Abstract
Use of a case-control design to compare the accuracy of two binary diagnostic tests is frequent in clinical practice. This design 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. This manuscript studies the comparison of the predictive values of two diagnostic tests subject to a case-control design. A global hypothesis test, based on the chi-square distribution, is proposed to compare the predictive values simultaneously, as well as other alternative methods. The hypothesis tests studied require knowing the prevalence of the disease. 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 proposed global hypothesis test was extended to the situation in which there are more than two diagnostic tests. The results have been applied to the diagnosis of coronary disease.
Highlights
The main parameters to assess and compare the accuracy of binary diagnostic tests (BDTs) are sensitivity and specificity
Regarding the method based on the individual hypothesis tests H0 : PPV1 = PPV2 and H0 : NPV1 = NPV2 to an error α = 5% each one of them, the type I error may clearly overwhelm the nominal error, especially when the correlations are not high
From the results obtained in the simulation experiments, we propose the following method to compare the predictive values (PVs) of two BDTs subject to a case-control design: (1) Applying the global hypothesis test based on the chi-square distribution (Equation (5)) to an α error; (2) If the global hypothesis test is not significant, the equality hypothesis of the PVs is not rejected; if the global hypothesis test is significant to an α error, the investigation of the causes of the significance is made by testing the individual tests (Equation (6)) and applying the Bonferroni method or the Holm method to an α error
Summary
The main parameters to assess and compare the accuracy of binary diagnostic tests (BDTs) are sensitivity and specificity. The comparison of the performance of two binary diagnostic tests is a topic of special importance in the study of statistical methods for the diagnosis of diseases This comparison is made through a paired-design or through a case-control design. Studied the joint comparison of the PPVs and NPVs of two BDTs, and proposed a global hypothesis test based on the chi-square distribution to simultaneously compare the PVs of two BDTs. In a case-control design, Mercaldo et al [9] have studied the estimation of the PVs of a BDT, assuming that the prevalence of the disease (p) is known.
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