Abstract
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.
Funder
ministry of education, singapore
duke-nus medical school
national institutes of health/national cancer center
cancer prevention and research institute of texas
national institutes of health
charles and daneen stiefel md anderson oropharynx program
patient-centered outcomes research institute
national cancer institute
national institute of dental and craniofacial research
thrive/hesi
atos medical
the nci early phase clinical trials in imaging and image-guided interventions program
nsf/nih joint smart connected health program
nci parent rpg mechanism
nih nibib research education programs for residents and clinical fellows grant
nidcr academic industrial partnership grant
nci parent research project grant
nih/nci cancer center support grant
pilot research program award from the ut md anderson ccsg radiation oncology and cancer imaging program
nsf division of civil, mechanical, and manufacturing innovation (cmmi) grant
elekta ab
the multidisciplinary the radiation oncology/cancer imaging program
md anderson cancer center support grant
md anderson program in image-guided cancer therapy
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications,Molecular Biology,Biochemistry,Structural Biology