Introduction

Ambulatory blood-pressure monitoring (ABPM) provides numerous measures beyond the arithmetic mean of the measurements determined.1 Measures derived from the linear relationship between systolic and diastolic pressures are becoming the target of research efforts and are believed to be associated with mechanical properties of the arteries (a physiological model has been proposed2). These include systolic-on-diastolic slope (Slope)3 and 1−(diastolic-on-systolic slope) called Ambulatory Arterial Stiffness Index (AASI).4 Slope and AASI have been shown to be independent of mean blood pressure,3 and to incorporate clinical and prognostic information.5, 6, 7, 8

One problem in using these parameters in clinical practice is their sensitivity to the estimation method applied: originally, AASI was derived by standard regression [hence, we identify it as AASI(standard)].4 Standard regression is known to be an inappropriate estimation method in this case (as systolic and diastolic cannot be described as ‘independent’ and ‘dependent’ variables),9, 10 leading to artifactual dependence of AASI(standard) on data scattering, and bias in relating this parameter to clinical variables.3 This bias is eliminated on deriving the regression parameters with a procedure (‘bisector regression’) that treats systolic and diastolic BP in a symmetrical manner.3 However, the specific method applied involves a mathematical expression that is too complex to have a simple clinical interpretation.

The rationale for this work stemmed from the finding that there is a symmetrical regression type called ‘reduced major axis regression’ that expresses Slope simply as the ratio between the standard deviation of the data along the Y axis (systolic BP) over that of the X axis (diastolic BP).9, 10 We named this ratio ‘blood pressure variability ratio’ (BPVR). Accordingly, by definition, AASI(BPVR)=1–1/BPVR. In this way, both parameters have a simple relationship with variability measures and their calculation does not require any statistical software! Furthermore, BP variability is a clinically meaningful parameter by itself. Ambulatory blood pressure variability, expressed by the standard deviation from the mean, is linked with mean BP levels,11 but independently associated with target organ damage12, 13, 14 and outcome.15, 16, 17

In this study, we used data from a clinical ABPM service to investigate the relationships between both blood pressure variability and BPVR and clinical, demographic as well as mortality outcome variables, and especially the contribution of BPVR as a predictor of all-cause mortality independently of established ABPM predictors. In addition, we evaluated the theoretical and phenomenological relationship between BPVR and Slope and AASI calculated by different regression methods.

Methods

Study population

Data were extracted from our entire ABPM service database, from 1991 through to 2005, which included 3433 eligible patients for whom blood pressure variability and ambulatory arterial stiffness indices could be extracted from raw monitoring data files. Excluded were patients less than 16 years old, pregnant women and subjects with poor-quality ABPM recordings (less than 15 valid measurements). Individuals with repeated monitoring(s) were included only once in the analyses, using data from the initial monitoring session. Patients had been referred for standard clinical indications at the discretion of the referring physician (mainly primary-care practitioners, who have been shown elsewhere to use ABPM for appropriate indications18). Baseline data collected included demographic characteristics, height and weight, and treatment for hypertension and diabetes. The outcome assessed was all-cause mortality, which was obtained by linkage (dated 20 January 2008) with the national population register by way of the individual national ID number.

Ambulatory blood-pressure monitoring and definitions

Twenty-four hour ABPM was executed with Spacelabs 90207 (Redmond, WA, USA), as described earlier.19 Before 1999, we used Accutracker II (Suntech, Raleigh, NC, USA).20, 21 The monitor was mounted on the non-dominant arm between 0800 and 1000 hours, and removed 24-h later. Recordings were made every 20 min between 0600 hours and midnight, and every 30 min between midnight and 0600 hours. A mercury sphygmomanometer was initially attached to the monitor through a Y-connector to verify agreement between the two modes of measurement (within a range of 5 mm Hg). Cuff size was selected according to measured arm circumference; up to 24 cm pediatric cuff, 24–32 cm standard adult cuff and over 32 cm large adult cuff. The average of 2–3 initial sphygmomanometer measurements taken by a trained technician, after the subject had been seated for 5 min, was considered the patient's clinic BP.22, 23 Sleep, including daytime naps, was logged in a diary. Sleep-related BP dipping refers to the relative reduction in BP from wakefulness levels to sleep levels, according to the logs.

Blood pressure variability and slope-related parameters

Systolic and diastolic BP variability was expressed, respectively, by within-subject standard deviation (s.d.) of systolic BP (SBP) and diastolic BP (DBP), that is, s.d.(SBP) and s.d.(DBP), as routinely included in every ABPM report. Variability was also expressed by the coefficient of variation (CV) of systolic or diastolic measurements, defined using relative changes (CV=100 × s.d./mean). The BP variability ratio (BPVR) was defined as (systolic BP variability)/(diastolic BP variability), namely, s.d.(SBP)/s.d.(DBP).

