Coverage Allocation in Two-Stage Conformal Prediction

Conformal prediction (CP) provides marginal coverage guarantees under exchangeability and is generally evaluated through mean coverage and interval length. In clinical settings, mean coverage says nothing about whether coverage is balanced across patient groups. One way to address this is by adapting interval length to prediction difficulty, but stronger adaptation does not necessarily lead to better intervals, and can leave patient subpopulations under-covered. We introduce CASCADE-CRC, a framework for studying how adaptation strength affects coverage and interval length reallocation in two-stage conformal prediction. We evaluate on inpatient and outpatient Parkinson's disease cohorts, an external zero-inflated insurance dataset, and synthetic data with known heteroscedasticity. Our experiments reveal that adaptation strength reallocates interval length and, with it, coverage across groups, reducing the coverage gap (CovGap) by $31.7\%$ on the outpatient cohort while keeping $80\%$ marginal coverage, with benefits that vary by setting. Our findings emphasize the importance of adaptation strength as a modeling choice, motivating joint evaluation of group coverage and interval length.