purpose. The arteriole to venule ratio (AVR) is widely used in studies of the associations of retinal microvascular disease with systemic and ocular outcomes. This is a discussion of the limitations of AVR; a comparison of its predictive information with that of its components, arteriolar and venular caliber; and a description of a suggested alternative method of modeling arteriolar and venular calibers directly.

methods. Data from the population-based Blue Mountains Eye Study were used to compare the predictive information in models using AVR with models using arteriolar and venular calibers directly. Determination was made of how the apparent relationship between vessel caliber and two systemic outcomes (blood pressure [BP] and white blood cell count [WBC]) was influenced by the choice of regression model. These findings were interpreted with reference to the known biological relationship among vessel calibers, BP, and WBC.

results. Models using arteriolar and venular calibers directly had more predictive information than models using AVR. The apparent relationship of vessel caliber to BP and WBC differed substantially, depending on the model chosen. For example, after adjustment for age, sex, and other covariates, decreasing venular caliber was associated with *higher* systolic BP when modeled separately, but was associated with *lower* systolic BP when modeled simultaneously with arteriolar caliber.

conclusions. The findings suggest AVR provides less information with regards to predicting systemic outcomes than its two components. Modeling arteriolar and venular calibers separately could be biased by confounding, while modeling both simultaneously appears to provide unbiased, biologically plausible results. The use of this approach is recommended in future research relating retinal vascular caliber to systemic or ocular outcomes.

^{ 1 }

^{ 2 }In particular, generalized narrowing of the retinal arterioles has long been known to be associated with chronic hypertension.

^{ 1 }However, because generalized retinal arteriolar narrowing proved extremely difficult to estimate precisely from clinical examination by ophthalmoscopy, a summary measure, the retinal arteriole-to-venule ratio (AVR; ratio of the caliber of arterioles to venules) was proposed by Wagener et al.

^{ 3 }as an index of the severity of generalized arteriolar narrowing. The use of the ratio implicitly assumes that in most cases, the venular diameter is relatively constant and does not change with blood pressure (BP), age, and other factors. Thus, a smaller AVR was thought to reflect narrower arterioles, relative to presumed stable venular caliber.

^{ 1 }

^{ 4 }

^{ 5 }

^{ 6 }

^{ 7 }

^{ 8 }When a low AVR was found to be associated with aging,

^{ 9 }cigarette smoking,

^{ 10 }current and past BP,

^{ 4 }

^{ 11 }open-angle glaucoma

^{ 12 }and cardiovascular outcomes such as incident stroke

^{ 13 }

^{ 14 }and coronary heart disease,

^{ 15 }the associations were initially thought to reflect generalized arteriolar narrowing, rather than changes in venular calibers.

^{ 16 }

^{ 17 }First, there are statistical reasons why ratios such as the AVR may capture less information with respect to prediction of outcomes than would consideration of the numerator and denominator separately.

^{ 18 }Second, studying the associations of arteriolar and venular calibers separately may shed light on underlying pathophysiological mechanisms. Retinal arteriolar and venular calibers themselves carry different prognostic information,

^{ 17 }

^{ 18 }and use of a summary measure such as AVR may lead to incorrect inferences.

^{ 17 }

^{ 18 }For example, if both arteriolar and venular calibers are associated with the study outcome in the same direction (such as narrowing of both with increasing BP), the magnitude of the association between arteriolar caliber and increasing BP may be masked substantially, as AVR will not appear to change much with BP. In contrast, if both vessel calibers are associated with the study outcome but in opposite directions, AVR may substantially exaggerate or mask the apparent magnitude of the association with arteriolar caliber, as has been shown in several recent studies.

^{ 17 }

^{ 19 }Clearly, further understanding of appropriate methods to analyze retinal vessel caliber, including whether the AVR is an appropriate summary indicator, is needed.

^{ 17 }

^{ 20 }However, neither study explored whether this approach provides more valid information than the AVR. Moreover, whether modeling arteriolar and venular caliber in separate models provides valid conclusions regarding their associations is uncertain, as arteriolar and venular caliber are highly correlated. The purpose of the present study was to explore these issues using data from the Blue Mountains Eye Study.

^{ 21 }

^{ 22 }The study was conducted according to the recommendations of the Declaration of Helsinki and was approved by the Western Sydney Area Health Service Human Research Ethics Committee. Written, informed consent was obtained from all participants.

^{ 17 }

^{ 23 }

^{ 5 }At the baseline examination (1992–1994), color retinal photographs (30°) of the macula and other retinal fields of both eyes were taken with a fundus camera after pupil dilation (model FF3; Carl Zeiss Meditec GmbH, Oberkochen, Germany). Detailed grading methods have been described

^{ 5 }and are identical with those used in large population-based studies.

^{ 24 }In brief, we used a computer-assisted method to measure the internal caliber of retinal arterioles and venules from digitized retinal images, which were then summarized with published formulas

^{ 7 }

^{ 25 }with correction for magnification.

