Construction and evaluation of optimal diagnostic tests with application to hepatocellular carcinoma diagnosis

Accurate diagnostic tests are crucial to ensure effective treatment, screening, and surveillance of diseases. However, the limited accuracy of individual biomarkers often hinders comprehensive screening. The heterogeneity of many diseases, particularly cancer, calls for the use of several biomarkers together into a composite diagnostic test. In this paper, we present a novel multivariate model that optimally combines multiple biomarkers using the likelihood ratio function. The model's parameters directly translate into computationally simple diagnostic accuracy measures. Additionally, our method allows for reliable predictions even in scenarios where specific biomarker measurements are unavailable and can guide the selection of biomarker combinations under resource constraints. We conduct simulation studies to compare the performance to popular classification and discriminant analysis methods. We utilize the approach to construct an optimal diagnostic test for hepatocellular carcinoma, a cancer type known for the absence of a single ideal marker. An accompanying R implementation is made available for reproducing all results.