The percentage flow-mediated dilation index: A large-sample investigation of its appropriateness,potential for bias and causal nexus in vascular medicine

Abstract

The percentage flow-mediated dilation index (FMD%) scales the increase in arterial diameter (D_diff) as a constant proportion of baseline artery diameter (D_base). We have demonstrated, albeit with small samples, that the scaling properties of FMD% can lead to biased inferences on endothelial dysfunction. Therefore, we aimed to investigate the underlying rationale and potential bias of FMD% using a selection of new examples from the large (n = 3499) and diverse Multi-Ethnic Study of Atherosclerosis (MESA). In this dataset, we found that smaller values of D_diff are associated with larger values of D_base, which contradicts the scaling properties of FMD%. Consequently, FMD% ‘over-scales’ and naturally generates an even stronger negative correlation between itself and D_base. Using a data simulation, we show that this FMD%–D_base correlation can be a statistical artefact due to inappropriate scaling. The new examples we present from MESA indicate that FMD% biases the differences in flow-mediated response between men and women, Framingham risk score categories, and diseased and healthy people. We demonstrate how FMD%, as an exposure for predicting cardiovascular disease, is confounded by its dependency on D_base, which itself could be clinically important. This critical review, incorporating an allometric analysis of a large dataset, suggests that the FMD% index has a less-than-clear rationale, can itself generate the D_base-dependency problem, provides biased estimates of differences in the flow-mediated response, complicates the interpretation of the flow-mediated protocol and clouds the causal pathway to vascular disease. These interpretative problems can be resolved by applying accepted allometric principles to the flow-mediated response.

Introduction

Percentage flow-mediated dilation (FMD%) has been said to: ‘measure the ability of the arteries to respond with endothelial nitric oxide release during reactive hyperemia (flow mediated) after a 5-minute occlusion of the brachial artery with a blood pressure cuff’. ¹

The FMD% index is calculated by dividing the ‘response’ or change in arterial diameter (D_diff) by the initial baseline diameter of the artery (D_base) and multiplying by 100. The FMD% index is just one of many percentage change indices used in the field of vascular medicine, others being the nitroglycerin-mediated percentage diameter change (NMD%) and, most recently, percentage flow-mediated constriction (FMC%). ² Researchers have also calculated ratios of FMD%, NMD% and FMC% (which are already ratios), resulting in other measures of vascular function. ² It is interesting to contrast the liberal use of these ratio indices in research on endothelial function with the established approaches of physiologists working in other fields. For example, Packard and Boardman ³ maintained that:

all authors discontinue using percentages and size-specific indices in an attempt to scale data for variation in body size within and among groups [and] not to take seriously the conclusions from any report that relies on percentages or size-specific indices to control for effects of body size on the variable of interest.

Since its inception, ⁴ FMD% has been the primary index in thousands of studies. Researchers are motivated by reports that clinical populations have a lower FMD% than healthy controls, and that a relatively low FMD% is predictive of an increased incidence of cardiovascular disease.^5,6 Importantly, a relatively high D_base is also associated with an increased incidence of cardiovascular disease and a faster progression of carotid artery intima–media thickness. ⁷ The baseline artery diameter is often systematically higher in diseased versus healthy people^5,6 and can change in response to many interventions, including red wine consumption and exercise.^8,9

Recently, we examined the potential for FMD% to bias estimates of differences in flow-mediated response between children and adults.^10,11 Here, and throughout this review, we refer to ‘bias’ in an inferential statistics context, whereby the magnitude of a population estimate is biased high or low by a certain confounder. Our previous studies were met with published concerns that we analysed relatively small sample sizes and had a rather narrow focus.^{12 –14} These editorials called for the appropriateness of FMD% to be investigated with larger samples drawn from different populations. Therefore, we now aim to investigate, in a more comprehensive manner than before, the dependency of FMD% on D_base, and the associated implications of this phenomenon. The investigations in this review are supported by evidence and new examples from the Multi-Ethnic Study of Atherosclerosis (MESA). This very large and diverse sample of open-access data offers the opportunity for excellent precision and generalisability to explore the potential for FMD% to bias inferences.

Our specific objectives were to:

• describe the fundamental size-scaling relationship between flow-mediated response and D_base in the large sample dataset from MESA

• investigate whether an allometric approach changes inferences on the relationship between the flow-mediated response and sex, age, Framingham risk scores (FRS), left ventricular mass and cardiovascular disease in MESA

• examine how measurement error in the components of FMD% (D_base and D_peak) propagates to the measurement error in FMD%

• explore how the dependency of FMD% on D_base influences the causal nexus between the flow-mediated response, as the ‘exposure’, and cardiovascular disease outcomes.

