Study On Statistical Methods Of Missing Data And Sensitivity Analysis

Missing data is a common problem in statistical analysis.Traditional analysis methods can not be directly applied to missing data.Therefore,the study of missing data statistical methods is becoming a hot issue.Methods of analysis for missing data can be divided into three categories: likelihood methods,weighting methods,and imputation methods.Likelihood methods are often used as an aid to imputation methods.Among the weighting methods,inverse probability weighting and augmented inverse probability weighting methods are more popular.Multiple imputation is widely used as a imputation method.The existing research m ainly focuses on the method of problem that misses covariate or response variable only.There are few studies on the possible absence of both.The study of such issues is not simply a simple nesting of single absence,and it will face new challenges.In this paper,a combination of theoretical study and simulation study is used to the problem that probably misses covariate and response variable both.The main contents and result of this paper are as follows:First,the general form of inverse probability w eighted and augmented inverse probability weighted estimation equations is generalized.The key to the study of these two methods is to establish a propensity score model.In order to ensure the consistency of the model,this paper models the propensity sc ores by establishing the marginal conditional densities of the response variable indicator variables and the covariate indicator variables,respectively.As a generalization of inverse probability weighting,augmented inverse probability weighting improves the instability of inverse probability weighting by introducing a working model.This paper analyzes the method of establishing propensity score model and working model in detail,thereby generalizes the general form of estimating equations of the two methods.The aversion parameters in the modeling are estimated using the methods suggested by Robins,Rotnitzky,and Zhao in the literature.Second,the general form of multiple imputation estimation equations is generalized.The modeling method of the imputation model and the extraction of the imputation value of the special distribution are analyzed in detail.The steps of extracting the imputation value of the sample importance resample method are introduced in detail and the rationality of the imputation v alue is proved.Finally,on the basis of theoretical study,simulation studies compare the estimated effects of the three methods and compare them with the results of the complete case estimation.Because the validity of the estimation depends on the modeling correctly,and the model test of such problem lacks a uniform evaluation standard,therefore,this paper further studies the estimate performance of the three methods under the misspecification and compares it with the complete case analysis.This paper uses the bias and mean square error to evaluate the performance of the estimate.