Calibrating Variations in Biomarker Measures for Improving Prediction with Time-to-event Outcomes

Novel biologic markers have been used to predict clinical outcomes of many diseases. One specific feature of biomarkers is that they often are measured with variations due to factors such as sample preparation and specific laboratory process. Statistical methods have been proposed to characterize the effects of underlying error-free quantity in association with an outcome, yet the impact of measurement errors in terms of prediction has not been well studied. We focus in this manuscript on using biomarkers for predicting an individual’s future risk for survival outcome. In the setting where replicates of error-prone biomarkers are available in a ‘training’ population and risk projection is applied to individuals in a ‘prediction’ population, we propose two-step measurement-error-corrected estimators of absolute risks. We conducted numerical studies to evaluate the predictive performance of the proposed and routine approaches under various assumptions about the measurement error distributions to pinpoint situations when correction of measurement errors might be necessary. We studied the asymptotic properties of the proposed estimators. We applied the estimators to a liver cancer biomarker study to predict risk of liver cancer incidence using age and a novel biomarker, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-Fetoprotein.