When Is a Conformal Guarantee Fair? Auditing Silent Subgroup Under-Coverage in Alzheimer's Disease Longitudinal Prediction

Longitudinal prediction of Alzheimer's disease biomarkers increasingly informs clinical decisions, and a forecast is only useful if it also reports how much to trust it. Conformal prediction supplies this by wrapping any forecaster in a prediction band with a finite-sample coverage guarantee under exchangeability. However, standard population-level conformal prediction guarantees only marginal coverage and may mask substantial under-coverage within clinically important subgroups. We introduce a general mechanism-driven framework for auditing and repairing such subgroup under-coverage. Across two cohorts (ADNI, OASIS-3), two base forecasters, and nine attributes spanning genetic risk, demographics, and clinical severity, we find that population-level bands under-cover high-risk subgroups in 57 of 68 audited combinations, despite achieving nominal marginal coverage. We trace these failures to two mechanisms: (A) \emph{rarity}, where a group-conditional band calibrated on only $n$ patients covers at most $k/(n+1)$; and (B) \emph{tail-heaviness}, where a population-wide band is too narrow for a heavy-tailed subgroup and additional data cannot close the gap. Under-coverage falls disproportionately on patients with high genetic risk and disease severity (6.1 pp mean deficit, 95\% CI [3.3, 8.9]), while demographic groups remain at the target level on average (0.0 pp, CI [$-1.9$, 1.7]). We pair each mechanism with a corresponding conformal correction: cross-conformal pooling for rarity, per-subgroup calibration for tail-heaviness, and a coverage-safe marginal floor when both arise. Together, these corrections restore target coverage for nearly every high-risk subgroup across both cohorts and forecasters.