Research On The Criteria For Confounders In Survival Function

In recent years,causal inference plays a unique role in the fields of epidemiology,computer science,economics and social science.In causal inference,confounding bias caused by confounders often leads to paradoxes in observational studies,thus making it an important obstacle to the correct estimation of causal effects.So the researches of detecting confounders have important significance.In the field of causal inference in survival analysis,so far,there is no research of the criteria of detecting the confounders in survival function.This paper will focus on the methods of detecting the confounders in survival function,and several criteria are determined for use in practical problems,which is divided into the following six parts:In the first part,we mainly introduce the research background,significance,literature review of the criteria for confounders in survival analysis,as well as the main content and innovation of this paper.In the second part,under the assumption that the differentiation and integration between covariates and exposure variables in survival function can be interchanged,the uniformly collapsibility conditions of conditional dependence measure for survival function and residual life function are obtained by using the properties of conditional probability.Simultaneously,the average collapsibility conditions of conditional dependence measure for survival function and residual life function are also obtained.Finally,we obtain the average collapsibility conditions of conditional dependence measure for the average life and average residual life.The collapsibility-based criteria for detecting confounders in survival function are obtained.In the third part,we discuss the criteria for detecting confounders in the survival function under the condition that the response and covariates are both continuous.By the partition-based method,we obtain the necessary and sufficient conditions for determining whether a one-dimensional covariate is a uniformly irrelevant factor.Then the sufficient conditions for determining whether a multidimensional covariate is a conditional uniformly irrelevant factor vector are also obtained.We propose the comparability-based criteria for detecting a single confounder and multiple confounders in survival function.In the fourth part,the criteria for confounders in survival function based on the interaction under the condition that the covariate is continuous are discussed.When the covariate is one-dimensional,the necessary and sufficient conditions for the uniform non-confounding and uniformly irrelevant factor are obtained by utilizing the potential distribution difference of the covariate between the population and subpopulation.Then the sufficient conditions for the conditional uniform non-confounding and conditional uniformly irrelevant factor vector are also obtained when the covariate is multidimensional.Further,the collapsibility-based criteria for detecting a single confounder and multiple confounders in survival function based on the interaction are proposed.In the fifth part,a method to test the existence of confounding bias is proposed by using Cox model from the point of view of the equality of survival functions,and then we give a test method to determine whether a discrete covariate is a confounder.Finally,a numerical example is given to illustrate the practicability of this method.The sixth part summarizes and looks forward to the research content of the full text.