Comparison of bayesian with the classical methods in estimating parameters of logistic regression and its application in respiratory

Logistic regression is an analytic tool widely used in medical and epidemiologic research. In many studies, we face data sets in which some of the data are not recorded. A simple way to deal with such "missing data" is to simply ignore the subjects with missing observations, and perform the analysis on cases for which complete data are available. We consider methods for analyzing logistic regression models with complete data recorded for some covariates (Z) but missing data for other covariates (X). When data on X are Missing At Random (MAR), we present a likelihood approach for the observed data that allows the analysis as if the data were complete. By this approach, estimation of parameters is done using both Maximum Likelihood and Bayesian methods through the Markov Chain Monte Carlo numerical computation scheme and the results are compared. The illustrative example considered in this article involves data from lung auscultations as part of a Health Survey in Tehran. In comparing different methods, Bayesian estimates using the model described in this study are much closer to those generated by analysis of the full data by the standard model.