International Research Journal of Natural Sciences (IRJNS)

EA Journals

Predicted Probability

Comparison of Two or More Correlated AUCS in Paired Sample Design (Published)

The performance of a diagnostic test when test results are measured on a binary or ordinal scale can be evaluated using the measures of sensitivity and specificity. In particular, when it is measured on a continuous scale, the assessment of the performance of a diagnostic test is always over the range of possible cut-off points for the predictor variable. This is achieved by the use of a receiver operating characteristic (ROC) curve which is a graph of sensitivity against 1-specificity across all possible decision cut-offs values from a diagnostic test result. This curve evaluates the diagnostic ability of tests to discriminate the true state of subjects and compare the performance of two alternative diagnostic tests performed on the same subject. These tasks of comparing diagnostic tests is always better achieved using a summary measure of accuracy across all possible ranges of cut-off values called the area under the receiver operating characteristic curve (AUC).So many parametric and nonparametric methods exist for comparing two or more correlated AUCs in diagnostic tests when the data is paired. In this paper, we proposed a simple and easy to understand chi-square method of comparing two or more AUCs in a paired sample design. The proposed method which does not require the knowledge of true status of subjects or gold standard in evaluating the accuracy of tests unlike the existing methods, it offers reliable statistical inferences even in small sample problems and circumvent the difficulties of deriving the statistical moments of complex summary statistics as seen in the Delong et al method. The proposed method provides for further analysis to determine the possible reason for rejecting the null hypothesis of equality of AUCs. The proposed method when applied on real data, was shown to be better than the Delong et al method as it avoids the lengthy and more difficult procedures of estimating the variances of two AUCs as a way of determining if two AUCs differ significantly. The method is validated using the Cochran Q test and was shown to compare favourably.  

Keywords: AUC, Chi-Square Test, Cochran Q Test, Cut-Off Value, Delong et al, Dichotomous Data, Predicted Probability, ROC

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