Adjusted Estimator of the Sum of Misclassification Errors of Youden’s Index in Sparse Data of a Diagnostic Study
Keywords: Diagnostic test, misclassification errors, Youden’s Index, zero variance correction
AbstractYouden’s index as a common measure of the accuracy of diagnostic test is defined by sensitivity + specificity −1 . In estimating the sum of two misclassification errors of Youden’s index, the conventional estimator, defined by =+= (xD /nD)+( xH/nH ) where is an error estimate of false negative, is a false positive error estimate, xD is the frequency of (falsely) negatively classified persons out of nD diseased groups, and xH is the frequency of (falsely) positively classified persons out of nH healthy ones, may have a considerable problem of zero variance in sparse data. The simple way to solve this problem is to add the constants cD and cH in the form of =+=(xD+cD)/(nD+2cD)+(xH+cH)(nH+2cH) The minimum Bayes risk approach is proposed in order to find the optimum points of cD and cH . Under each arm of prior errors ranged between 0 to 0.25, the optimal value of cD and cH equals 5/14. The simulation techniques are provided to confirm that the simple adjusted estimator, c , has the best performance with the smallest average mean square errors.
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