Likelihood methods for missing covariate data in highly stratified studies

The paper considers canonical link generalized linear models with stratum-specific nuisance intercepts and missing covariate data. This family includes the conditional logistic regression model. Existing methods for this problem, each of which uses a conditioning argu- ment to eliminate the nuisance intercept, model either the missing covariate data or the missingness process. The paper compares these methods under a common likelihood framework. The semiparametric efficient estimator is identified, and a new estimator, which reduces dependence on the model for the missing covariate, is proposed. A simulation study compares the methods with respect to efficiency and robustness to model misspecification.