Abstract
Currently, assessing superiority of a diagnostic test requires cumbersome calculations and confusing interpretations because of nonlinear Receiver Operating Characteristic Curve (ROC). To remedy these difficulties, this article prepares, provides an easier alternate geometric approach. That is, a simple but more effective visual approach with two complementary mosaic masonries are constructed with their properties, superimposed and utilized. First masonry is conditional on disease status. The second masonry is conditional on test outcomes. By superimposing both masonries and visualizing their overlap territory, our approach utilizes an angle, θ to assess superiority of a diagnostic test. A hypothesis testing procedure is also devised to compute the significance level of an estimated angle. The statistical power to accept a true angle is developed in the procedure. In the end, the concepts, properties and advantages of mosaic masonries are illustrated using medical and public health data sets.
Highlights
Mosaic masonry to be constructed in this article based on Positive Predictive Value (PPV) and NPV is a better alternate to the restrictive measure J about the superiority of a diagnostic test
A mosaic masonry connecting sensitivity and specificity can be constructed in a unit square, as in Fig
Based on the complementary mosaic masonries which are introduced in this article, it is quite simple and easy to visualize how superior is a diagnostic test without conditioning on test results or on the presence or absence of disease status
Summary
A prelude to select a suitable medical treatment, a physician or surgeon demands the patient to undergo a diagnostic test. H−D = (1-π)Se signify alternate discards respectively in the sets (+, D) and (-, D) These harmonies and discards are complementary basis to formulate an alternate mosaic masonry later in the article. A mosaic masonry to be constructed in this article is a better alternate to the disadvantageous Youden Index, I. The mosaic area denotes superiority of a diagnostic test in the same conditional scenario of Youden index but is more a visual. Shanmugam (2008) for definition and properties of the index, J This index is a restrictive measure to indicate superiority of a diagnostic test only in a given scenario of details about test results. Mosaic masonry to be constructed in this article based on PPV and NPV is a better alternate to the restrictive measure J about the superiority of a diagnostic test.
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