Comparison of the predictive values of diagnostic tests subject to a case-control sampling with application to the diagnosis of Human African Trypanosomiasis

Abstract

Case-control sampling to compare the accuracy of two binary diagnostic tests is frequent in clinical practice. This type of sampling consists of applying the two diagnostic tests to all of the individuals in a sample of those who have the disease and in another sample of those who do not have the disease. In this sampling, the sensitivities are compared from the case sample applying the McNemar’s test, and the specificities from the control sample. Other parameters of binary tests are the positive and negative predictive values. The predictive values of a diagnostic test represent the clinical accuracy of a binary diagnostic test when it is applied to the individuals in a population with a determined disease prevalence. This article studies the comparison of the predictive values of two diagnostic tests subject to a case-control sampling. A global hypothesis test, based on the chi-square distribution, is proposed to compare the predictive values simultaneously. The comparison of the predictive values is also studied individually. The hypothesis tests studied require knowledge of the disease prevalence. Simulation experiments were carried out to study the type I errors and the powers of the hypothesis tests proposed, as well as to study the effect of a misspecification of the prevalence on the asymptotic behavior of the hypothesis tests and on the estimators of the predictive values. The results obtained were applied to a real example on the diagnosis of the Human African Trypanosomiasis. The model proposed was extended to the situation in which there are more than two diagnostic tests.