Estimation Of Treatment Effects In Nonlinear Models And Its Applications

In the fields of epidemiology,medicine,sociology,and economics,researchers are often concerned about the estimation of treatment effects.Since the effect size of policy intervention influences whether the policy needs to be widely implemented,and the size of the effect of a new drug influences whether or not a new drug is produced,the size of these effects can be characterized by the treatment effect.Therefore,the estimation of treatment effect is extremely important.In the disciplines of epidemiology,medicine,sociology and economics,many response variables are discrete,so it is important to estimate the treatment effects in nonlinear models.Due to the particularity of the nonlinear model and the existence of unobservable and heterogeneous variables in the model,the general estimation method of average treatment effects is not suitable for the nonlinear model.In this paper,we mainly consider the estimation method of treatment effects in nonlinear model and apply the theoretical method to real data analysis.In this paper,our main research work is as follows.(1)Given the probit model with heterogeneity between groups in the matchedpairs data,when there are large differences between groups(group effects are large),we propose a new method to estimate the treatment effect in models,and theoretically prove that the proposed estimator is consistent and asymptotic normal.In addition,the simulation study show that the proposed estimators have well properties of small samples,and when the group effect is bimodal and asymmetric,the proposed estimator is superior to the Heckman method,the proposed estimator is better than inverse probability weighting estimator and conditional likelihood estimator in terms of Bias and RMSE.The proposed method was applied to the effect of maternal smoking during pregnancy on the low birth weight infants.(2)Considering nonlinear models with unobservable confounders,we allows the unobserved confounders for distinct individuals to be heterogeneous.When the unobserved confounder is large,we propose a new method to estimate the treatment effect in the nonlinear model and a statistic to test the existence of the treatment effect in the nonlinear model,and theoretically prove that the proposed estimator is consistent and asymptotically normal.The simulation results show that the proposed estimation method is robust for all kinds of unobserved confounding distributions,and the proposed estimation method is not change the direction of treatment effects in the model.We applied the proposed method to estimate the effect of maternal alcohol consumption during pregnancy on low birth weight infants.(3)Considering nonlinear models,it allows the influence directions of unobservable confounding on treatment variables and outcome variables are inconsistent,and the relationship between unobserved confounders and random terms is arbitrary.We take advantage of the quasi-likelihood method to estimate the treatment effect in models,and prove that the quasi-likelihood estimator is consistent and asymptotically normal relative to the pseudo-true parameter,and the proposed quasi-likelihood estimator is superior to the special regression estimator when the treatment variable is weak endogeneity.We applied the proposed theory to evaluate the impact of having private health insurance on patient’s decisions for making medical visits.