A Vector Theory of Assessing Clinical Trials: An Application to Bioequivalence

Abstract

A novel idea is introduced regarding the statistical comparisons of endpoints in clinical trials. Currently, the (dis)similarity of measured endpoints is not assessed. Instead, statistical analysis is directly applied, which can lead to multiplicity issues, reduced statistical power, and the recruitment of more subjects. The Vector-Based Comparison (VBC) approach originates from vector algebra and considers clinical endpoints as “vectors”. In the general case of N clinical endpoints, a Cartesian coordinate system is defined, and the most important primary endpoint (E1) is set. Following an explicitly defined procedure, the pairwise relationships of the remaining N-1 endpoints with E1 are estimated, and the N-1 endpoints are decomposed into axes perpendicular to E1. The angle between vectors provides insight into the level of dependency between variables. Vectors that are perpendicular to each other are considered independent, and only these are used in the statistical analysis. In this work, VBC is applied to bioequivalence studies of three anti-hypertensive drugs: amlodipine, irbesartan, and hydrochlorothiazide. The results suggest that VBC is a reproducible, easily applicable method allowing for the discrimination and utilization of the endpoint component expressing different attributes. All clinical characteristics are assessed with increased statistical power, without inflation of type I error.