An Extended Mcnemar Test for Comparing Correlated Proportion of Positive Responses


The area under a ROC curve (AUC) is an important summary measures useful in assessing the accuracy of a diagnostic test in discriminating true disease status when the data for measurement is paired. This assessment is most important when the AUCs of different diagnostic test procedures are compared. These comparisons are not without some problem associated with it such as the inability of some test such as the McNemar test to adjust for the possible presence of ties in the data, thereby leading to erroneous conclusions in data analysis occasioned by committing Type II error more often than not. This is evident when the use of the traditional McNemar test in data analysis yielded high value of variance and low chi-square value thereby making one to accept a false null hypothesis more often than expected. To be able to tackle this challenge, we extend the usual McNemar test adopted by Sumi et al by adjusting for the possible presence of ties in the data when measurements of data may be on any scale. The extended McNemar test can enable one to easily estimate the probability that randomly selected pair of subjects from two diagnostic test procedures respond positive or both respond negative and it can be used to test the null hypothesis of equality of proportion of positive responses in two diagnostic test procedures. An extensive simulation study was carried out to determine the Type I error and statistical power of the existing and extended tests and the application of the tests to standard and real data, was carried out and result showed that in all the McNemar test demonstrates superior statistical power and less conservative type I error compared to DeLong et al area test, Bandos et al area test and the usual McNemar area test and so compares favorably.

Keywords: correlated data, diagnostic tests, extended mcnemar test, nonparametric test, positive response, type ii error

Article Review Status: Published

Pages: 49-80 (Download PDF)

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