Variable Selection For Causal Inference

In causal inference,comparing with randomized controlled trials,estimating causal effects from observational data has become an attractive research direction,and various methods for estimating causal effects from observational data have emerged at the historic moment,among which propensity score method is widely used.Traditionally,all covariates are used to estimate the propensity score,but doing so will affect the deviation and statistical efficiency of the propensity score estimation.In particular,the inclusion of variables that affect the treatment but not the outcome will increase the standard error but not decrease the deviation,while the inclusion of variables that affect the outcome but not the treatment will improve the accuracy.This paper aims to estimate the average treatment effect under the condition of high dimensional covariates.By using variable selection method the outcome-adaptive Lasso to identify important covariates for estimating propensity score,compared with traditional Logistic model to estimate propensity score,this paper uses binary quantile regression model,and finally uses inverse probability weighting method to estimate average treatment effect.The theoretical and simulation results show that the variable selection method based on binary quantile regression model is indeed better than the method based on Logistic model in the estimation deviation and standard error of average treatment effect,and inherits the Oracle property of the outcome-adaptive Lasso method based on Logistic model.