FMD% is an isometric ratio scaling index

As a ‘change in size’ problem, the increase in arterial diameter measured in the FMD% protocol is a classic candidate for the application of allometric principles rather than the ubiquitous acceptance of a percentage change index, which is the current status quo. Allometry is the study of relationships between biological processes and size. ¹⁵ The FMD% index is an example of an ‘isometric index’ in allometry, whereby FMD% is reliant on the assumption that the change in arterial diameter is a direct and constant proportion of initial artery diameter. Allometric scaling is used when any size–change relationship is suspected to deviate from this isometry. Therefore, the precise description of the relationship between initial size and final size is a fundamental part of allometric scaling.

The FMD% index is mathematically equivalent to the ratio of peak diameter (D_peak) and D_base. For example, an FMD% of 5% equates to a D_peak/D_base ratio of 1.05. An FMD% of 10% equates to a D_peak/D_base ratio of 1.10, and so on. This ratio is isometric in that it always scales the differences in D_peak (or D_diff) as a constant proportion of differences in D_base (e.g. for a small brachial D_base of 3.0 mm, an FMD% of 5% translates to a D_diff of 0.15 mm). For a large D_base of 6.0 mm, the same FMD% of 5% (and presumably the same endothelial function) translates to a D_diff of 0.30 mm. Clearly, the validity of FMD% depends on this assumption that differences in D_diff are directly and consistently proportional to D_base in all circumstances.

Allometric ‘red flags’ for FMD%

It has been reported that, ‘Absolute change in FMD (millimetre) is unrelated to resting vessel size’. ¹⁶ This claim, supported by the observations of Herrington et al., ¹⁷ seems incompatible with a proportional size-adjustment index such as FMD%. Although we could not locate any rationale in the literature for the original choice of the FMD% index, it is likely that it was selected to ‘normalise’ for variability in D_base, and, presumably, it must have been assumed that larger values of D_base are associated with larger changes in diameter during the FMD% protocol.

Paradoxically, it was clear, even in the very first studies on this topic, that FMD% is still sometimes strongly inversely related to D_base. ⁴ Therefore, if the initial intention was to ‘normalise’ D_diff for variability in D_base, FMD% has been apparently unsuccessful at this task. Nevertheless, researchers have persevered with FMD%, while forwarding mainly physiological-based explanations for its dependence on D_base ¹⁸ and somewhat convoluted solutions for interpreting differences in FMD% in light of the D_base-dependency problem (see below).

Statistics are the fundamental outcomes in quantitative research and are, therefore, the bases of all inferences in physiology. These statistical inferences from physiological research can inform clinical importance and practice. If a sample statistic is biased high or low, then study conclusions could be compromised, leading to imprecise information about the clinical importance of a physiological measurement. Statistical bias is ideally resolved by applying the correct statistical solutions at the level of the sample statistic itself.

Are the underlying assumptions of FMD% upheld?

As part of the present review, we can extract new examples from a subsample (n = 3499) of the whole MESA study population (n = 6814) which, together with the FMD% protocol, is detailed in full by Yeboah et al. ⁶ There have also been over 700 MESA-related publications in which the sample and protocols are detailed. Our particular subsample involved all participants who were measured for FMD% in MESA, except for two extremely high outliers, which were removed prior to our analyses according to recognised procedures. ¹⁹

In this MESA subsample, the correlation between D_diff and D_base is actually negative in sign (95% confidence interval (CI): −0.12 to −0.19; Figure 1). This correlation was found to be stable across sexes, age groups and categories of FRS. The use of FMD% hinges on the assumption that D_diff is directly and consistently proportional to D_base. Therefore, one would expect at least a moderate positive correlation between D_diff and D_base. Because this assumption is violated in the MESA dataset, FMD% is likely to be a biased index across the measurement range. The dashed line in Figure 1 represents how the sample mean FMD% of 4.4% (standard deviation (SD) = 2.9) would translate to respective values of D_diff for each participant across the measurement range in MESA. It can be seen that FMD% is misrepresenting the true negative relationship between D_base and D_diff in MESA participants. The 95% CI of the estimate of mean FMD% is a precise 4.3–4.5% in MESA, indicating that sampling error cannot explain this discrepancy.

Figure 1.

(Top) The negative regression slope (solid line) between D_base and D_diff in the MESA subsample (n = 3499). This negative correlation was found to be similar between sexes, age groups and Framingham risk categories. The dashed line represents the clearly erroneous proportionality between D_base and D_diff that is assumed when using FMD% (the sample mean FMD% in the MESA being 4.4%). (Bottom) The negative correlation between D_base and FMD% caused by the erroneous application of a size-proportion ratio (FMD%) where no proportionality actually exists.

Why is FMD% so dependent on D_base?

Since FMD% is based on the apparently false premise that D_diff varies in direct proportion to D_base, FMD% actually causes an even stronger negative correlation between itself and D_base in MESA. The 95% CI for this correlation between FMD% and D_base is −0.45 to −0.40, which can be described as ‘moderate’ in terms of effect size thresholds ¹⁹ (Figure 1). Again, this D_base–FMD% correlation is of similar magnitude between sexes, age groups and Framingham risk categories in MESA.

