Priyam Das1, Debsurya De2, Raju Maiti3, Mona Kamal4, Katherine A Hutcheson5, Clifton D Fuller4, Bibhas Chakraborty3,6,7, Christine B Peterson8. 1. Department of Biomedical Informatics, Harvard Medical School, Boston, MA, USA. pdasvcu@gmail.com. 2. Indian Statistical Institute, Kolkata, India. 3. Centre for Quantitative Medicine, Duke-National University of Singapore Medical School, Singapore, Singapore. 4. Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, TX, USA. 5. Department of Head and Neck Surgery, The University of Texas MD Anderson Cancer Center, Houston, TX, USA. 6. Department of Statistics and Applied Probability, National University of Singapore, Singapore, Singapore. 7. Department of Biostatistics and Bioinformatics, Duke University, Durham, NC, USA. 8. Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX, USA.
Abstract
BACKGROUND: In the context of a binary classification problem, the optimal linear combination of continuous predictors can be estimated by maximizing the area under the receiver operating characteristic curve. For ordinal responses, the optimal predictor combination can similarly be obtained by maximization of the hypervolume under the manifold (HUM). Since the empirical HUM is discontinuous, non-differentiable, and possibly multi-modal, solving this maximization problem requires a global optimization technique. Estimation of the optimal coefficient vector using existing global optimization techniques is computationally expensive, becoming prohibitive as the number of predictors and the number of outcome categories increases. RESULTS: We propose an efficient derivative-free black-box optimization technique based on pattern search to solve this problem, which we refer to as Spherically Constrained Optimization Routine (SCOR). Through extensive simulation studies, we demonstrate that the proposed method achieves better performance than existing methods including the step-down algorithm. Finally, we illustrate the proposed method to predict the severity of swallowing difficulty after radiation therapy for oropharyngeal cancer based on radiation dose to various structures in the head and neck. CONCLUSIONS: Our proposed method addresses an important challenge in combining multiple biomarkers to predict an ordinal outcome. This problem is particularly relevant to medical research, where it may be of interest to diagnose a disease with various stages of progression or a toxicity with multiple grades of severity. We provide the implementation of our proposed SCOR method as an R package, available online at https://CRAN.R-project.org/package=SCOR .
BACKGROUND: In the context of a binary classification problem, the optimal linear combination of continuous predictors can be estimated by maximizing the area under the receiver operating characteristic curve. For ordinal responses, the optimal predictor combination can similarly be obtained by maximization of the hypervolume under the manifold (HUM). Since the empirical HUM is discontinuous, non-differentiable, and possibly multi-modal, solving this maximization problem requires a global optimization technique. Estimation of the optimal coefficient vector using existing global optimization techniques is computationally expensive, becoming prohibitive as the number of predictors and the number of outcome categories increases. RESULTS: We propose an efficient derivative-free black-box optimization technique based on pattern search to solve this problem, which we refer to as Spherically Constrained Optimization Routine (SCOR). Through extensive simulation studies, we demonstrate that the proposed method achieves better performance than existing methods including the step-down algorithm. Finally, we illustrate the proposed method to predict the severity of swallowing difficulty after radiation therapy for oropharyngeal cancer based on radiation dose to various structures in the head and neck. CONCLUSIONS: Our proposed method addresses an important challenge in combining multiple biomarkers to predict an ordinal outcome. This problem is particularly relevant to medical research, where it may be of interest to diagnose a disease with various stages of progression or a toxicity with multiple grades of severity. We provide the implementation of our proposed SCOR method as an R package, available online at https://CRAN.R-project.org/package=SCOR .
Authors: Cliff C Kerr; Salvador Dura-Bernal; Tomasz G Smolinski; George L Chadderdon; David P Wilson Journal: PLoS One Date: 2018-03-16 Impact factor: 3.240