A comparative study of methods for logistic regression with separated or nearly separated data

Abstract

Objective To introduce a comparative study of methods for Logistic regression with separated or nearly separated data. Methods Human immunodeficiency virus (HIV) infection and its influential factors, 75 drug users were analyzed by maximum Likelihood estimate, exact Logistic regression and Firth's penalized maximum Likelihood estimate, then results of the three methods were compared. Results Both of penalized maximum Likelihood estimation and exact Logistic regression produced valid parameter estimates and confidence interval of the latter was wider. The results of penalized maximum Likelihood estimation and exact Logistic regression showed that race was significantly associated with HIV infection, and Yi people with HIV infection was higher than Han people. Conclusions The maximum Likelihood estimate for separated or nearly separated data is invalid. However, exact Logistic regression and Firth's penalized maximum Likelihood estimate can get valid estimates. Since exact Logistic regression have problems of complex calculations, over-conditioning and conditional distributions degenerated, Firth's penalized maximum Likelihood estimate is recommended to Logistic regression with separated or nearly separated data.