Multiplicity Adjustments for Differences in Proportion Parameters in Multiple-Sample Misclassified Binary Data

Generally, following an omnibus (overall equality) test, multiple pairwise comparison (MPC) tests are typically conducted as the second step in a sequential testing procedure to identify which specific pairs (e.g., proportions) exhibit significant differences. In this manuscript, we develop maximum likelihood estimation (MLE) methods to construct three different types of confidence intervals (CIs) for multiple pairwise differences in proportions, specifically in contexts where both types of misclassifications (i.e., over-reporting and under-reporting) exist in multiple-sample binomial data. Our closed-form algorithm is straightforward to implement. Consequently, when dealing with multiple sample proportions, we can readily apply MPC adjustment procedures—such as Bonferroni, Šidák, and Dunn—to address the issue of multiplicity. This manuscript advances the existing literature by extending from scenarios with only one type of misclassification to those involving both. Furthermore, we demonstrate our methods using a real-world data example.