Estimating the AUC with a graphical lasso method for high-dimensional biomarkers with LOD

Abstract

This manuscript estimates the area under the receiver operating characteristic curve (AUC) of combined biomarkers in a high-dimensional setting. We propose a penalization approach to the inference of precision matrices in the presence of the limit of detection. A new version of expectation-maximization algorithm is then proposed for the penalized likelihood, with the use of numerical integration and the graphical lasso method. The estimated precision matrix is then applied to the inference of AUCs. The proposed method outperforms the existing methods in numerical studies. We apply the proposed method to a data set of brain tumor study. The results show a higher accuracy on the estimation of AUC compared with the existing methods.

Keywords:

• Receiver operating characteristic curve
• area under the ROC curve
• graphical lasso
• EM algorithm
• high-dimensional biomarkers

Disclosure statement

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

Notes

1 For notational convenience, the variance of the kth biomarker's original values is denoted by ${\sigma }_{kk}$ not ${\sigma }_{kk}^2$ hereafter.

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.

Notes on contributors

Jirui Wang

Jirui Wang is a biostatistician in the Department of Biostatistics at Medpace, Inc. He got his PhD degree in the Department of Statistics in the Volgenau School of Engineering at George Mason University. His dissertation was on network analysis and high dimensional data analysis under the supervision of Dr. Yunpeng Zhao and Dr. Larry Tang. He is now working on study designs and statistical analysis in clinical trials.

Yunpeng Zhao

Yunpeng Zhao is an assistant professor in the School of Mathematical and Natural Sciences in New College of Interdisciplinary Arts and Sciences at Arizona State University. His primary research interest includes machine learning methodology and theory in network analysis with applications in biology and the social sciences. He is also working on high dimensional data analysis with applications in genomics.

Liansheng Larry Tang

Liansheng Larry Tang is a statistician specializing in statistical methodology and collaborative research. His current methodological research areas include statistical methods in forensics, diagnostic medicine, group sequential designs and substance abuse research and criminology.