Average kappa coefficient: a new measure to assess a binary test considering the losses associated with an erroneous classification

The weighted kappa coefficient of a binary diagnostic test (BDT) is a measure of performance of a BDT, and is a function of the sensitivity and the specificity of the diagnostic test, of the disease prevalence and the weighting index. Weighting index represents the relative loss between the false positives and the false negatives. In this study, we propose a new measure of performance of a BDT: the average kappa coefficient. This parameter is the average function of the weighted kappa coefficients and does not depend on the weighting index. We have studied three asymptotic confidence intervals (CIs) for the average kappa coefficient, Wald, logit and bias-corrected bootstrap, and we carried out some simulation experiments to study the asymptotic coverage of each of the three CIs. We have written a program in R, called ‘akcbdt’, to estimate the average kappa coefficient of a BDT. This program is available as supplementary material. The results were applied to two examples.