Vector-based comparison as a novel framework for assessing multi-endpoint clinical trials: Applications to actual data

Abstract

Background: For clinical trials, the vector-based comparison (VBC) technique presented provides an alternative approach to solve a traditional problem caused by multiple endpoints. VBC uses vector algebra to form an endpoint vector and decompose it into different parts, thus reducing heterogeneity, increasing precision, and establishing a structure for the evaluation of clinical trial outcomes.

Methods: In this study, VBC was applied to 5 clinical trials with 695 patients. The primary clinical endpoint (E1) was defined as the reference endpoint, and the remaining endpoints were expressed relative to the primary endpoint. A paired t-test of the confidence interval widths, per decomposed endpoint, was conducted to test the effect of the VBC. Furthermore, machine learning and principal component analysis were applied to analyze whether the decomposed endpoints maintained the properties of the initial measures.

Results: The vector angle between E1 and the decomposed endpoints remained smaller than 45° in a typical study, which, before decomposing, was found to be correlated. Use of VBC brought down confidence interval widths by approximately 50%, implying less variability. Principal component analysis confirmed preservation of endpoint-specific properties, while Type I error simulations showed that VBC did not elevate false-positive rates under null conditions. Endpoint-specific type I error rates have been close to the nominal value of 0.05.

Conclusions: VBC can decompose clinical endpoints into nonredundant components while preserving endpoint-specific information and reducing variability without inflating Type I error. VBC serves as a reproducible and practical preprocessing method for clinical trials with many endpoints.

Keywords

clinical trials / endpoints / machine learning / vector-based comparison

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2026 The Author(s). Clinical and Translational Discovery published by John Wiley & Sons Australia, Ltd on behalf of Shanghai Institute of Clinical Bioinformatics.