Uncertainty-Calibrated Prediction of Randomly-Timed Biomarker Trajectories with Conformal Bands

We introduce a novel conformal prediction framework for constructing conformal prediction bands with high probability around biomarker trajectories observed at subject-specific, randomly-timed follow-up visits. Existing conformal methods typically assume fixed time grids, limiting their applicability in longitudinal clinical studies. Our approach addresses this limitation by defining a time-varying nonconformity score that normalizes prediction errors using model-derived uncertainty estimates, enabling conformal inference at arbitrary time points. We evaluate our method on two well-established brain biomarkers-hippocampal and ventricular volume-using a range of standard and state-of-the-art predictors. Across models, our conformalized predictors consistently achieve nominal coverage with tighter prediction intervals compared to baseline uncertainty estimates. To further account for population heterogeneity, we develop group-conditional conformal bands with formal coverage guarantees across clinically relevant and high-risk subgroups. Finally, we demonstrate the clinical utility of our approach in identifying subjects at risk of progression to Alzheimer's disease. We introduce an uncertainty-aware progression metric based on the lower conformal bound and show that it enables the identification of 17.5% more high-risk subjects compared to standard slope-based methods, highlighting the value of uncertainty calibration in real-world clinical decision making. We make the code available at github.com/vatass/ConformalBiomarkerTrajectories.

• Conformal methods typically require that the calibration and test data are exchangeable-a milder condition than that of independent and identically distributed data (see Appendix A).