There are reports of even stronger negative correlations (r < −0.8) between D_base and FMD%, stretching back to early studies. ⁴ FMD% also tends to be skewed in distribution, even if D_base and D_peak are normally distributed variables, and this is the case in MESA. Substantial skewness is confirmed in the MESA sample because the mean FMD% of 4.4% is smaller than two times the sample SD (2 × 2.9%). ²⁰ Skewness is common with most ratio indices and can also bias parametric analyses.^19,20 These statistical and size-scaling ‘red flags’ increase the concern that FMD% is an unreliable metric for population estimates of endothelial function.

A relevant question is whether the dependency of FMD% on D_base is explained fully by physiology or is, at least in part, a statistical artefact. This question can be answered with a simple data simulation, where data realistic to the sample estimates from MESA are produced by a random number generator (e.g. within the Microsoft Excel program). Therefore, we generated 2000 realistic (to the sample characteristics of MESA), and normally distributed, values of D_base (mean = 4.31 mm, SD = 0.82 mm). Similarly, realistic and normally distributed values of D_diff were generated (mean = 0.18 mm, SD = 0.11 mm). This allowed calculation of FMD% in the normal way. One can see in Figure 2 that a negative correlation is obtained between calculated FMD% and D_base (95% CI of r: −0.22 to −0.32). As expected, the FMD% index is not a normally distributed outcome in this data simulation even though D_base and D_peak are normally distributed. These findings agree with the similar simulations presented by Vickers ²¹ in the context of randomised controlled trials. The fact that a negative correlation between FMD% and D_base can be derived from simulated data with no physiological link at all between D_base and D_diff indicates that the correlation is, at least in part, a statistical artefact resulting from the inappropriate use of a ratio index.

Figure 2.

The negative correlation between randomly generated values of D_base and calculated FMD%. This correlation is present with no physiological relationship at all between the values of D_base and D_diff, proving that the dependency of FMD% on D_base is, at least in part, an allometric problem, and not wholly a physiological phenomenon.

Application of allometric principles to the flow-mediated response

An important part of allometry is quantification of the exponent which describes the relationship between initial and final artery size. From the regression slope between logarithmically transformed values of both D_base and D_peak, one can derive the correct scaling exponent for any dataset, and this approach is fully detailed in our previous studies.^10,11 In a supplementary file, we also present the SPSS steps for comparing independent samples in terms of D_base-adjusted flow-mediated dilation (Appendix). This log-log slope (b exponent in the simple allometric model of D_peak = a × D_base ^b ) should ideally be verified using an appropriate form of nonlinear regression working in the raw arithmetic space. ²² The regression slope for logarithmically transformed D_base and D_peak is 0.942 in MESA (95% CI: 0.937 to 0.946), rather than the value of 1 necessary for the appropriate use of FMD%.^10,11 Again, this allometric slope exponent was found to be similar between sexes, age groups and Framingham risk categories in MESA. The slope is also similar to those reported previously for smaller datasets.^10,11 Nevertheless, we do not necessarily suggest at present that this allometric exponent is universally applied to all data from the flow-mediated dilation protocol. Rather, the analysis of covariance approach we detail in previous studies,^10,11 and in the supplementary SPSS steps, is based on an allometric exponent that is unique to each dataset. This more ‘tailored’ approach is preferable to the ubiquitous selection of FMD% as the statistical outcome in all studies. The FMD% index is based on the allometric exponent being assumed to be a value of 1 in all studies and all samples.^10,11

When two or more samples are being compared in terms of D_base-adjusted flow-mediated response, it is important to derive the exponent from the statistical model itself rather than from the separate samples. The allometric exponent can be derived from this model when log-transformed D_peak is selected as the outcome. However, we prefer D_diff (on the logged scale) to be the outcome of interest because sample estimates from the model can then be back-transformed to represent ‘adjusted’ mean values of flow-mediated response. When logD_diff is the outcome, its parameter estimate derived from the statistical model does not represent the exponent as such. But if this parameter estimate is subtracted from 1, then this will represent the allometric exponent for the fundamental relationship between D_base and D_peak. For example, if the parameter estimate for the influence of logD_base on logD_diff is 0.06, then the allometric exponent would be 1 − 0.06 = 0.94. One can check whether this exponent is substantially and significantly different between samples by adding a logD_base × group interaction to the statistical model. In MESA and in our previous analyses, we have not found a substantial difference between samples in this respect. Moreover, Senn ²³ has argued, in the context of randomised controlled trials, that analysis of covariance (ANCOVA) is still preferred over percentage change analyses, even if this assumption called ‘parallelism’ is violated.