The original AASI, AASI(standard), is defined as 1−(diastolic-on-systolic slope), wherein the slope was determined from a DBP vs. SBP plot by a standard regression procedure.4 Viewed in the reciprocal SBP vs. DBP plot, this regression line has the slope of 1/(diastolic-on-systolic slope), which is generally different from the systolic-on-diastolic slope10 (as shown in Figure A1, see Appendix). As a result, AASI(standard) displays an artifactual dependence on data scattering, as expressed by the correlation coefficient R between SBP and DBP.3, 24, 25 The use of symmetric regression of the bisector type (see Figure A1)10 eliminates this problem,3 with the estimated systolic-on-diastolic slope, Slope(bisect) and AASI(bisect)=1–1/Slope(bisect). The current work applies the symmetric regression of the ‘reduced axis type’, according to which the estimated systolic-on-diastolic slope is given by BPVR (see Figure A1),9, 10 which is far simpler than the mathematical expression for Slope(bisect). Accordingly, AASI(BPVR) is given by 1–1/BPVR. It is important to mention that the relationship, AASI(standard)=1–R/BPVR, is a mathematical identity that does not require experimental validation. All relevant statistical background, including the relationship between the various parameters, is outlined in Appendix.

Statistical analysis

The distribution of systolic BP variability, diastolic BP variability and BPVR was skewed (skewness 0.911±0.042, 0.885±0.042 and 1.195±0.042). Thus, log-transformed values were used to characterize relationships with other variables. Determinants of the BP variability indices were assessed by multivariable regression models including, demographic characteristics (age, sex and BMI), treatment (medical treatment for hypertension and diabetes) and monitoring measures (mean arterial pressure (MAP) and MAP dip).

Analysis of outcome consisted of Cox proportional hazards models predicting all-cause mortality. However, for the variables under investigation (BPVR and slope-related parameters), the proportional hazards assumption (as assessed by including an appropriate time-dependent covariate) was not valid. Specifically, the hazards associated with increased AASI(standard), AASI(bisect) or BPVR seemed to decrease with time. Thus, Cox proportional hazards modeling with two time-dependent covariates was used. The first time-dependent covariate consisted of the index measure (BPVR, AASI, and so on) multiplied by 1 for time ⩾1.5 years or by 0 for time <1.5 years, whereas the second covariate was for 7 years (defined similarly). Mortality was analyzed for three different time frames. These time points were chosen because they yielded the best-fitting models, according to log-likelihood scores.26, 27 Covariate adjustment in Cox models included age (introduced as an exponential term, which yielded a more robust association with mortality), gender, treatment variables and BP-monitoring variables. BMI was not included, as it did not predict mortality in this database. Confirmation of the time-dependent Cox calculations was obtained by logistic regression modeling examining the odds ratios for all-cause mortality at 2–10 years after the index ABPM session.

Data are expressed as mean±s.d. or as HR (95% CI), unless specified otherwise. Two-sided nominal P-values <0.05 were considered significant. Calculations of the slope-related parameters and its inter-relationships were carried out using the statistical software, SYSTAT7.0, whereas calculations related to prognostic power were undertaken using SPSS 15.0 (both from SPSS Inc., Chicago, IL, USA).

Results

Study population

Our ABPM service database included 3433 eligible individuals. Their demographic and clinical characteristics are depicted in Table 1 . Mean age was 56±16 years; 55% were women and 59% were treated with antihypertensive medications and 10% with hypoglycemic agents.

Table 1 Various demographic and ambulatory blood pressure monitoring characteristics of the study population according to treatment status
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Correlates of blood-pressure variability

Median systolic and diastolic BP variabilities, defined as the coefficient of variation of 24-h ambulatory BP, were 10.9% (IQR 9.3–12.9) and 14.2% (IQR 12.3–16.7), respectively (Table 1). The mean ratio of systolic standard deviation to diastolic standard deviation (BPVR) was 1.33 (IQR 1.16–1.55). Various correlations were found between these log-transformed indices and clinical variables (Table 2 ).

