Estimation of parameters of logistic regression with covariates missing separately or simultaneously

A joint conditional likelihood (JCL) method, which is a semiparametric approach, is proposed to estimate the parameters of a logistic regression model when two covariate vectors are missing separately or simultaneously. The proposed method uses one validation and three non validations data sets; it is an extension of the method of Wang et al. who studied the case of one covariate missing at random. The asymptotic results of the JCL estimators are established under the assumption that all covariate variables are categorical. Simulation results show that the proposed method is the most efficient compared to the complete-case, semi-parametric inverse probability weighting, and validation likelihood methods. The proposed methodology is illustrated by a real data example.