Inferences on the Weighted Kappa Coefficient of Binary Diagnostic Tests

Abstract

Diagnostic Methods are fundamental in Clinical Medicine and in Epidemiology. Therefore, part of the discipline of Statistics has focused on the development of new methods to solve the problems that have been posed in this field, leading to what are known as Statistical Methods for Diagnosis in Medicine. This doctoral thesis seeks to contribute to research into new methods of estimation of parameters of binary diagnostic tests. It focuses on the study of binary diagnostic tests, whose assessment in relation to a gold standard gives rise to a 2x2 table when there is a single diagnostic test, or a 2x4 table when there are two binary diagnostic tests. In all the situations analysed in this Thesis, it is assumed that the disease status of all the individuals in the sample, or samples, is known. This doctoral thesis is structured in three Chapters. In Chapter 1, the main parameters of a binary diagnostic test are defined and studied: sensitivity and specificity, likelihood ratios, predictive values and the weighted kappa coefficient. Chapter 2 studies the estimations of the parameters presented in Chapter 1 when the study is cross-sectional and when it is case-control. The cross-sectional study consists of the application of the binary diagnostic test and the gold standard to all the individuals in a random sample; and the case-control study consists of applying the binary diagnostic test to all of the individuals in two samples, one of individuals with the disease (case sample) and another of individuals without the disease (control sample). The contribution made by this Chapter is the estimation of the weighted kappa coefficient subject to case-control sampling. Several confidence intervals are studied for this parameter, Monte Carlo simulation experiments are carried out to study the asymptotic coverage of these intervals and a method is proposed to calculate the size of each sample. The results obtained are applied to real example. Chapter 3 studies two different problems: the comparison of parameters of two binary diagnostic tests subject to a paired design and the combination of parameters of two binary diagnostic tests. On the one hand, we present the hypothesis tests and confidence intervals to compare the parameters of two binary diagnostic tests, and on the other, we study the combination of parameters of two binary diagnostic tests. The contribution of this Chapter is the combination of the weighted kappa coefficients of two binary diagnostic tests in parallel testing, defining the weighted kappa coefficient of the combination of the two diagnostic tests and studying its properties. We have studied the conditions in which the combination of the two diagnostic tests produces an increase in the weighted kappa coefficient of the combination. Fieller’s method is applied to obtain a confidence interval for the ratio between the weighted kappa coefficient of the combination and each weighted kappa coefficient, and Monte Carlo simulation experiments are carried out to study the asymptotic behaviour of this interval. An R program is written to solve the problem posed and the results were applied to a real example.