Table 2 Partial correlation coefficients of blood pressure variability indices (log-transformed) and clinical characteristics in untreated (n=1408) and treated (n=2025) patients
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Standard deviation of systolic and diastolic BP was linearly correlated with deciles of systolic and diastolic BP, respectively. Figure 1 shows that these linear associations are practically located on the same regression line, when BP variability is plotted against the corresponding BP decile (r=0.984, P<0.0001). Importantly, the ratio of systolic to diastolic BP variability, BPVR, was found to be independent of mean arterial pressure (MAP); r=0.013 and P=0.43 (see Figure 1 inset for analysis by deciles and Table 2 for partial coefficients). This was true in both treated (r=0.019) and untreated (r=0.11) patients. In addition, Figure 2 shows that, although systolic and diastolic BP variabilities were found to be profoundly dependent on R (the systolic vs. diastolic correlation coefficient), BPVR was nearly free of this association.

Figure 1
figure 1

A scatter plot illustrating the standard deviation of blood pressure vs. 24-h blood pressure (partitioned by deciles). Diastolic blood pressure (open squares) and systolic blood pressure (black circles) are plotted separately. Correlation was tight; R=0.984, P<0.0001. Inset: the blood pressure variability ratio (BPVR) plotted vs. mean arterial blood pressure deciles, showing no apparent association: r=0.029, P=0.13.

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Figure 2
figure 2

Systolic and diastolic blood pressure (BP) variability (top) or blood pressure variability ratio (BPVR) (bottom) are plotted against deciles of the correlation coefficient of the linear relationship between systolic and diastolic BP (R). Deciles of R are adjusted for age, gender, body mass index (BMI) and systolic blood pressure (SBP) or diastolic blood pressure (DBP) (top) or mean arterial pressure (MAP) (bottom), by means of analysis of covariance (ANCOVA) (F=29.2/43.8 for SBP/DBP, P<0.0001; F=2.36 for BPVR, P=0.012). Standard error is within the size of the data points.

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We reanalyzed 3401 patients (99%) with separable BP reading in either wakefulness or during sleep (based on the patient's diary). BPVR calculated over 24-h correlated with both awake and sleep values (r=0.84 and r=0.65, respectively). Awake and sleep BPVR displayed similar distributions, and were correlated (r=0.38). BPVR value was slightly but significantly higher at wakefulness compared with that at sleep (1.44±0.39 vs. 1.35±0.43, P<0.001), suggesting that, basically, BPVR calculated over 24-h (1.39±0.33) fairly represents both day and night values and relates to a property that is insensitive to the circadian cycle.

Comparisons between BPVR and the ambulatory arterial stiffness index determined by different methods

BPVR and Slope(bisect) are highly correlated (r=0.87, P<0.001). Figure 3 shows that the magnitude of this association depends on the correlation R between systolic and diastolic BP for individual patients, reaching r=0.996 (P<0.0001) for the vast majority of patients (n=3086, 90%) in whom R>0.5, with r=0.439 for the rest (R⩽0.5). Very similar correlations are found for the corresponding AASI(BPVR) and AASI(bisect) (see Methods). The correlation between AASI(BPVR) and AASI(standard) is r=0.830 for R>0.5, with r=0.480 for R⩽0.5, which may reflect the explicit dependence of AASI(standard) on R (see Appendix).

Figure 3
figure 3

Scatter plots illustrating the regression line (and 95% CI) between blood pressure variability ratio (BPVR) and Slope(bisect), for patients with linearly (R>0.5) related systolic and diastolic 24-h blood pressure (BP) (right plot, correlation coefficient r=0.996) and for patients with low (R⩽0.5) correlation between systolic and diastolic BP (left plot, r=0.439).

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Blood pressure variability and all-cause mortality

During the mean follow-up of 7.6 years, 237 patients died. After adjustment for demographic and treatment variables, as well as for MAP and MAP dip, the variability (CV) of systolic BP was marginally associated with all-cause mortality; hazards ratio (HR) 1.12 (95% confidence intervals (95%CI) 0.97–1.28, P=0.1) per 1 s.d. increase. In a parallel model of diastolic BP variability, HR was 1.04 (0.92–1.16) per 1 s.d.. However, an analogous model of the BP variability ratio, BPVR, yielded a significant HR of 1.21 (1.05–1.40) per 1 s.d. increase in log-transformed BPVR (P=0.007). Introduction of BPVR did not materially change the prognostic significance of other established parameters, such as age, systolic BP, BP dipping, and so on28 (data not shown). In the latter model, however, the proportional hazards assumption was not valid (see Methods). More specifically, the hazards ratio per unit increase in BPVR seemed to dampen with time (see also Supplementary mortality figures). Thus, time-dependent covariates were introduced. We chose covariates that partitioned follow-up time at 1.5 and 7 years, as this yielded the best-fitting model.26, 27 With these terms in the model, hazards ratios per 1 s.d. increase in log-transformed BPVR were 2.21 (95% CI 1.36–3.59) in the first 1.5 years, 1.28 (1.06–1.54) between 1.5 and 7 years and 0.90 (0.68–1.20) thereafter. A simplified analysis of mortality by quartiles of BPVR, displayed in Figure 4, shows that compared with the first quartile, patients at the highest quartile of BPVR had increased mortality up to 7 years, HR 2.30 (1.26–4.21).

