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A regression approach to ROC surface, with applications to Alzheimer’s disease
Authors:JiaLiang Li  XiaoHua Zhou  Jason P Fine
Institution:1. Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, Singapore, 117546, Singapore
2. Duke-NUS Graduate Medical School, 8 College Road, Singapore, 169857, Singapore
3. Singapore Eye Research Institute, 11 Third Hospital Avenue, Singapore, 168751, Singapore
4. Department of Biostatistics, University of Washington, Seattle, WA, 98195, USA
5. Department of Biostatistics and Department of Statistics, University of North Carolina, Chapel Hill, NC, 27599, USA
Abstract: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.
Keywords:receiver operating characteristic surface  volume under ROC surface  rank regression  transformation model  maximum likelihood estimation  bootstrap
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