Science China Mathematics

, Volume 55, Issue 8, pp 1583–1595

A regression approach to ROC surface, with applications to Alzheimer’s disease


    • Department of Statistics and Applied ProbabilityNational University of Singapore
    • Duke-NUS Graduate Medical School
    • Singapore Eye Research Institute
  • XiaoHua Zhou
    • Department of BiostatisticsUniversity of Washington
  • Jason P. Fine
    • Department of Biostatistics and Department of StatisticsUniversity of North Carolina
Articles Methods for Diagnostic Tests and Biomarkers

DOI: 10.1007/s11425-012-4462-3

Cite this article as:
Li, J., Zhou, X. & Fine, J.P. Sci. China Math. (2012) 55: 1583. doi:10.1007/s11425-012-4462-3


We consider the estimation of three-dimensional ROC surfaces for continuous tests given covariates. Three way ROC analysis is important in our motivating example where patients with Alzheimer’s disease are usually classified into three categories and should receive different category-specific medical treatment. There has been no discussion on how covariates affect the three way ROC analysis. We propose a regression framework induced from the relationship between test results and covariates. We consider several practical cases and the corresponding inference procedures. Simulations are conducted to validate our methodology. The application on the motivating example illustrates clearly the age and sex effects on the accuracy for Mini-Mental State Examination of Alzheimer’s disease.


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© Science China Press and Springer-Verlag Berlin Heidelberg 2012