Semiparametric analysis of randomized response data with missing covariates in logistic regression

In this article, two semiparametric approaches are developed for analyzing randomized response data with missing covariates in logistic regression model. One of the two proposed estimators is an extension of the validation likelihood estimator of Breslow and Cain [Breslow, N.E., and Cain, K.C. 1988. Logistic regression for two-stage case-control data. Biometrika. 75, 11–20]. The other is a joint conditional likelihood estimator based on both validation and non-validation data sets. We present a large sample theory for the proposed estimators. Simulation results show that the joint conditional likelihood estimator is more efficient than the validation likelihood estimator, weighted estimator, complete-case estimator and partial likelihood estimator. We also illustrate the methods using data from a cable TV study.