Sample size for comparing correlated concordance rates

We consider collecting the measurements of a gold standard and two methods with error from each site of subjects. We propose an asymptotic test statistic to compare the concordance rates of two methods with the gold standard and a closed-form sample size formula. Through simulations, we show that the test statistic accurately controls the type I error in small sample sizes, and the sample size formula accurately maintains the power in various settings. The proposed test statistic and the sample size formula can be easily modified for other indices for agreement such as sensitivity and specificity. A real eye study is taken as an example.