^{ 3 }

^{ 8 }The formulas take into account branching patterns and allow all measured vessel calibers in an eye to be summarized as an index representing the mean arteriolar or venular caliber of that eye and AVR to be calculated from these indices. An AVR of 1.0 suggests that arteriolar calibers are, on average, the same as venular calibers in that eye, whereas a lower AVR suggests either relatively narrower arterioles compared with venules, or relatively wider venules, compared with arterioles.

*Y*is the outcome variable,

*A*and

*V*are arteriolar and venular calibers respectively,

*a*and

*d*are regression parameters, and ε is a random error term with mean = 1. The equivalent multiplicative model using arteriolar and venular calibers instead of AVR would be

*b*and

*c*are regression parameters. For AVR (

*A*/

*V*) to contain all the predictive information of arteriolar (

*A*) and venular (

*V*) calibers, the two equations would have to be equivalent:

*b*= −

*c*=

*d*. There is no a priori reason to assume this, but use of the AVR requires this assumption.

*n*− 3 degrees of freedom, and we rejected the null hypothesis, if it reached statistical significance.

^{ 26 }given the correlation between arteriolar and venular calibers in this population (

*r*= 0.58; Liew G, unpublished data, 2006), we compared regression coefficients, standard errors (in the form of confidence intervals; [CIs]) and variance inflation factors (VIFs).

^{ 26 }VIFs are a measure of the degree of collinearity, with high values indicating severe collinearity. If severe collinearity (VIF close to 10) were present, we would expect to find unstable regression coefficients and large CIs.

^{ 21 }Of the 3000 participants included in this analysis, 1288 (42.9%) were male, 1066 (35.5%) were ex-smokers, and 437 (14.6%) were current smokers. The average age was 65.5 (SD 9.4) years, with mean BMI 26.2 (4.6) kg/m

^{2}, mean SBP 145.7 (21.3) mm Hg, mean DBP 83.4 (10.1) mm Hg, and mean WBC 6.52 (1.77) × 10

^{9}/L. Age- and sex-adjusted SBP and DBP were almost identical in the study group (146.1/83.3 mm Hg) and in the group excluded (

*n*= 654), because of ungradable photographs or lack of data on refraction or WBC (146.6/83.6 mm Hg).

*P*< 0.0001), indicating that models with AVR are substantially different from models with both arteriolar and venular calibers. Although the

*R*

^{2}s of all three models were low, those of the models with both arteriolar and venular calibers were more than twice the

*R*

^{2}of the models with AVR (0.069 vs. 0.029 for SBP, and 0.015 vs. 0.007 for WBC, respectively), demonstrating that models with both arteriolar and venular calibers together predicted these two outcomes better than models using AVR.

*higher*SBP, but decreasing venular caliber was strongly associated with

*lower*SBP, demonstrating a reversal in the direction of the association with venular calibers. Additional adjustment for BMI, fasting plasma glucose, total serum cholesterol, and smoking status attenuated the magnitude of the changes in SBP, with changes in arteriolar or venular caliber, but the directions of the associations remained as in the age- and sex-adjusted models. We found a similar reversal in the direction of the associations when DBP instead of SBP was modeled as the outcome variable (data not shown). The change in direction of the association between venular caliber and BP is unlikely to be due to collinearity between these two correlated variables, as the CIs for both terms remained narrow and the VIFs for both terms were low (approximately 1.5).

*R*

^{2}) regarding these two endpoints than that provided by individual arteriolar and venular calibers. A major reason for the initial use of AVR, to correct for magnification differences, may not be as important as previously thought. Refractive error, when available, can be used to control for magnification,

^{ 8 }whereas, in its absence, bias from magnification differences is not profound in most eyes within the refractive power range of ±3 D.

^{ 8 }Further, refractive errors are usually not associated with many outcomes of interest and thus are unlikely to confound the associations assessed. Hence, analyses for BP, WBC, and other similar systemic (or ocular) endpoints, should ideally be performed using individual vessel calibers.

^{ 24 }On the other hand, including both components in the same model would provide an adjustment that would avoid this confounding effect, but this approach has not been used previously, and there are no data on its merits. Thus, currently there is no consensus as to the most appropriate approach for analyzing the relationship of retinal vessel calibers and systemic outcomes: Should one continue to use the AVR on its own, analyze vessel calibers separately, or include both vessel calibers simultaneously in the same model?

*separately*into different regression models, we found that both caliber terms were strongly and negatively associated with higher systolic and DBP, after adjusting for age, sex, and other covariates. In contrast, when both arteriolar and venular caliber terms were entered

*simultaneously*into the same model, decreasing arteriolar caliber, but

*increasing*venular caliber, was associated with higher systolic and DBP. Similarly, when modeled separately, both increasing arteriolar and venular caliber terms were strongly associated with higher WBC, but when modeled simultaneously, venular caliber remained strongly and positively associated with higher WBC, whereas the positive association with arteriolar caliber attenuated considerably and became nonsignificant.

