A resample-replace lasso procedure for combining high-dimensional markers with limit of detection

Abstract

In disease screening, a biomarker combination developed by combining multiple markers tends to have a higher sensitivity than an individual marker. Parametric methods for marker combination rely on the inverse of covariance matrices, which is often a non-trivial problem for high-dimensional data generated by modern high-throughput technologies. Additionally, another common problem in disease diagnosis is the existence of limit of detection (LOD) for an instrument – that is, when a biomarker's value falls below the limit, it cannot be observed and is assigned an NA value. To handle these two challenges in combining high-dimensional biomarkers with the presence of LOD, we propose a resample-replace lasso procedure. We first impute the values below LOD and then use the graphical lasso method to estimate the means and precision matrices for the high-dimensional biomarkers. The simulation results show that our method outperforms alternative methods such as either substitute NA values with LOD values or remove observations that have NA values. A real case analysis on a protein profiling study of glioblastoma patients on their survival status indicates that the biomarker combination obtained through the proposed method is more accurate in distinguishing between two groups.

Keywords:

• Limit of detection (LOD)
• graphical lasso
• precision matrix
• area under the receiver operating characteristic curve (AUC)
• high-dimensional data
• imputation

2020 Mathematics Subject Classification:

• 97K80

Acknowledgments

We thank the editor, the associate editor, and the three anonymous referees for the valuable comments on our previous manuscript. We also thank Emanuel Petricoin at George Mason University, Helen Fillmore and William Broaddus at Virginia Commonwealth University for access to the data, generated the proteomic data and the clinical specimens that underpinned the generation of the data.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported in part by the Intramural Research Program of the National Institutes of Health and the US Social Security Administration. The opinions expressed in this article are the author's own and do not reflect the view of the National Institutes of Health, the Department of Health and Human Services, US Social Security Administration, or the United States government. Besides, this work is partially supported by Beijing Natural Science Foundation [grant number Z180006], National Nature Science Foundation of China [grant number 11722113].