Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification

In this paper we derive five first-order likelihood-based confidence intervals for a population proportion parameter based on binary data subject to false-positive misclassification and obtained using a double sampling plan. We derive confidence intervals based on certain combinations of likelihood, Fisher-information types, and likelihood-based statistics. Using Monte Carlo methods, we compare the coverage properties and average widths of three new confidence intervals for a binomial parameter. We determine that an interval estimator derived from inverting a score-type statistic is superior in terms of coverage probabilities to three competing interval estimators for the parameter configurations examined here. Utilizing the expressions derived, we also determine confidence intervals for a binary parameter using real data subject to false-positive misclassification.