Multiply Robust Estimation Of Multivalued Treatment Effects With Missing Data

In recent years,there has been a growing interest in the development of multivalued treatment effect estimators using observational data.It is often the case that the outcome is missing in practice,which brings great challenges to the estimation of treatment effects.Based on the idea of inverse probability weighting(IPW),we propose a double inverse probability weighting method to estimate the multivalued average treatment effect(ATE)and quantile treatment effect(QTE)with response missing at random,and further propose a multiply robust estimator.In the proposed multiply robust estimator,we consider multiple candidate models for the propensity score and the probability of being observed,respectively,as long as the candidate models for the propensity score contain the correct model and so does the candidate models for the probability of being observed,the ATE and QTE estimators are root-n consistent and asymptotic normal.We assess the performance of the proposed estimator by simulation studies,and the results verify the superiority and robustness of the proposed estimator.Finally,this paper analyzes the real data CHARLS with about 21% of the outcome missing,and quantitatively studies the average treatment effects and quantile treatment effects of three types of social activities on cognitive function of middle-aged and elderly people in China.