Bias correction in logistic regression with missing categorical covariates

Logistic regression plays an important role in many fields. In practice, we often encounter missing covariates in different applied sectors, particularly in biomedical sciences. Ibrahim (1990) proposed a method to handle missing covariates in generalized linear model (GLM) setup. It is well known that logistic regression estimates using small or medium sized missing data are biased. Considering the missing data that are missing at random, in this paper we have reduced the bias by two methods; first we have derived a closed form bias expression using Cox and Snell (1968), and second we have used likelihood based modification similar to Firth (1993). Here we have analytically shown that the Firth type likelihood modification in Ibrahim led to the second order bias reduction. The proposed methods are simple to apply on an existing method, need no analytical work, with the exception of a little change in the optimization function. We have carried out extensive simulation studies comparing the methods, and our simulation results are also supported by a real world data.