Semi-parametric area under the curve regression method for diagnostic studies with ordinal data

• Published in: Biometrical journal Vol. 54; no. 1; pp. 143 - 156
• Main Authors: Rajan, Kumar B., Zhou, Xiao-Hua
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY-VCH Verlag 01.01.2012; WILEY‐VCH Verlag; Wiley-VCH
• Subjects: Applications; Area Under Curve; Area under the curve; Biology, psychology, social sciences; Diagnosis; Diagnostic markers; Exact sciences and technology; Female; General topics; Humans; Linear inference, regression; Male; Mathematics; Medical Informatics - methods; Multicenter Studies as Topic; Multivariate analysis; Probability and statistics; Prostatic Neoplasms - diagnosis; Regression Analysis; Regression for ordinal data; ROC Curve; Sciences and techniques of general use; Statistics; Vascular Diseases - diagnosis; Biometrics; Bias; Non parametric estimation; Multivariate analysis; Covariate; Statistical simulation; Statistical test; Diagnostic test; Regression for ordinal data; Area under the curve; Random variable; Method study; Discriminant analysis; Diagnostic markers; Life science; Asymptotic behavior; Roc curve; Discrete data; Statistical estimation; Statistical method; Statistical regression; Diagnostic techniques; Correlation analysis; Regression diagnostics; Risk factor; Receiver operating characteristic curves; Asymptotic approximation; Mean error; Biased estimation; Ordinal data
• ISSN: 0323-3847; 1521-4036; 1521-4036
• DOI: 10.1002/bimj.201100025

The classification accuracy of new diagnostic tests is based on receiver operating characteristic (ROC) curves. The area under the ROC curve (AUC) is one of the well‐accepted summary measures for describing the accuracy of diagnostic tests. The AUC summary measure can vary by patient and testing characteristics. Thus, the performance of the test may be different in certain subpopulation of patients and readers. For this purpose, we propose a direct semi‐parametric regression model for the non‐parametric AUC measure for ordinal data while accounting for discrete and continuous covariates. The proposed method can be used to estimate the AUC value under degenerate data where certain rating categories are not observed. We will discuss the non‐standard asymptotic theory, since the estimating functions were based on cross‐correlated random variables. Simulation studies based on different classification models showed that the proposed model worked reasonably well with small percent bias and percent mean‐squared error. The proposed method was applied to the prostate cancer study to estimate the AUC for four readers, and the carotid vessel study with age, gender, history of previous stroke, and total number of risk factors as covariates, to estimate the accuracy of the diagnostic test in the presence of subject‐level covariates.