Abstract:
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It is important to develop classification methods and predictive modeling when there is significant sample size balance and heterogeneity between two or more classes. A useful method for deriving the optimal threshold is based on the Youden's index (YI), which is a function of the sensitivity (the true positive fraction) and specificity (the negative positive fraction) against a binary gold standard. In this research, a generalized YI, called the GYI, is proposed to account for the following, respectively: (1) Unequal sample sizes, e.g., those of two groups based on a gold standard; (2) Multiple ordinal classes, e.g., order-restricted groups (e.g., monotherapy vs. combination therapy or placebo vs. higher dose levels); (3) Multiple nominal classes, e.g., different competing therapies. The GYI may be estimated using receiver operating characteristics (ROC) curve analysis, which helps derive optimal thresholds for discriminant purposes. We illustrate the GYI estimates using existing data from the literature, under the normality or alternative assumptions. Monte-Carlo simulations are performed to compare their performance.
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