Likelihood-based confidence intervals for the risk difference of two-sample binary data with a fallible classifier and a gold standard

We develop likelihood-based confidence intervals for risk difference in two-sample misclassified binary data. Such data consist of two studies. The first study is the main study where individuals are classified by an inexpensive fallible classifier which may misclassify. The second study is a validation substudy where individuals are classified by using both the fallible classifier and an expensive gold standard which classifies perfectly. We propose and examine three likelihood-based confidence interval methods and conclude that the modified Wald method applied to small-number adjusted new data performs well and has nominal coverage probabilities.