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.

翻译：准确的诊断测试对于确保疾病的有效治疗、筛查和监测至关重要。然而，单一生物标志物的有限准确性常常阻碍了全面筛查的实施。许多疾病（尤其是癌症）的异质性要求将多种生物标志物联合使用，以形成复合诊断测试。本文提出了一种基于似然比函数的多变量模型，能够最优地组合多种生物标志物。该模型的参数可直接转化为计算简单的诊断准确性指标。此外，我们的方法即使在部分特定生物标志物测量值缺失的情况下也能提供可靠的预测，并可在资源受限时指导生物标志物组合的选择。我们通过模拟研究将该方法的性能与流行的分类和判别分析方法进行了比较。同时，该方法被用于构建肝细胞癌（一种缺乏单一理想标志物的癌症类型）的最优诊断测试。我们提供了配套的R语言实现代码，用于复现所有结果。