Research On Robustness Of Causal Inference For Partial Linear Models

Causal inference is a subject developed based on statistics,which is devoted to exploring causal relationship between things.It is widely used in epidemiology,medicine,sociology,econometrics,behavioral science and other disciplines.Causal inference originally studied by using directed acyclic graph to express the unidirectional relationship between cause and result.However,the amount of data that graph model can handle is limited,and the algorithms based on graph model are mostly used in low-dimensional causal networks.In order to deal with more complex and higher dimensional data,scholars based on statistical model causal inference to deal with linear,nonlinear,continuous,discrete and other characteristics of complex data.This combination makes the application of causal inference more extensive.Confounding variable is the common causes of response variables and predictors in causal inference.If there exist confounding variable,it will lead to false correlation between dependent variables and independent variables,which will affect the conclusion of causal inference.Therefore,it is necessary to control the confounding variable as far as possible to ensure the correctness of inference.In reality,there is no way to control the potentially endless confounding variable.Therefore,it is great theoretical and practical significance to study the robustness of causal inference in the presence of confounding factors.This paper studies the influence of confounding variable on the robustness of causal inference in partial linear models.In the course of the study,we proposes an impact index to reflect the influence of confounding variable which suitable for partial linear model from the perspective of parameter significance test,in order to obtain the judgment criteria for judging whether causal inference is robust or not,we calculates threshold of the impact index.Finally,the rationality of the proposed theory is verified by data simulation and case analysis.The structure of this paper is as follows: Chapter 1 introduces the research background,theory and practical significance of this paper,and summarizes the research history and current situation of related problems and models.Chapter 2 gives a brief account of the theory of robustness of causal inference,and introduction some important theorems and properties involved.Chapter 3 establishes the theory of causal inference in partial linear models.In this chapter,we firstly use kernel technique to map the relation of partial linear into the reproducing kernel Hilbert space of higher dimension,so that it is linearly separable in the high dimension space.Then,according to the difference of model parameter significance test statistics between confounding variables and non-confounding variable,we quantify the influence of confounding variables on the parameters of partial linear model,and obtain the impact index of influence of confounding variables in partial linear model.Finally,according to the impact index of partial linear models,we get the criterion of whether the causal inference is robust or not.Chapter 4 illustrates the rationality of the proposed robust theory of causal inference for partial linear models by simulation.In chapter 5,we use two medical cases to describe the application of the robust theory of causal inference for partial linear models proposed in this paper in detail.The first is the analysis of the robustness of causal inference of dietary habits to hypertension addiction,and the second is the robustness of causal inference of metastasis of solitary-papillary thyroid carcinoma metastasis.To sum up,we establish a robustness theory of casual inference for partial linear model of confounding variable in this paper which have important theoretical significance and practical application value in the field of causal inference.