Two-phase sampling designs, including nested case-control and case-cohort designs, are frequently utilized in large cohort studies involving expensive biomarkers. To analyze data from two-phase designs with a binary outcome, parametric models such as logistic regression are often adopted. However, when the model assumptions are not valid, parametric models may lead to biased estimation and risk evaluation. In this paper, we propose a robust semiparametric regression model for binary outcomes and an easy-to-implement computational procedure that combines the pool-adjacent violators algorithm with inverse probability weighting. The asymptotic properties are established, including consistency and the convergence rate. Simulation studies show that the proposed method performs well and is more robust than logistic regression methods. We demonstrate the application of the proposed method to real data from the Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial.
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