The interpretation of FMD% data

Researchers have been well aware of the negative correlation between D_base and FMD%, but awareness itself might not necessarily eradicate the problems it creates without the proper application of allometric principles. Instead of the D_base–FMD% correlation being recognised as a fundamental scaling problem, various interpretative constraints seem to have been placed on FMD%, and/or it has been deemed necessary to consider differences in other variables in order to interpret FMD% reliably.^1,16 For example, Corretti et al. ²⁴ provided the following suggestions for coping with the D_base-dependency problem:

Reporting absolute change in diameter will minimize this [the D_base-dependency] problem … For studies in which comparisons are made before and after an intervention in the same individuals, percent change might be the easiest method to use if baseline diameter remains stable over time. However, the best policy may be to measure and report baseline diameter, absolute change and percent change in diameter.

It is unclear how the three variables mentioned in this coping strategy (D_diff, D_base and FMD%) should be weighted and combined to arrive at a reliable interpretation of FMD%. These complications and a ‘report everything’ tactic could be redundant if D_diff is scaled correctly to D_base using the most appropriate index in the first place.

Significance testing for D_base stability

Corretti et al. ²⁴ maintained that FMD% could be the most amenable index if ‘baseline diameter remains stable over time’. And it is a common practice amongst researchers on FMD% to test whether there are statistically significant differences between groups or repeated measures in D_base. ²⁵ First, even in placebo-controlled and randomised studies, checking whether baseline measurements differ significantly between samples is known to be an unsound and illogical approach to the analysis of change because a lack of significant difference cannot be treated as a proof of equivalence.^10,11,23 Indeed, in a randomised trial one should not test for pre-intervention differences statistically, as any observed baseline imbalance must be due to chance, by definition. There will always be some degree of baseline imbalance because randomisation procedures do not guarantee exact equivalence, especially in small samples. Moreover, the ‘D_base should not differ’ constraint is particularly unhelpful because D_base is often substantially different between the very samples and interventions that researchers are interested in (e.g. clinical versus healthy cohorts).^5,6

The problems of making the appropriateness of FMD% conditional on the stability of mean D_base between samples or repeated measures can be demonstrated from the standpoint of statistical power. Let us assume that a mean difference in D_base between the samples of interest is 0.2 mm. Only a sample size of 363 participants (in each sample) would have sufficient statistical power (90%) for this difference in D_base to be deemed statistically significant (p < 0.05), assuming that the common standard deviation is 0.83 mm, as it is in MESA. Similarly, only a sample size of 75 would have 90% power to detect a mean pre–post change in D_base of 0.2 mm, assuming that the correlation between pre–post measures is 0.8. Put another way, the 95% confidence limits for an observed mean pre–post change in D_base of 0.2 mm would be an unreasonably wide −0.05 to 0.45 to arrive at a reliable inference, if there are typically 20 participants in an experiment. Using D_base stability as a condition for judging the appropriateness of FMD% is clearly philosophically unsound. The ‘stability’ of D_base would be almost guaranteed in many studies with relatively small sample sizes.

The influence of shear rate on the flow-mediated response

‘Normalisation’ of FMD% for variability in shear rate has also been considered as a general approach to interpreting differences in the flow-mediated response.^1,26 Nevertheless, this practice seems academic if FMD% is not ‘normalising’ the flow-mediated response for variability in D_base correctly in the first place. It is interesting that shear rate tends to be negatively correlated with D_base, ¹⁶ which increases the chance that any correlation between FMD% and shear rate is spuriously influenced by D_base as the ‘third variable’. The fact that D_base is correlated to both shear and FMD%, and that all these variables are essentially measured at the same time, leads to an unclear causal pathway between shear rate and the flow-mediated response per se when FMD% is selected as the outcome in cross-sectional studies. Nevertheless, shear rate can be added as a covariate, together with D_base (or indeed any other appropriate covariates), to an ANCOVA-based allometric model. As long as the influence of D_base is adjusted for, using the allometric approach we detail,^10,11 other covariates such as shear rate can be added to the same statistical model in order to explore whether there is significant contribution to explained variability in flow-mediated dilation. In this way, researchers would be exploring the true relationship between shear rate and the flow-mediated response per se. It seems logical that a D_base-adjusted index of flow-mediated response is the primary unit of analysis, which can then also be adjusted for the influence of any other potential covariates. Unfortunately, shear rate was not measured in the MESA.

Covariate-adjusting FMD% itself for D_base

Another suggestion in the literature for coping with the D_base–FMD% correlation is adjusting FMD% itself for D_base (or 1/D_base) using ANCOVA. However, D_base is already the denominator in the FMD% calculation.^10,11 It is highly unusual to covariate-control a study outcome for another variable when that variable is already an inherent component of the study outcome. For example, it would be unusual for a researcher to covariate-adjust body mass index for its denominator, height-squared, or for maximal oxygen consumption (ml/kg/min) to be covariate-adjusted for the denominator, body mass. This practice might exacerbate the distributional problems of FMD%. It is the choice of FMD% as the outcome which could be the fundamental problem and not the proposed use of ANCOVA to adjust for covariates that influence flow-mediated dilation.

