  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.
