A Resample-Replace Lasso Procedure for Combining High-Dimensional Markers with Limit of Detection

• Activity Number: 159 - Novel Approaches for Diagnostics and Prediction with Complex Data
• Type: Topic Contributed
• Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Yunpeng Zhao* and Jinjuan Wang and Larry Tang and Claudius Mueller and Qizhai Li
• Companies: Arizona State Univ and University of Chinese Academy of Sciences and George Mason University and George Mason University and Academy of Mathematics and Systems Science, Chinese Academy of Science
• Keywords: Limit of detection; Graphical lasso; Precision matrix; Area under the receiver operating characteristic curve; High dimensional data; Imputation

Abstract

In disease screening, the combination of multiple markers tends to have higher sensitivity than an individual marker. Parametric methods for marker combination are closely related to the linear discriminant analysis and rely on sample means and sample covariance matrices. A common problem in diagnostic studies is the limit of detection (LOD) when the biomarker’s value falls below the range of detection by the instrument. In addition, cancer screening studies based on modern high-throughput technology have more biomarkers than subjects. Due to the challenge of the presence of LOD in such high dimensional data, existing methods are no longer applicable for combining biomarkers. In this article, we propose a resample-replace lasso procedure to first impute the values below LOD, and then use the graphical lasso method to estimate the means and precision matrices for the combination of high-dimensional biomarkers. The simulation results show that our method outperforms alternative methods that either substitute NA with LOD value or ignore the NA values. We apply the proposed method to a protein profiling study of glioblastoma patients on their survival status.