We describe an estimator of the parameter indexing a model for the conditional odds ratio between a binary exposure and a binary outcome given a high-dimensional vector of confounders, when the exposure and a subset of the confounders are missing, not necessarily simultaneously, in a subsample. We argue that a recently proposed estimator restricted to complete-cases confers more protection to model misspecification than existing ones in the sense that the set of data laws under which it is consistent strictly contains each set of data laws under which each of the previous estimators are consistent.