Adjusted Estimator of the Sum of Misclassification Errors of Youden’s Index in Sparse Data of a Diagnostic Study

  • Kamonwan Soonklang Department of Biostatistics, Faculty of Public Health, Mahidol University, Bangkok 10400, Thailand.
  • Chukiat Viwatwongkasem Department of Biostatistics, Faculty of Public Health, Mahidol University, Bangkok 10400, Thailand.
  • Pratana Satitvipawee Department of Biostatistics, Faculty of Public Health, Mahidol University, Bangkok 10400, Thailand.
  • Rujirek Busarawong Department of Applied Statistics, Faculty of Science, King Mongkut’s Institute of Technology, Ladkrabang, Bangkok 10520, Thailand.
  • Ramidha Srihera Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Klongluang, Pathum Thani 12121, Thailand.
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 \hat{\lambda }=\hat{\alpha }+\hat{\beta }= (xD /nD)+( xH/nH ) where \hat{\alpha } is an error estimate of false negative, \hat{\beta } 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 \hat{\lambda ^{_{c}}}=\inline \hat{\alpha}_{CD}+\inline \hat{\beta }_{CH}=(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, \hat{\lambda }c , has the best performance with the smallest average mean square errors.
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