The negative correlation between flow-mediated dilation (FMD) and arterial size may be ascribed to a mathematical artefact

The use of variables computed as a ratio of two measures, especially in correlation/ regression analysis, has been repeatedly criticized by statisticians. The brachial artery Flow-Mediated Dilation (FMD%), a non invasive marker of endothelial function widely applied in clinical studies, is a typical ratio variable, being calculated as: (absolute diameter change after stimulus)/ (resting diameter) x 100. Unsurprisingly, significant correlations between FMD% and resting diameter have been repeatedly reported, with coefficients ranging from -0.2 to -0.8. These correlations have been tentatively explained by a variety of biological reasons, but instead they may be largely accounted by a mathematical artifact called mathematical coupling. To test this hypothesis we used a Monte-Carlo approach by computing a simulated FMD% in which the numerator and the denominator were lacking of any real biological or physical relation. We started from real measurements of resting diameters and of diameter changes obtained from 189 patients with cardiovascular risk factors attending the Monzino Cardiology Centre in Milan. To disrupt the biological link between the two variables, we created a dataset of virtual patients by randomly coupling the resting diameter with the diameter change belonging to different subjects. FMD% was then computed from the two unrelated measures according to the above formula. The random coupling was reiterated 1000 times. The overall mean correlation coefficient between simulated FMD% and resting diameter was -0.170 (95% confidence interval -0.166, -0.174), a value very close to that observed in the original data (-0.168), and in the same range of those reported in the literature. These results indicate that the correlation between FMD% and artery size at rest is likely due to mathematical coupling.