One relevant question is whether the use of D_diff itself is preferable as the outcome of interest. Vickers ²¹ compared statistical bias and power between simple change scores, percentage changes and the use of ANCOVA, and found the latter approach to be superior in all circumstances. Vickers ²¹ confirmed that only the ANCOVA approach can provide generally consistent and unbiased estimates of change, especially when baseline measurements differ between samples.

Why is FMD% less repeatable than D_base and D_peak?

It has been reported that the test-retest repeatability of FMD%, as measured by the coefficient of variation (CV) statistic, can be markedly worse than that of D_base and D_peak. ¹⁷ There is a mathematical explanation for this observation. Specifically, measurement errors (or variances) can naturally propagate to increase markedly through the equation for FMD%. For example, using the statistical tool presented by John Pezulo (statpages.org/erpropgt.html), one can observe how typical measurement errors associated with the measurements of D_base and D_peak can mathematically propagate to a much larger measurement error for FMD%.

Measurements of D_base and D_peak are typically highly correlated (r = 0.992 in the MESA). Both these variables have a relatively low repeatability CV of 4–5%. ¹⁷ Nevertheless, these errors can propagate, first, through the calculation of D_diff, then through the division of D_diff by D_base, and finally through the ×100 step to form the FMD% ratio. This error propagation can result in a CV of 25% for FMD%, which is similar to the CVs that are reported in the literature. ¹⁷ Again, it is important to consider mathematics alongside any physiological or protocol explanations for the relatively poor repeatability of FMD% compared with D_base and D_peak.

New examples of FMD% bias from the MESA

A D_base-independent estimate of D_diff is obviously the outcome of interest for endothelial function. What is clearly needed is a metric which accurately and specifically quantifies the ‘response’ that is fundamental to the flow-mediated dilation protocol. But FMD% overestimates endothelial function when D_base is small and vice versa, thereby compromising study conclusions. Although an allometric exponent of 0.94 does not appear to be substantially different from 1.00, this exponent is part of a power function so that small differences between the true (0.94) and perceived (1.00) could lead to clinically important differences in estimates of differences in the flow-mediated response. Some new relevant examples to illustrate these differences are now presented from MESA. Full details of the proper D_base-adjustment approach can be found in references 7 and 8. This approach has also been adopted to analyse the data in two other recent studies.^8,27 The suggested steps in SPSS for comparing samples in terms of the D_base-adjusted flow-mediated response are provided in a supplementary file.

Sex and age differences in the flow-mediated response

In MESA, the mean (SD) FMD% is 4.5% (3.1) in women and 3.8% (2.5) in men. However, the mean D_base is approximately 1 mm lower in women versus men. When differences in D_base are properly adjusted for, the ‘corrected’ FMD% is 3.5% (4.2) in women and 4.4% (4.2) in men, completely contrary to the FMD% results. In contrast to recent suggestions, ²⁵ women in the MESA do not have better endothelial function than men across most age categories (Figure 3). Researchers may adjust FMD% for various potential covariates but this approach might be in vain if FMD% is the inappropriate outcome to select in the first place.

Figure 3.

Mean (+95% CI) FMD% and allometric D_base-adjusted FMD in the male and female age categories in MESA. Women do not necessarily have a higher flow-mediated response than men when the influence of D_base is properly adjusted for.

The association between flow-mediated response and Framingham risk scores

Between the lowest and highest quartiles of FRS in the MESA subsample, the mean (SD) FMD% decreases from 5.6% (3.3) to 3.3% (2.2). Importantly, D_base is 1 mm higher in the highest FRS quartile compared with the lowest quartile. D_base-adjusted estimates of FMD% can be derived using the approach detailed in references 10 and 11, and these adjusted estimates of FMD% are 4.7% (3.0) and 3.7% (2.8) in the 1st and 4th quartiles, respectively, a difference of only 1 percentage point between the upper and lower quartiles. Here, the negative association between FRS and FMD% seems inflated because FMD% is dependent on D_base, which is also positively associated with FRS.

The association between flow-mediated response and left ventricular mass index (LVMI)

In MESA, FMD% is negatively correlated with LVMI, ²⁸ but the positive correlation between LVMI and D_base is substantially stronger (Figure 4). Baseline artery diameter is also positively correlated to body surface area (even when adjusted for age and sex), and this is the denominator in the LVMI ratio (Figure 4). The dependency of FMD% on D_base and the dependency of D_base on body size clearly enters FMD% into the murky world of spurious correlations. A spurious correlation is one where an apparent correlation between x and y is actually explained by a third variable z, which is related to both x and y. There have also been other criticisms levelled at the scaling properties of LVMI. ²⁹

Figure 4.

