap, the multiple imputation procedures based on separate BART or GAM models in each treatment group are generally superior to weighting based methods and have similar and sometimes better performance than matching on the logit of the generalized propensity score. Another advantage of these multiple imputation procedures is the ability to provide point and interval estimates to a wide range of causal effect estimands. We apply the proposed procedures to comparing multiple nursing homes in Massachusetts for readmission outcomes. The proposed approach can be applied to other causal effects applications with multiple treatments.