  In biomedical and public health association studies, binary outcome variables
may be subject to misclassification, resulting in substantial bias in effect
estimates. The feasibility of addressing binary outcome misclassification in
regression models is often hindered by model identifiability issues. In this
paper, we characterize the identifiability problems in this class of models as
a specific case of ''label switching'' and leverage a pattern in the resulting
parameter estimates to solve the permutation invariance of the complete data
log-likelihood. Our proposed algorithm in binary outcome misclassification
models does not require gold standard labels and relies only on the assumption
that the sum of the sensitivity and specificity exceeds 1. A label switching
correction is applied within estimation methods to recover unbiased effect
estimates and to estimate misclassification rates. Open source software is
provided to implement the proposed methods. We give a detailed simulation study
for our proposed methodology and apply these methods to data from the 2020
Medical Expenditure Panel Survey (MEPS).