An example of a possibly spurious correlation between FMD% and another variable (left ventricular mass index) that is also correlated to D_base. ²⁸ A spurious correlation exists when a correlation between two variables is actually explained by both variables being correlated to a ‘third variable’, which in this case is D_base. A greater left ventricular mass index (LVMI) is associated with a higher D_base, which is the denominator of FMD%. Therefore, potential spuriousness could exist in the LVMI-FMD% correlation. LVMI is normalised (as a ratio) to BSA. If D_base was also normalised in this way, spuriousness could be even worse due to another common covariate (BSA) being present in the x–y variables that are correlated.

The flow-mediated response and cardiovascular disease

Many studies have involved a comparison of FMD% between healthy people and people with cardiovascular disease. In prognostic studies, FMD% may be measured at baseline and then people are followed up to see if they develop a cardiovascular event.^5,6 Typically, D_base is also found to be higher in cases versus controls in these studies, and the MESA is no exception ⁶ (Table 1). The sample of people that did eventually develop ‘all-cause’ cardiovascular disease at the fourth follow-up in MESA had a mean FMD% at baseline that was almost 1% lower than those people who remained healthy (controls). Nevertheless, cases had a mean D_base which was more than 0.3 mm higher than controls. As well as rendering the ‘D_base should not be significantly different’ mantra redundant when interpreting FMD%, this higher D_base biases the FMD% index. When proper allometric analyses are applied to these data,^10,11 the difference in D_base-adjusted flow-mediated response is less than half than that when FMD% is selected as the outcome (Table 1). This reduction in the difference in flow-mediated response between cases and controls obviously influences the general quantification of response that is deemed clinically significant. The FMD% index clouds the interpretation of the minimal clinically important difference in flow-mediated response.

Table 1.

Variables measured during the flow-mediated dilation protocol for people in MESA who did, and did not, develop all-cause cardiovascular disease.

Variable	Cases (n = 300)Mean (SD)	Controls (n = 3198)Mean (SD)	95% CI for difference between samples
Dbase	4.61 (0.77)	4.30 (0.83)	0.61 to 1.20
Dpeak	4.77 (0.77)	4.48 (0.82)	0.19 to 0.39
Ddiff	0.16 (0.10)	0.18 (0.11)	0.01 to 0.04
FMD%	3.6 (2.5)	4.5 (2.9)	0.6 to 1.2
Dbase-adjusted FMD	4.0 (2.5)	4.4 (2.5)	0.1 to 0.7

The difference between samples in terms of D_base-adjusted FMD% (0.4%) is less than half the difference observed when FMD% itself is selected as the outcome (0.9%). This is because D_base itself is larger in cases versus controls and FMD% is negatively correlated to D_base.

Such differences in study conclusions between FMD% and properly scaled D_diff might not occur all the time due to sampling error, especially in small studies. Nevertheless, these large-sample examples should encourage researchers to revisit study conclusions. Worryingly, many of the interventions suggested for improving endothelial function, including exercise and red wine for example, also mediate changes in D_base.^8,9

The causal pathway between FMD% and arterial morphological changes

An association has been reported between FMD% and the progression of structural arterial changes, especially those in carotid intima–media thickness (cIMT). ⁷ Such observations are used to support the notion that changes in FMD% precede changes in arterial morphological changes. However, it could be considered that a structural measure of the brachial artery (D_base) is already inherent in the FMD% index, and this structural measure might be correlated to other structural measures in the carotid and/or coronary arteries.

In the MESA, four subsamples of participants can be formed on the basis of low-high values of cIMT. Between the lowest cIMT sample and the highest cIMT sample in the MESA, FMD% reduces from a mean of 5.2% to a mean of 3.5% as one would expect (p < 0.0005). Nevertheless, the mean D_base is 4.1 mm in the lowest cIMT sample and 4.6 mm in the highest cIMT sample (p < 0.0005). Therefore, the D_base-adjusted estimates of flow-mediated response become 4.9% and 3.8% for these samples, respectively, a much smaller difference of 1.1%. The Pearson’s correlation coefficient between cIMT and D_base of 0.17 is larger than the correlations between cIMT and body mass, height and body mass index, and the same as the correlation between cIMT and waist circumference. Here, the door is opened to let spurious correlations cloud the interpretation of the relationship between cIMT and FMD%.

Halcox et al. ⁷ reported that D_base is also related to the progression in cIMT, but data were not presented and this finding was not discussed nor is it often cited in the literature. Unfortunately, cIMT was only measured in the MESA at baseline, and not at the follow-up times, but these relationships between cIMT, FMD%, D_base and measures of body size demonstrate the importance of accounting for scaling influences when FMD% is correlated to structural arterial variables.

