Multiply robust estimation for general multivalued treatment effects with missing outcomes

Interventions with multivalued treatments are common in medical and health research, leading to a growing interest in developing estimators for multivalued treatment effects using observational data. In practice, missing outcome data is a common occurrence, which poses significant challenges to the estimation of treatment effects. In this paper, we propose two multiply robust estimators for estimating the general multivalued treatment effects with outcome missing at random, including the average treatment effect (ATE), quantile treatment effect (QTE), and expectile treatment effect (ETE). The resulting estimators are root-n consistent and asymptotically normal, provided that the candidate models for the propensity score contain the correct model, and so do the candidate models for either the probability of being observed or outcome regression. Extensive simulation studies are conducted to investigate the finite-sample performance of the proposed estimators. The proposed methods are also applied to a real-world dataset of the Chinese Health and Retirement Longitudinal Study (CHARLS) with about 21% outcome missing, estimating the ATE, QTE and ETE of three types of social activities on the cognitive function of middle-aged and elderly people in China.