Estimating the optimal linear combination of predictors using spherically constrained optimization.

Area of Science:

• Statistical modeling
• Machine learning
• Biostatistics

Background:

• Maximizing the area under the receiver operating characteristic curve (AUC) estimates optimal linear combinations for binary classification.
• For ordinal responses, maximizing the hypervolume under the manifold (HUM) is analogous but computationally challenging due to HUM's properties.
• Existing global optimization techniques for HUM are computationally expensive, especially with numerous predictors or outcome categories.

Purpose of the Study:

• To develop an efficient, derivative-free optimization technique for estimating optimal predictor combinations in ordinal classification.
• To address the computational limitations of existing methods for maximizing the hypervolume under the manifold (HUM).

Main Methods:

• Proposed Spherically Constrained Optimization Routine (SCOR), an efficient derivative-free black-box optimization technique based on pattern search.
• Evaluated SCOR's performance through extensive simulation studies against existing methods, including the step-down algorithm.

Main Results:

• SCOR demonstrated superior performance compared to existing methods in simulation studies.
• The method was successfully applied to predict the severity of swallowing difficulty after oropharyngeal cancer radiation therapy, using radiation dose data.

Conclusions:

• The SCOR method effectively addresses the challenge of combining multiple biomarkers for predicting ordinal outcomes, relevant in medical research for disease staging or toxicity grading.
• An R package implementing the SCOR method is publicly available for use.