Marginalized Frailty-Based Illness-Death Model: Application to the UK-Biobank Survival Data

The UK Biobank is a large-scale health resource comprising genetic, environmental, and medical information on approximately 500,000 volunteer participants in the United Kingdom, recruited at ages 40–69 during the years 2006–2010. The project monitors the health and well-being of its participants. This work demonstrates how these data can be used to yield the building blocks for an interpretable risk-prediction model, in a semiparametric fashion, based on known genetic and environmental risk factors of various chronic diseases, such as colorectal cancer. An illness-death model is adopted, which inherently is a semi-competing risks model, since death can censor the disease, but not vice versa. Using a shared-frailty approach to account for the dependence between time to disease diagnosis and time to death, we provide a new illness-death model that assumes Cox models for the marginal hazard functions. The recruitment procedure used in this study introduces delayed entry to the data. An additional challenge arising from the recruitment procedure is that information coming from both prevalent and incident cases must be aggregated. Lastly, we do not observe any deaths prior to the minimal recruitment age, 40. In this work, we provide an estimation procedure for our new illness-death model that overcomes all the above challenges. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.英国生物样本库（UK Biobank）是一项大规模健康研究资源，收纳了2006至2010年间招募的、年龄介于40至69岁的约50万名英国志愿者参与者的遗传、环境与医疗信息。该项目长期追踪参与者的健康状况与福祉水平。本研究展示了如何以半参数化方式，基于结直肠癌等多种慢性病已知的遗传与环境风险因素，利用上述数据构建可解释性风险预测模型的基础组件。本研究采用了疾病-死亡模型，该模型本质上属于半竞争风险模型，原因在于死亡可作为疾病发病的删失因素，而疾病发病无法成为死亡的删失因素。我们采用共享脆弱性方法处理疾病诊断时间与死亡时间之间的相关性，由此提出了一种新型疾病-死亡模型，该模型针对边缘风险函数采用Cox模型。本研究采用的招募流程导致数据存在延迟入组现象。此外，招募流程还带来了另一项挑战：需同时整合现患病例与新发病例的相关信息。最后，我们未观测到最小招募年龄（40岁）之前发生的任何死亡事件。针对我们提出的新型疾病-死亡模型，本研究提供了一套估算流程，可克服上述全部挑战。本文的补充材料（包含可用于复现本研究的标准化材料说明）可在线获取。