Estimating the optimal linear combination of predictors using spherically constrained optimization

Year: 2022

Type: article

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 .

Source: BMC Bioinformatics

DOI: 10.1186/s12859-022-04953-y

Authors: Priyam Das, Debsurya De, Raju Maiti, Mona Kamal, Katherine A. Hutcheson, Clifton D. Fuller, Bibhas Chakraborty, Christine B. Peterson

Institutions: Harvard University, Indian Statistical Institute, National University of Singapore, Duke-NUS Medical School, The University of Texas MD Anderson Cancer Center, Duke University

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $2,690

Funders: National Science Foundation, Cancer Prevention and Research Institute of Texas, Patient-Centered Outcomes Research Institute, Elekta, Duke-NUS Medical School, Ministry of Education - Singapore, Ministry of Education, India, National Institutes of Health, University of Texas MD Anderson Cancer Center, National Cancer Institute, National Institute of Biomedical Imaging and Bioengineering, National Institute of Dental and Craniofacial Research, Division of Civil, Mechanical and Manufacturing Innovation

OpenAlex ID: W4306790221