Is the ratio of flow-mediated dilation and shear rate a statistically sound approach to normalization in cross-sectional studies on endothelial function?

Abstract

It has been deemed important to normalize flow-mediated dilation (FMD), a marker of endothelial function, for between-subject differences in the eliciting shear rate (SR) stimulus. Conventionally, FMD is divided by the area under the curve of the SR stimulus. In the context of a cross-sectional comparison across different age cohorts, we examined whether this ratio approach adhered to established statistical assumptions necessary for reliable normalization. To quantify brachial artery FMD and area under the curve of SR, forearm cuff inflation to suprasystolic pressure was administered for 5 min to 16 boys aged 10.9 yr (SD 0.3), 48 young men aged 25.3 yr (SD 4.2), and 15 older men aged 57.5 yr (SD 4.3). Mean differences between age groups were statistically significant ( P < 0.001) for nonnormalized FMD [children: 10.4% (SD 5.4), young adults: 7.5% (SD 2.9), older adults: 5.6% (SD 2.0)] but not for ratio-normalized FMD ( P = 0.10). Moreover, all assumptions necessary for reliable use of ratio-normalization were violated, including regression slopes between SR and FMD that had y-intercepts greater than zero ( P < 0.05), nonlinear and unstable relations between the normalized ratios and SR, skewed data distributions, and heteroscedastic variance. Logarithmic transformation of SR and FMD before ratio calculation improved adherence to these assumptions and resulted in age differences similar to the nonnormalized data ( P = 0.03). In conclusion, although ratio normalization of FMD altered findings about age differences in endothelial function, this could be explained by violation of statistical assumptions. We recommend that exploration of these assumptions should be routine in future research. If the relationship between SR and FMD is generally found to be weak or nonlinear or variable between samples, then ratio normalization should not be applied.