Cohen’s Kappa Coefficient as a Measure to Assess Classification Improvement following the Addition of a New Marker to a Regression Model

The need to search for new measures describing the classification of a logistic regression model stems from the difficulty in searching for previously unknown factors that predict the occurrence of a disease. A classification quality assessment can be performed by testing the change in the area under the receiver operating characteristic curve (AUC). Another approach is to use the Net Reclassification Improvement (NRI), which is based on a comparison between the predicted risk, determined on the basis of the basic model, and the predicted risk that comes from the model enriched with an additional factor. In this paper, we draw attention to Cohen's Kappa coefficient, which examines the actual agreement in the correction of a random agreement. We proposed to extend this coefficient so that it may be used to detect the quality of a logistic regression model reclassification. The results provided by Kappa's reclassification were compared with the results obtained using NRI. The random variables' distribution attached to the model on the classification change, measured by NRI, Kappa, and AUC, was presented. A simulation study was conducted on the basis of a cohort containing 3971 Poles obtained during the implementation of a lower limb atherosclerosis prevention program.