The prognostic value of FMD%

If FMD% predicts cardiovascular disease, then this might provide good reason to measure it in clinical practice and undertake research on it. The FMD% index and D_diff seem to be the most common exposure variables investigated for predictive value, although a greater focus towards D_base is emerging.^5,6 The influence of D_base is not necessarily a simple issue of normalisation because D_base is, itself, predictive of progression of atherosclerosis and future cardiovascular disease.^{5 –7} Therefore, a question of interest, which is important to answer in the context of translational physiology, ³⁰ is whether D_base supplies at least the same clinical usefulness as FMD%. Factors influencing the translation of a physiological exposure to public health include cost of equipment and technical training, level of expertise required, amount of discomfort associated with measurement and the error associated with these measurements. All these factors are ‘worse’ for the measurement of FMD% compared with D_base.

In Table 2, we present a summary of all the prognostic-type studies that were recently meta-analysed by Inaba et al. ³¹ It can be seen that the consideration of D_base, and how it is built into any analyses, varies greatly between studies. More than half of the studies do not report any details about how the influence of D_base was accounted for. Four of the studies seem not to report any information about D_base at all. In the study by Yeboah et al., ⁵ the prognostic value of D_base was examined after expressing it relative to the height of the participant. Nevertheless, this same body size adjustment approach was not applied to FMD%. If a lack of adjustment for the influence of D_base generally leads to inflated estimates of sample differences in endothelial function, then the minimal clinically important difference in flow-mediated response becomes less clear. In one recent study, the mean difference in D_base-adjusted flow-mediated response between ‘binge drinkers’ and controls can be estimated to be only a third as large as the mean difference in FMD% between samples (0.75% vs 2.6%). ³²

Table 2.

Information relevant to D_base and its influence in the studies meta-analysed by Inaba et al. ³¹

Studies meta-analysed (in alphabetical order)	Reporting of information on Dbase	Management of any Dbase influence	Relative risks per 1% point increase in FMD
Brevetti et al. (2003)	None reported	None reported	0.870 (0.782–0.967)
Fathi et al. (2004)	Dbase reported to be 3.3 mmfor pooled sample	None reported	0.975 (0.939–1.012)
Frick et al. (2005)	Dbase found to be 0.5 mm lower in cases vs controls	Dbase found not to be a univariate predictor of disease	0.928 (0.817–1.053)
Gokce et al. (2003)	Dbase found to be negatively correlated to FMD% and 0.2 mm higher in cases vs controls (p = 0.19)	Absolute change in diameter explored as a predictor	0.767 (0.689–0.855)
Karatzis et al. (2006)	None reported	None reported	0.855 (0.745–0.981)
Katz et al. (2005)	Dbase 4.13 mm in survivors vs 4.03 mm in non-survivors	None reported	0.833 (0.702–0.989)
Meyer et al. (2005)	Dbase 0.3–0.4 mm higher in older diseased subjects compared to young healthy subjects	Differences in Dbase were reported as not statistically significant but reported means, SD and sample size indicate otherwise (e.g. young vs survivors; p = 0.047)	0.853 (0.737–0.988)
Muiesan et al. (2008)	None reported	None reported	0.851 (0.755–0.960)
Neunteufl et al. (2000)	None reported	None reported	0.774 (0.666–0.900)
Patti et al. (2005)	Dbase 4.48 mm in cases vs 4.16 mm in controls at second measurement	None reported	0.764 (0.686–0.851)
Rossi et al. (2008)	Mean Dbase similar (difference < 0.1 mm) between cohorts formed on basis of FMD%	None reported	0.893 (0.843–0.945)
Shechter et al. (2009)	Mean Dbase 0.78 mm higher in the low FMD% cohort (p < 0.001)	Dbase reported to be related to FMD% but not a significant predictor (no odds ratio reported)	0.829 (0.720–0.956)
Shimbo et al. (2007)	Dbase for pooled sample reported to be 3.8 mm	Hazard ratio for Dbase as a predictor reported to be 1.43 (p = 0.15); Dbase not followed up in multivariate model	0.935 (0.844–1.035)
Yeboah et al. (2007)	Mean Dbase higher by 0.34 mmin the low FMD% cohort	Dbase found to be a significant predictor of events in univariate model	0.961 (0.928–0.995)

Full reference details for the various studies can be found in Inaba et al. ³¹

It is clear that the scaling problems of FMD% are, again, pivotal for unravelling the causal pathway and prognostic value of the flow-mediated response. Even if FMD% predicts cardiovascular disease, one does not know whether the important prognostic component of FMD% is properly scaled D_diff per se (i.e. endothelial function) or the D_base that explains much of the variability in FMD%. It is also possible that D_base and D_diff (adjusted for the influence of D_base) combine to render FMD% a ‘hybrid’ index that is predictive of cardiovascular disease. These three possible causal pathways involving the exposure of FMD% are presented in Figure 5. It is of overriding importance to know whether it is D_base and/or D_base-adjusted D_diff that explains the predictive value of FMD%. Given that D_base is easier to measure with better reproducibility than FMD%, and is known to be predictive of cardiovascular events already (without being mathematically coupled to any other variable in its calculation), the predictive component of the D_base-adjusted flow-mediated response should be isolated and quantified.^5,6

Figure 5.

