Development of a Diagnostic Evaluation Framework of Correlated Biomarkers for Survival Outcome Using Nested Copula Models

Abstract

Robust evaluation of biomarker performance for survival outcomes is critical in precision medicine, particularly when multiple, dependent biomarkers are involved. Traditional regression based approaches typically focus on marginal effects and overlook inter-marker dependencies, often treating them merely as sources of multicollinearity. To address this limitation, we propose a diagnostic evaluation framework based on fully nested Archimedean copulas (FNACs), which flexibly model the joint distribution of two dependent biomarkers and a survival outcome. FNACs accommodate hierarchical, asymmetric dependence, enabling simultaneous modeling of both inter-marker and marker–outcome relationships within a unified probabilistic framework. This approach is particularly useful for evaluating the contribution of a new biomarker in the presence of an already established one. The framework employs two complementary strategies: conditional evaluation, which quantifies the added value of a new biomarker given an existing one; and joint evaluation, which assesses their combined utility using an and-classifier that defines positive cases as those exceeding predefined thresholds for both biomarkers. These strategies support tailored interpretation depending on the clinical objectives and biomarker characteristics. Simulation studies across varying censoring levels, prediction time horizons, and copula families (Frank, Clayton, Gumbel) demonstrate the framework’s accuracy in estimating performance metrics and recovering the true dependence structure. Application to the Mayo Clinic PBC dataset further illustrates its practical utility in real-world clinical settings.