Maximum likelihood estimation for the proportion difference of two-sample binomial data subject to one type of misclassification

In this manuscript, we derived three likelihood-based interval estimation methods using a closed-form algorithm for the difference of two independent binomial proportion parameters with one type of misclassification. We acquired an identifiable model by using a double-sampling scheme. We also employed simulations to examine the robustness of our three likelihood-based interval estimation methods and summarize that our modified Wald method implemented to new data with Agresti-Coull type of adjustment performs well and has nominal coverage probabilities. This method was adapted to traffic data for an illustration.