About the Authors

Tao He

Affiliation Department of Statistics and Probability, Michigan State University, East Lansing, Michigan, United States of America

Jian Sa

Affiliations Department of Statistics and Probability, Michigan State University, East Lansing, Michigan, United States of America, Division of Medical Statistics, School of Public Health, Shanxi Medical University, Taiyuan, Shanxi, China

Ping-Shou Zhong

Affiliation Department of Statistics and Probability, Michigan State University, East Lansing, Michigan, United States of America

Yuehua Cui

cui@stt.msu.edu

Affiliations Department of Statistics and Probability, Michigan State University, East Lansing, Michigan, United States of America, Division of Medical Statistics, School of Public Health, Shanxi Medical University, Taiyuan, Shanxi, China

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: YC. Analyzed the data: TH. Wrote the paper: TH YC. Participated in analysis: JS PSZ.