Application of Bayesian Method in Parameters Estimation of Logistic Regression Model with Missing at Random Covariate

Logistic Regression is a general model for medical and epidemiological data analysis. Recently few researchers have directed their studies to analysis of Logistic Regression with missing value at covariate variable. While the missing is a major threat in results authenticity of data set, in many studies the researchers face data with missing value and it is difficult to avoid such a case in studies.
Material & Satten and Carroll, in the case of completely observed value of covariate variable and some covariate variable with missing at random mechanism (MAR), introduced a special likelihood function for parameters estimation of Logistic Regression model. In this research the above- mentioned likelihood function has been used in Bayesian analysis for parameters estimation of Logistic Regression model and the conclusions are compared with the Multiple Imputation method and Complete Case method. The above-mentioned methods were applied on both simulation data and dentistry data and concluded that The parameters estimation from SCMCMC method had less variance in comparison with parameters estimation from Multiple Imputation and Complete Case methods. After comparison of the three mentioned methods results it had been concluded that if the mechanism is of missing at random the application of Bayesian analysis with MCMC causes to more accurate estimation and shorter Confidence Intervals than the Multiple Imputation method and Complete Case.