Combination of the weighted kappa coefficients of two binary diagnostic tests.

The combination of two binary diagnostic tests in order to increase the accuracy of the diagnosis of a disease is a frequent procedure in clinical practice. When considering the losses associated with an erroneous classification with a binary diagnostic test, the parameter that is used to assess the diagnostic test is the weighted kappa coefficient. The weighted kappa coefficient depends on the sensitivity and the specificity of the diagnostic test, on the disease prevalence and on the weighting index. In this article, we study the combination of the weighted kappa coefficients of two binary diagnostic tests, defining the parameters and studying the conditions under which the combination of the two diagnostic tests increases the value of the weighted kappa coefficient of the combination. The Fieller method has been applied to obtain a confidence interval for the ratio between the combined weighted kappa coefficient and the weighted kappa coefficient of each diagnostic test. A program in R has been written to solve the problem studied and it is available as complementary material. The results have been applied to a real example.