Statistical inference for the two-sample problem under likelihood ratio ordering, with application to the ROC curve estimation

被引:4
作者
Hu, Dingding [1 ]
Yuan, Meng [1 ]
Yu, Tao [2 ]
Li, Pengfei [1 ]
机构
[1] Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON, Canada
[2] Natl Univ Singapore, Dept Stat & Data Sci, Singapore, Singapore
基金
加拿大自然科学与工程研究理事会;
关键词
area under the ROC curve; Bernstein polynomials; likelihood ratio ordering; ROC curve; Youden index; REGRESSION;
D O I
10.1002/sim.9823
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
The receiver operating characteristic (ROC) curve is a powerful statistical tool and has been widely applied in medical research. In the ROC curve estimation, a commonly used assumption is that larger the biomarker value, greater severity the disease. In this article, we mathematically interpret "greater severity of the disease" as "larger probability of being diseased." This in turn is equivalent to assume the likelihood ratio ordering of the biomarker between the diseased and healthy individuals. With this assumption, we first propose a Bernstein polynomial method to model the distributions of both samples; we then estimate the distributions by the maximum empirical likelihood principle. The ROC curve estimate and the associated summary statistics are obtained subsequently. Theoretically, we establish the asymptotic consistency of our estimators. Via extensive numerical studies, we compare the performance of our method with competitive methods. The application of our method is illustrated by a real-data example.
引用
收藏
页码:3649 / 3664
页数:16
相关论文
共 23 条
[1]  
[Anonymous], 2012, DATA COLLECTION PROB
[2]   Construction of confidence intervals for the maximum of the Youden index and the corresponding cutoff point of a continuous biomarker [J].
Bantis, Leonidas E. ;
Nakas, Christos T. ;
Reiser, Benjamin .
BIOMETRICAL JOURNAL, 2019, 61 (01) :138-156
[3]   Using a Monotonic Density Ratio Model to Find the Asymptotically Optimal Combination of Multiple Diagnostic Tests [J].
Chen, Baojiang ;
Li, Pengfei ;
Qin, Jing ;
Yu, Tao .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2016, 111 (514) :861-874
[4]   INFERENCE FOR LIKELIHOOD RATIO ORDERING IN THE 2-SAMPLE PROBLEM [J].
DYKSTRA, R ;
KOCHAR, S ;
ROBERTSON, T .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1995, 90 (431) :1034-1040
[5]   Regularization Paths for Generalized Linear Models via Coordinate Descent [J].
Friedman, Jerome ;
Hastie, Trevor ;
Tibshirani, Rob .
JOURNAL OF STATISTICAL SOFTWARE, 2010, 33 (01) :1-22
[6]  
Gneiting T., RECEIVER OPERATING C
[7]  
Hsieh FS, 1996, STAT SINICA, V6, P47
[8]   A DIRECT SEMIPARAMETRIC RECEIVER OPERATING CHARACTERISTIC CURVE REGRESSION WITH UNKNOWN LINK AND BASELINE FUNCTIONS [J].
Lin, Huazhen ;
Zhou, Xiao-Hua ;
Li, Gang .
STATISTICA SINICA, 2012, 22 (04) :1427-1456
[9]  
Owen A.B., 2001, EMPIRICAL LIKELIHOOD
[10]   DUCHENNE MUSCULAR-DYSTROPHY CARRIER DETECTION USING LOGISTIC DISCRIMINATION - SERUM CREATINE-KINASE, HEMOPEXIN, PYRUVATE-KINASE, AND LACTATE-DEHYDROGENASE IN COMBINATION [J].
PERCY, ME ;
ANDREWS, DF ;
THOMPSON, MW .
AMERICAN JOURNAL OF MEDICAL GENETICS, 1982, 13 (01) :27-38