# 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

### Abstract

Youden’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 =+= (x_{D}/n

_{D})+( x

_{H}/n

_{H}) where is an error estimate of false negative, is a false positive error estimate, x

_{D}is the frequency of (falsely) negatively classified persons out of n

_{D}diseased groups, and x

_{H}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 c

_{D}and c

_{H}in the form of =+=(x

_{D}+c

_{D})/(n

_{D}+2c

_{D})+(x

_{H}+c

_{H})(n

_{H}+2c

_{H}) The minimum Bayes risk approach is proposed in order to find the optimum points of c

_{D}and c

_{H}. Under each arm of prior errors ranged between 0 to 0.25, the optimal value of c

_{D}and c

_{H}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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