A causal pathway showing the ambiguity in how FMD% might be predictive of a cardiovascular event. Pathway A: a reduced flow-mediated response per se is predictive of a cardiovascular event (this is the perceived causal nexus at present). Pathway B: the pathophysiological effects of an increased D_base and a decreased flow-mediated response combine to be predictive of a cardiovascular event. Pathway C: an increased D_base per se is predictive of a cardiovascular event, and its negative influence on FMD% makes it merely appear as though FMD% has predictive value. (Drawn using information in ref. 16.)

We hope that the information presented in this review can inform a future study on the prognostic value of a measure of the flow-mediated response that is free from the influence of D_base. It is proposed that D_base-adjusted D_diff derived from an ANCOVA model provides a more representative and statistically parsimonious indicator of endothelial function.^7,8 For the analysis of the prognostic value of the flow-mediated response, D_diff (on a logarithmic scale) could first be modelled properly to logarithmically transformed D_base. The residuals from this model would then correspond to properly scaled D_base-adjusted diameter change, ¹⁵ which could then be entered as a predictor in a Cox regression analysis of a large dataset with a relatively long follow-up duration. Other covariates, selected using directed acyclic graphs (DAG), ³³ could also be included in the statistical model. This important process of selection of covariates would need careful consideration prior to any prognostic-type study. We note that a DAG has not yet been formulated for the flow-mediated response or D_base. Such important considerations in a future prognostic-type study would help to elucidate whether the flow-mediated response per se has sufficient predictive value and clinical significance.

Conclusions and recommendations

• Percentage flow-mediated dilation is the ubiquitously selected index for quantifying the flow-mediated arterial response. In all the relevant studies, researchers use sample estimates of FMD% in order to arrive at population inferences, ultimately to inform clinical significance and practice. The present review is relevant to all such studies.

• The FMD% index relies on the assumption that the flow-mediated response increases as a constant proportion of D_base. The FMD% index is mathematically equivalent to the ratio of D_peak/D_base ¹ , where 1 is the allometric size-scaling exponent that is ubiquitous across all samples. The presence of D_base as the denominator in the FMD% ratio is clearly an attempt to normalise the flow-mediated response to initial artery size.

• For the first time, we have analysed a very large sample of FMD% data (n = 3499) from an allometric perspective. We have found that the increase in flow-mediated response is neither constantly nor directly proportional to D_base, irrespective of age, sex, race/ethnicity and disease status in the MESA.

• Because of the incongruity between the true scaling properties of the flow-mediated response and how FMD% describes that response, FMD% actually mediates a moderate-to-large dependency on D_base. A negative correlation between FMD% and D_base can be obtained with randomly generated data where there is no physiological link at all between D_base and D_diff.

• An allometric model involving the flow-mediated response (on a log scale) as the outcome and D_base (log-transformed) as a covariate can completely eradicate the problem of D_base dependency. This is analysis of covariance, which is a common approach in medical research and available in most statistical software packages.

• The complete eradication of D_base-dependency with the allometric-based approach is achieved without the need for shear rate normalisation, although the the need for shear rate normalisation, although the important influence of shear rate on the flow-mediated response can still be quantified with the allometric model.

• The complete eradication of D_base-dependency means that secondary scrutiny of sample differences in D_base and/or absolute flow-mediated change is not necessary. There would be no need for researchers to discount the influence of D_base on the basis of a non-significant hypothesis test; a practice which has been much criticised by statisticians.

• Retaining FMD% as the study outcome and covariate-adjusting statistical models by D_base is illogical in allometric terms, since D_base is already the denominator of FMD%. This approach would be unacceptable in other similar contexts (e.g. a researcher adjusting statistical models for height or height ² when body mass index (kg/m²) is the outcome of interest).

• We have presented new examples from MESA to show how the incongruous scaling properties of FMD%, and the associated dependency on D_base, bias conclusions regarding the influence of age, sex, left ventricular mass, Framingham risk score and disease status on the flow-mediated response. FMD% typically overestimates differences in endothelial function between samples, thus clouding the minimal clinically important difference in flow-mediated response.

• We posit that use of the FMD% index, and associated dependency on D_base, clouds knowledge about the causal pathway between the flow-mediated responses and disease outcome. This is because D_base itself predicts future cardiovascular disease and intermediary outcomes such as the yearly progression in cIMT. While it may appear appealing that the prognostic value of D_base and the flow-mediated response ‘come together’ into an integrated exposure variable, it is imperative to establish whether D_base has at least the same clinical significance as the flow-mediated response, especially since D_base is inherently more repeatable than FMD% (due to mathematical error propagation) and easier to measure than the flow-mediated response.