A Bayesian Stochastic Order-Based C-Index to Quantify the Association Between Jointly Modeled Longitudinal Biomarkers and Survival Data

Thomas M. Menino Convention & Exhibition Center 

Joint models are widely used to link longitudinal biomarker trajectories with time-to-event outcomes. A key question is how well the longitudinal component discriminates between subjects who experience events earlier versus later. The concordance index (C-index) is the standard measure for this purpose, but its classical definition assumes a time-invariant risk score—an assumption violated when risk evolves with the biomarker trajectory.
We propose a generalized C-index grounded in stochastic-order preference that directly accommodates time-dependent risk scores from joint models with random effects. Our measure quantifies the probability that a subject with a higher predicted risk at any given time experiences the event before a subject with lower risk, fully accounting for how risk rankings may change over time. The generalization is interpretable, handles non-monotonic risk dynamics, and reduces to the classical C-index when risk is time-invariant.
The empirical performance of the proposed metric was assessed via simulation studies. Real-world data analysis was conducted on the Mayo Clinic's Primary Biliary Cirrhosis (PBC) clinical trial data to further demonstrate the robustness of the proposed index.

C-index

Longitudinal biomarkers

Stochastic order

Survival analysis

PBC trial