Risk-matched case-control sampling and semiparametric weight calibration for efficient biomarker assessment with binary outcomes

Abstract

Two-phase designs provide a cost-effective framework for biomarker studies and have been widely used to reduce the burden of collecting expensive biomarker measurements. Most methodological research has focused on efficient Phase II sampling and estimation of biomarker--outcome associations. A natural subsequent step, however, is to incorporate identified biomarkers into risk prediction models, where measures of predictive performance become important inferential targets. Even for binary outcomes, methodological developments for two-phase designs that jointly address association parameters and predictive performance remain limited. Building on classical case-control and matched case-control designs developed primarily for association inference with binary outcomes, we propose a risk-matched case-control (RMCC) design that uses a scalar disease-risk score constructed from Phase I variables to define matching strata and guide Phase II sampling. To address the limitations of existing likelihood-based approaches, which typically require correct specification of the nuisance distribution of biomarkers, we develop a unified design-based inference framework based on inverse probability weighting for both association parameters and predictive performance measures, including positive predictive value and the area under the receiver operating characteristic curve. We further introduce target-specific weight scaling and calibration procedures and derive variance estimators that account for sampling variability in both phases. Simulation studies demonstrate the efficiency and robustness of the proposed design and inference procedures, and an application to a Taiwanese oral cancer cohort illustrates their potential utility.