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Maiti R, Li J, Das P, Liu X, Feng L, Hausenloy DJ, Chakraborty B. A distribution-free smoothed combination method to improve discrimination accuracy in multi-category classification. Stat Methods Med Res 2023; 32:242-266. [PMID: 36384309 DOI: 10.1177/09622802221137742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Results from multiple diagnostic tests are combined in many ways to improve the overall diagnostic accuracy. For binary classification, maximization of the empirical estimate of the area under the receiver operating characteristic curve has widely been used to produce an optimal linear combination of multiple biomarkers. However, in the presence of a large number of biomarkers, this method proves to be computationally expensive and difficult to implement since it involves maximization of a discontinuous, non-smooth function for which gradient-based methods cannot be used directly. The complexity of this problem further increases when the classification problem becomes multi-category. In this article, we develop a linear combination method that maximizes a smooth approximation of the empirical Hyper-volume Under Manifolds for the multi-category outcome. We approximate HUM by replacing the indicator function with the sigmoid function and normal cumulative distribution function. With such smooth approximations, efficient gradient-based algorithms are employed to obtain better solutions with less computing time. We show that under some regularity conditions, the proposed method yields consistent estimates of the coefficient parameters. We derive the asymptotic normality of the coefficient estimates. A simulation study is performed to study the effectiveness of our proposed method as compared to other existing methods. The method is illustrated using two real medical data sets.
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Affiliation(s)
- Raju Maiti
- Economic Research Unit, Indian Statistical Institute Kolkata, Kolkata, India
| | - Jialiang Li
- Department of Statistics and Data Science, National University of Singapore, Singapore, Singapore
| | - Priyam Das
- Department of Biomedical Informatics, 1811Harvard Medical School, Boston, MA, USA
| | - Xueqing Liu
- Centre for Quantitative Medicine, 121579Duke-NUS Medical School, Singapore, Singapore
| | - Lei Feng
- Department of Psychological Medicine, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Derek J Hausenloy
- Cardiovascular and Metabolic Disorders Program, 121579Duke-NUS Medical School, Singapore, Singapore.,National Heart Research Institute Singapore, National Heart Centre, Singapore, Singapore.,Yong Loo Lin School of Medicine, National University Singapore, Singapore, Singapore.,The Hatter Cardiovascular Institute, University College London, London, UK.,Cardiovascular Research Center, College of Medical and Health Sciences, Asia University, Taichung
| | - Bibhas Chakraborty
- Department of Statistics and Data Science, National University of Singapore, Singapore, Singapore.,Centre for Quantitative Medicine, 121579Duke-NUS Medical School, Singapore, Singapore.,Department of Biostatistics and Bioinformatics, Duke University, USA
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