Negative correlation between flow-mediated dilation (FMD) and arterial size: true association or mathematical artefact?

Objective: FMD is a marker of endothelial function often used as a surrogate endpoint in lipid lowering clinical trials. It is computed as the ratio of the brachial artery absolute diameter change (ADC), over the baseline diameter (BD). The rationale for this formula is the assumption of a proportionality between ADC and BD. A negative correlation between FMD and BD has been systematically reported in many contexts and explained with a variety of biological reasons. Besides this, the explanation may be purely mathematical, because BD is the denominator of the FMD formula. Aim of the present study was to assess the influence of mathematical artefacts on this correlation. Methods: we measured FMD on 119 dyslipidemic patients and we computed the correlation coefficient (R) between FMD and BD and between ADC and BD. We also run 1000 computer-simulations of the same correlations in virtual patients having, in place of BD and ADC, two variables totally random and uncorrelated, produced by a random number generator. The correlations obtained in the real and simulated contexts were then compared. Results: Similarly to what reported in the literature, in the real data the R between FMD and BD was -0.28 (95% C.I. -0.44 to -0.11) but the assumed proportionality between ADC and BD was not confirmed (r=-0.13, 95% C.I. -0.31 to 0.05). Using simulated data the R between FMD and BD was -0.27 (95%C.I. -0.39 to -0.12). Conclusions: The lack of proportionality between ADC and BD as well as the almost identical correlation coefficients obtained using the real and the simulated variables suggest that the association between FMD and BD is mostly attributable to mathematical artefacts.