^{ 27 }

^{ 28 }from chronic hypertensive damage to the microcirculation. Hence, the apparent relationship between narrower venules and higher SBP when venules were modeled separately is probably a biased finding resulting from confounding by arteriolar caliber, which is strongly associated with both BP and venular caliber. Similarly, the apparent positive association between arteriolar caliber and WBC in the age-sex adjusted model without venular diameter is likely to be a result of confounding by venular caliber.

^{ 29 }

^{ 1 }

^{ 30 }though much work is still needed before it can be implemented in routine clinical practice.

^{ 18 }Based on prior biological knowledge of the likely associations between BP and arteriolar and venular calibers, we believe that there is a possibility of confounding by the other fellow component variable, when analyzing the two correlated vessel calibers in separate models. We thus recommend that models including both arteriolar and venular caliber terms together should be considered in situations where possible confounding from the other vessel caliber is likely to exist—for example, when assessing the relationship of vessel calibers to systemic or ocular outcomes. This approach would adjust for possible confounding from the other correlated variable, and confirm the robustness of findings from models that include vessel calibers separately. Our propositions must be explored and confirmed in other datasets.

Outcome | Test Statistic | Model with ln(A), ln(V) | Model with ln(A/V) | Regression Coefficients | F Statistic | df | P Value | ||||
---|---|---|---|---|---|---|---|---|---|---|---|

b | c | d | |||||||||

Systolic BP | Residual SS | 116.23 | 121.16 | −0.354 | 0.033 | −0.256 | 127.1 | 1, 2997 | <0.0001 | ||

Residual MS | 0.0388 | 0.0404 | |||||||||

R^{2} | 0.069 | 0.029 | |||||||||

WBC | Residual SS | 403.71 | 407.23 | −0.14 | 0.412 | −0.223 | 26.1 | 1, 2997 | <0.0001 | ||

Residual MS | 0.1348 | 0.1359 | |||||||||

R^{2} | 0.015 | 0.007 |

Retinal Vessel Index | Models 7, 8, 9^{*} Single Variable Entry | Model 10^{, **} Simultaneous Entry | Models 11, 12, 13^{, †} Single Variable Entry | Model 14^{, ‡} Simultaneous Entry | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Change in SBP (mmHg) | 95% CI | P Value | Change in SBP (mmHg) | 95% CI | P Value | VIF | Change in SBP (mmHg) | 95% CI | P Value | Change in SBP (mmHg) | 95% CI | P Value | VIF | |||||||||||

Per SD decrease in arteriolar caliber | 4.3 | 3.6, 5.0 | <0.0001 | 5.0 | 4.2, 5.9 | <0.0001 | 1.54 | 2.1 | 1.8, 2.5 | <0.0001 | 2.6 | 2.2, 3.0 | <0.0001 | 1.57 | ||||||||||

Per SD decrease in venular caliber | 1.2 | 0.4, 1.9 | 0.0015 | −1.4 | −2.3, −0.6 | 0.0006 | 1.49 | 0.5 | 0.08, 0.83 | 0.02 | −0.9 | −1.3, −0.5 | <0.0001 | 1.56 | ||||||||||

Per SD decrease in AVR | 3.4 | 2.7, 4.0 | <0.0001 | NA | NA | NA | NA | 1.8 | 1.5, 2.2 | <0.0001 | NA | NA | NA | NA |

Retinal Vessel Index | Models 7, 8, 9^{*} Single Variable Entry | Model 10^{, **} Simultaneous Entry | Models 11, 12, 13^{, †} Single Variable Entry | Model 14^{, ‡} Simultaneous Entry | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Change in WBC (×10^{9}/L) | 95% CI | P Value | Change in WBC (×10^{9}/L) | 95% CI | P Value | VIF | Change in WBC (×10^{9}/L) | 95% CI | P Value | Change in WBC (×10^{9}/L) | 95% CI | P Value | VIF | |||||||||||

Per SD increase in arteriolar caliber | 0.10 | 0.04, 0.17 | 0.002 | −0.03 | −0.11, 0.04 | 0.41 | 1.54 | 0.04 | −0.03, 0.10 | 0.25 | −0.04 | −0.12, 0.03 | 0.27 | 1.57 | ||||||||||

Per SD increase in venular caliber | 0.24 | 0.17, 0.30 | <0.0001 | 0.26 | 0.18, 0.33 | <0.0001 | 1.49 | 0.13 | 0.07, 0.19 | <0.0001 | 0.15 | 0.08, 0.23 | <0.0001 | 1.56 | ||||||||||

Per SD increase in AVR | −0.1 | −0.17, −0.04 | 0.001 | NA | NA | NA | NA | −0.07 | −0.13, −0.009 | 0.02 | NA | NA | NA | NA |

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