Statistical inference for association studies in the presence of binary outcome misclassification

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 outcomes are correctly classified at least 50% of the time. A label switching correction is applied within estimation methods to recover unbiased effect estimates and to estimate misclassification rates in cases with one or more sequential observed outcomes. Open source software is provided to implement the proposed methods for single- and two-stage models. We give a detailed simulation study for our proposed methodology and apply these methods to data for single-stage modeling of the Medical Expenditure Panel Survey (MEPS) from 2020 and two-stage modeling of data from the Virginia Department of Criminal Justice Services.