Beyond kappa: an informational index for diagnostic agreement in dichotomous and multivalue ordered-categorical ratings

Abstract

Agreement measures are useful tools to both compare different evaluations of the same diagnostic outcomes and validate new rating systems or devices. Cohen's kappa (κ) certainly is the most popular agreement method between two raters, and proved its effectiveness in the last sixty years. In spite of that, this method suffers from some alleged issues, which have been highlighted since the 1970s; moreover, its value is strongly dependent on the prevalence of the disease in the considered sample. This work introduces a new agreement index, the informational agreement (IA), which seems to avoid some of Cohen's kappa's flaws, and separates the contribution of the prevalence from the nucleus of agreement. These goals are achieved by modelling the agreement-in both dichotomous and multivalue ordered-categorical cases-as the information shared between two raters through the virtual diagnostic channel connecting them: the more information exchanged between the raters, the higher their agreement. In order to test its fair behaviour and the effectiveness of the method, IA has been tested on some cases known to be problematic for κ, in the machine learning context and in a clinical scenario to compare ultrasound (US) and automated breast volume scanner (ABVS) in the setting of breast cancer imaging. Graphical Abstract To evaluate the agreement between the two raters [Formula: see text] and [Formula: see text] we create an agreement channel, based on Shannon Information Theory, that directly connects the random variables X and Y, that express the raters outcomes. They are the terminals of the chain X⇔ diagnostic test performed by [Formula: see text] ⇔ patient condition[Formula: see text] ⇔ diagnostic test performed by [Formula: see text] ⇔ Y.

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