Ensemble and calibration multiply robust estimation for quantile treatment effect

Quantile treatment effects can be important causal estimands in the evaluation of biomedical treatments or interventions for health outcomes such as birthweight and medical cost. However, the existing estimators require either a propensity score model or a conditional density vector model is correctly specified, which is difficult to verify in practice. In this paper, we allow multiple models for propensity score and conditional density vector, then construct a class of calibration estimators based on multiple imputation and inverse probability weighting approaches via empirical likelihood. The resulting estimators multiply robust in the sense that they are consistent if any one of these models is correctly specified. Moreover, we propose another class of ensemble estimators to reduce computational burden while ensuring multiple robustness. Simulations are performed to evaluate the finite sample performance of the proposed estimators. Two applications to the birthweight of infants born in the United States and AIDS Clinical Trials Group Protocol 175 data are also presented.