Causal Inference Of Multivariate Treatment Variables Based On Generalized Propensity Score

The weighting method via generalized propensity score is a common method to estimate the causal effect of continuous treatment variables.This method requires a more accurate estimation of generalized propensity score.The covariate balancing generalized propensity score method proposed by Fong et al.in 2018 improves the robustness of the generalized propensity score estimation of continuous treatment variables.In this paper,we extend this method to the case of multivariate treatment variables,and give the multivariate treatment variables covariate balancing generalized propensity score method（MCBGPS）.This method is a parametric method.The main idea is to construct a parametric model of generalized propensity score,construct a stablized weight based on the generalized propensity score,optimize the covariate balance by minimizing the weighted correlation coefficient between multivariate treatment variables and covariates,construct the moment conditions,and obtain the parameter estimation of the generalized propensity score model through the generalized method of moments.Then,based on the estimated weight,the causal effect estimation of multivariate treatment variables is obtained by using the inverse probability weighting method.In addition,we also give the asymptotic properties of the estimation.In the simulation study,the performance of this method in different situations is evaluated by specifying different generalized propensity score models and response variable models.The simulation results show that this method is more robust than using the traditional maximum likelihood method to estimate the generalized propensity score.Finally,we apply the method proposed in this paper to the annual medical expenditure survey data of the United States in 1987 to study the influence of smoking behavior on medical expenditure.