Improved Estimation of Diagnostic Cut-Off Point Associated with Youden Index Using Ranked Set Sampling

Diagnostic cut-off point of biomarker measurements is needed for classifying a random subject to be either diseased or healthy. However, such cut-off point is usually unknown and needs to be estimated by some optimization criteria, among which, Youden index has been widely adopted in practice. Youden index, defined as max (sensitivity + specificity -1), directly measures the largest total diagnostic accuracy a biomarker can achieve. Therefore, it is desirable to estimate the optimal cut-off point associated with Youden index. Sometimes, taking the actual measurements of a biomarker is very difficult and expensive, while ranking them without actual measurements can be easy. In such cases, ranked set sampling would give more accurate estimation than simple random sampling, since ranked set samples are more likely to span the full range of population (thus is more representative). In this study, kernel density estimation is utilized to numerically solve for the nonparametric estimate of the optimal cut-off point. Intensive simulations are carried out to compare the proposed method using ranked set samples with the one using simple random samples and the proposed method outperforms universally with much smaller mean squared error (MSE). A real data set is analyzed for illustrating the proposed method.