Estimating causal effects for multivalued treatments: a comparison of approaches

Interventions with multivalued treatments are common in medical and health research, such as when comparing the efficacy of competing drugs or interventions, or comparing between various doses of a particular drug. In recent years, there has been a growing interest in the development of multivalued treatment effect estimators using observational data. In this paper, we compare the performance of commonly used regression-based methods that estimate multivalued treatment effects based on the unconfoundedness assumption. These estimation methods fall into three general categories: (i) estimators based on a model for the outcome variable using conventional regression adjustment; (ii) weighted estimators based on a model for the treatment assignment; and (iii) 'doubly-robust' estimators that model both the treatment assignment and outcome variable within the same framework. We assess the performance of these models using Monte Carlo simulation and demonstrate their application with empirical data. Our results show that (i) when models estimating both the treatment and outcome are correctly specified, all adjustment methods provide similar unbiased estimates; (ii) when the outcome model is misspecified, regression adjustment performs poorly, while all the weighting methods provide unbiased estimates; (iii) when the treatment model is misspecified, methods based solely on modeling the treatment perform poorly, while regression adjustment and the doubly robust models provide unbiased estimates; and (iv) when both the treatment and outcome models are misspecified, all methods perform poorly. Given that researchers will rarely know which of the two models is misspecified, our results support the use of doubly robust estimation.