Nonparametric Maximum Likelihood Estimators of Time-Dependent Accuracy Measures for Survival Outcome Under Two-Stage Sampling Designs

Large prospective cohort studies of rare chronic diseases require thoughtful planning of study designs, especially for biomarker studies when measurements are based on stored tissue or blood specimens. Two-phase designs, including nested case–control and case-cohort sampling designs, provide cost-effective strategies for conducting biomarker evaluation studies.Existing literature for biomarker assessment under two-phase designs largely focuses on simple inverse probability weighting (IPW) estimators. Drawing on recent theoretical development on the maximum likelihood estimators for relative risk parameters in two-phase studies, we propose nonparametric maximum likelihood-based estimators to evaluate the accuracy and predictiveness of a risk prediction biomarker under both types of two-phase designs. In addition, hybrid estimators that combine IPW estimators and maximum likelihood estimation procedure are proposed to improve efficiency and alleviate computational burden. We derive large sample properties of proposed estimators and evaluate their finite sample performance using numerical studies. We illustrate new procedures using a two-phase biomarker study aiming to evaluate the accuracy of a novel biomarker, des-γ-carboxy prothrombin, for early detection of hepatocellular carcinoma. Supplementary materials for this article are available online.