Logistic regression with outcome and covariates missing separately or simultaneously

Estimation methods are proposed for fitting logistic regression in which outcome and covariate variables are missing separately or simultaneously. One of the two proposed estimators is an extension of the validation likelihood estimator of Breslow and Cain (1988). The other is a joint conditional likelihood estimator that uses both validation and non-validation data. Large sample properties of the proposed estimators are studied under certain regularity conditions. Simulation results show that the joint conditional likelihood estimator is more efficient than the validation likelihood estimator, weighted estimator, and complete-case estimator. The practical use of the proposed methods is illustrated with data from a cable TV survey study in Taiwan.