Effect Estimation And Inference In Linear Mediation Model

Causal mediation analysis is a mechanism to identify and explain the relationship between independent variables and dependent variables through mediated variables.At present,the research of mediation analysis mainly focuses on the inference of natural direct and indirect effects,and few studies about the estimation and distribution of effects are carried out.In this dissertation,the natural direct and indirect effects are estimated in the simple mediation model,the mediation model with confounding variables,the mediation model with interaction and the mediation model with multiple mediated variables,and the distributions of estimators are obtained by Delta method.The main work of this paper includes the following four parts.In the first part,for the setting of single mediated variable,the structural equation about independent variable,mediated variable and dependent variable is established by the linear regression.The parameter estimators and indirect effect estimator are obtained by maximum likelihood estimatie method,and the asymptotic normal distribution of indirect effect estimator is obtained by Delta method.We consider simulation studies under the limited sample to show that our proposed method performs well.Finally,we apply our proposed method to evaluate the mediated role of DNA methylation CpG sites in the causal path from socioeconomic index to body mass index.In the second part,for the causal mediation model with confounding variables,the structural equation is established by linear regression,and the parameter estimators are obtained by least square estimate.The estimators of natural direct effects and natural indirect effects obtained by the properties of normal distribution and Delta method obey the asymptotic normal distribution.We conduct simulation studies under the limited sample to illustrate the effectiveness of our method,and analyze a set of real data.In the third part,for the causal mediation model with interaction,the structural equation is established by using linear regression,and the expressions of indirect effect and direct effect are given based on counterfactual framework.The maximum likelihood estimators of indirect effect and direct effect are obtained,and the distributions of effect estimators are obtained by Delta method.We conduct simulation studies under the limited sample to illustrate the effectiveness of our method,and analyze a set of real data.In the fourth part,for the causal mediating model with both continuous and binary mediated variables,the structural equation is established by using linear regression and Logit regression,and the definitions of indirect effect and direct effect based on counterfactual framework are given,and the effect expression is derived.The natural direct and indirect effect estimators are obtained by maximum likelihood estimate and gradient descent methods,and the distributions of effect estimators are obtained by Delta method.The simulation results show that our proposed methods has good performance.Finally,we apply our methods to the data of physical obesity.Figure 8 table 8 reference 54...