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Uncertainty-Calibrated Prediction of Randomly-Timed Biomarker Trajectories with Conformal Bands
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Extends split conformal prediction with a max-normalized nonconformity score to produce coverage-guaranteed bands for randomly-timed biomarker trajectories, applied to hippocampal and ventricular volume with five predictors and group-conditional variants.
Problem
Biomarker trajectories are observed at subject-specific random visit times, but existing conformal methods for trajectories assume fixed time grids, so uncertainty-calibrated bands with coverage guarantees are not available for such data.
Approach
A time-varying, max-over-observed-visits normalized nonconformity score with a predictive-std normalizer lets split conformal bands be evaluated at any time point, including arbitrary random visit times, with simultaneous coverage over the trajectory; Mondrian-style group-conditional bands extend this to subpopulations.
Key results
- At nominal 0.9 coverage, conformalized DQR, DRMC and Bootstrap reach the desired coverage while their baselines undercover, and conformalized DKGP/DME give tighter bands than their baselines.
- For the MCI progression task with DRMC, the rate-of-change bound raises recall from 67.1% (predicted RoC) to 88.4%, and the conformalized CP-DRMC raises it from 74.0% to 91.5%.
- The paper reports identifying 17.5% more high-risk subjects than standard risk scores.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RoCB instead of predicted RoC | DRMC · MCI-stable vs MCI-progressors | recall: 0.671 ± 0.058 -> 0.884 ± 0.058 | Helped |
| Use RoCB instead of predicted RoC | CP-DRMC · MCI-stable vs MCI-progressors | recall: 0.740 ± 0.095 -> 0.915 ± 0.095 | Helped |
| Use RoCB instead of predicted RoC | DRMC · MCI-stable vs MCI-progressors | precision: 0.436 ± 0.022 -> 0.403 ± 0.022 | Hurt |
| Use RoCB instead of predicted RoC | DRMC · MCI-stable vs MCI-progressors | F1: 0.528 ± 0.023 -> 0.553 ± 0.023 | No clear effect |
| Use RoCB instead of predicted RoC | CP-DRMC · MCI-stable vs MCI-progressors | precision: 0.432 ± 0.022 -> 0.395 ± 0.022 | Hurt |
| Use RoCB instead of predicted RoC | CP-DRMC · MCI-stable vs MCI-progressors | F1: 0.546 ± 0.024 -> 0.552 ± 0.024 | No clear effect |
| Conformalize DRMC prediction bands | DRMC · MCI-stable vs MCI-progressors | recall using RoCB: 0.884 ± 0.058 -> 0.915 ± 0.095 | Helped |
| Use group-conditional rather than population conformal bands | DKGP · Hippocampal- and ventricular-volume subgroups | coverage | Helped |
| Conformalize trajectory predictors for randomly-timed visits | DKGP, DME, DQR, DRMC, and Bootstrap · Hippocampal- and ventricular-volume trajectories | coverage | Helped |
| Use uncertainty-calibrated RoCB instead of standard risk scores | MCI subjects · High-risk subject identification | high-risk subjects identified: 17.5% more | Helped |
Surprising findings
- Population conformal bands fail to reach nominal coverage for MCI patients, APOE4 homozygotes, and Asian subjects, while group-conditional bands attain it.
- Only 37 of 2200 trajectories have observations at all four fixed time points, showing that fixed-grid adaptations would discard most data.
Limitations
- Coverage guarantees require exchangeability between calibration and test data; distribution shift across sites or cohorts may break them.
- Group-conditional variants only handle single covariates, not intersections of multiple covariates.
- Only two biomarkers (hippocampal and ventricular volume) and univariate predictors are studied.
Experimental setup
Datasets: ADNI BLSA iSTAGING consortium cohorts (OASIS, WRAP, AIBL, CARDIA, PreventAD, PENN) for external populations
Benchmarks: ADNI+BLSA hippocampal volume trajectories ADNI+BLSA ventricular volume trajectories
Metrics: mean coverage mean interval width precision recall F1 Youden-optimal threshold discrimination
Baselines: DKGP DME DQR DRMC Bootstrap population conformal prediction
Builds on: conformal prediction for fixed-time trajectories (Lu et al.) Mondrian conformal prediction deep kernel learning Monte Carlo dropout
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