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

Abstract

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.

KEYWORDS:

• Delayed entry
• Dependent left truncation
• Frailty model
• Random effect
• Risk prediction
• Semi-competing risks

Supplementary Materials

The Supplementary Materials include proof of Lemma 1 and main steps of the proof of Theorem 1; a comparison with Gorfine et al. (2009); details of the likelihood function, of ${\widehat{A}}_{j}k$ under gamma frailty model, and of Approach (ii); additional simulation results and additional results of the UKB data analysis.

Additional information

Funding

The authors gratefully acknowledge support from the NIH (R01CA189532), the U.S.-Israel Binational Science Foundation (BSF, 2016126), and the Israel Science Foundation (ISF, 1067/17) in carrying out this work. This research has been conducted using the UK Biobank Resource, under project number 8614.