ABSTRACT 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.

中文翻译：

---

两阶段抽样设计下生存结果的时间相关精度测量的非参数最大似然估计

摘要 罕见慢性疾病的大型前瞻性队列研究需要深思熟虑的研究设计规划，特别是对于基于储存的组织或血液样本进行测量的生物标志物研究。两阶段设计，包括嵌套病例对照和病例队列抽样设计，为进行生物标志物评估研究提供了具有成本效益的策略。两阶段设计下生物标志物评估的现有文献主要集中于简单的逆概率加权（IPW）估计器。利用两阶段研究中相对风险参数的最大似然估计器的最新理论发展，我们提出了基于非参数最大似然估计器来评估两种类型的两阶段设计下风险预测生物标志物的准确性和预测性。此外，还提出了将 IPW 估计器和最大似然估计程序相结合的混合估计器，以提高效率并减轻计算负担。我们推导出所提出的估计量的大样本属性，并使用数值研究评估其有限样本性能。我们使用两阶段生物标志物研究来说明新程序，旨在评估新型生物标志物，脱-γ-羧基凝血酶原，用于早期检测肝细胞癌的准确性。本文的补充材料可在线获取。