  In the last decade, the secondary use of large data from health systems, such
as electronic health records, has demonstrated great promise in advancing
biomedical discoveries and improving clinical decision making. However, there
is an increasing concern about biases in association studies caused by
misclassification in the binary outcomes derived from electronic health
records. We revisit the classical logistic regression model with misclassified
outcomes. Despite that local identification conditions in some related settings
have been previously established, the global identification of such models
remains largely unknown and is an important question yet to be answered. We
derive necessary and sufficient conditions for global identifiability of
logistic regression models with misclassified outcomes, using a novel approach
termed as the submodel analysis, and a technique adapted from the
Picard-Lindel\"{o}f existence theorem in ordinary differential equations. In
particular, our results are applicable to logistic models with discrete
covariates, which is a common situation in biomedical studies, The conditions
are easy to verify in practice. In addition to model identifiability, we
propose a hypothesis testing procedure for regression coefficients in the
misclassified logistic regression model when the model is not identifiable
under the null.
