Performance of diagnostic tests based on continuous bivariate markers

In medical diagnostic research, it is customary to collect multiple continuous biomarker measures to improve the accuracy of diagnostic tests. A prevalent practice is to combine the measurements of these biomarkers into one single composite score. However, incorporating those biomarker measurements into a single score depends on the combination of methods and may lose vital information needed to make an effective and accurate decision. Furthermore, a diagnostic cut-off is required for such a combined score, and it is difficult to interpret in actual clinical practice. The paper extends the classical biomarkers' accuracy and predictive values from univariate to bivariate markers. Also, we will develop a novel pseudo-measures system to maximize the vital information from multiple biomarkers. We specified these pseudo-and-or classifiers for the true positive rate, true negative rate, false-positive rate, and false-negative rate. We used them to redefine classical measures such as the Youden index, diagnostics odds ratio, likelihood ratios, and predictive values. We provide optimal cut-off point selection based on the modified Youden index with numerical illustrations and real data analysis for this paper's newly developed pseudo measures.