Figure 4
figure 4

All-cause mortality by quartiles of blood pressure variability ratio (BPVR). Hazards ratios and 95% confidence intervals (bars), plotted against the median BPVR value of each quartile, were generated by a Cox proportional model with a single time-dependent partition at 7 years. Covariates included in the model: age (exponential term), gender, treatment for hypertension and diabetes, mean arterial pressure and mean arterial blood pressure dip. P-value for the trend up to 7 years (black diamonds)=0.02; P-value for the trend beyond 7 years (gray squares)=0.6.

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We further explored the prognostic ability of BPVR compared with that of standard and symmetric AASI with additional adjustment for 24-h pulse pressure (PP) (Table 3 and Supplementary mortality figures). All-cause mortality during the first 1.5 years of follow-up, adjusted for demographic as well as for monitoring parameters (including 24-h MAP, 24-h PP and dipping magnitude), increased with BPVR: HR 1.97 (1.20–3.21) per 1 s.d.; AASI(standard): HR 1.58 (0.95–2.64) and AASI(bisect): HR 1.35 (1.05–1.75). Between 1.5 and 7 years, the corresponding hazards ratios had borderline significance: BPVR, 1.17 (0.96–1.41); AASI(standard), 1.19 (0.94–1.51); and AASI(bisect); 1.10 (0.92–1.32). Thereafter, these indices were no longer associated with increased mortality (Table 3 and Supplementary mortality figures). In sensitivity analyses limited to individuals treated or not treated for hypertension, Cox coefficients did not differ from those derived for the total population (data not shown).

Table 3 Association of BPVR and other Slope-related parameters with all-cause mortality: Cox-proportional hazards models
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We used logistic regression to confirm the results of time-dependent Cox proportional hazards models. We examined the odds ratios for all-cause mortality at 2 years (n=2796), 5 years (n=2187) and 7 years (n=1542) after the index ambulatory monitoring session (Table 4). The results were consistent with the Cox models in showing a declining strength of association with increasing duration of follow-up.

Table 4 Association of BPVR and other Slope-related parameters with all-cause mortality: logistic regression models
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Discussion

Our foremost finding that BPVR—the ratio of the standard deviation of systolic ambulatory BP to that of diastolic ambulatory BP—is nearly identical to the slope of the systolic vs. diastolic BP relationship estimated by the bisector regression method should not come as a surprise, as it is the realization of a mathematical relationship (the same slope calculated by two symmetric regression methods, see Appendix). Nevertheless, the identity (which reaches r=0.996 in patients with linearly related s.d.(SBP) and s.d.(DBP)) between these variables is impressive. The main importance of this relationship is that it eliminates the need for all raw data points and statistical software to regress them, as the s.d. of the 24-h ambulatory BP is available from any report.

AASI and its related slope have been shown to predict outcome,5, 7, 8, 29 as well as target organ damage.6, 30 However, the importance of these parameters as measures of arterial properties has been questioned by downplaying the role of AASI as a genuine correlate of arterial stiffness31, 32 because of its strong dependence on age, gender,31, 32 pulse pressure32 and nocturnal BP decline.3, 25, 32 We report here that the slope-related indices, AASI, AASI(bisect), Slope(bisect) and BPVR, all predict mortality to a certain extent, and that the indices derived from the proper symmetric regression8 and the calculated BPVR, tend to predict even better. Indeed, after adjustment for age, ambulatory BP level, 24-h PP (an arterial stiffness characteristic) and the corresponding decline of ambulatory BP or PP during sleep (an independent mortality predictor in this patient population28), BPVR remains significantly associated with increased mortality.

The slope of systolic vs. diastolic BP is unlikely to link directly to arterial stiffness, as the latter is a strictly BP-related variable, whereas BPVR (and related indices) are independent of mean arterial pressure.3 Theoretical considerations predicting that the systolic vs. diastolic slope is equivalent to the relative increase of arterial stiffness during systole2 are supported by its being typically greater than unity, a reflection of a higher systolic than diastolic stiffness.3 Folkow et al.33, 34 recognized decades ago that the arterial reactivity to pressors is higher in hypertensive than in normotensive rats. Such increased vascular reactivity, also found in human hypertension,35 is believed to reflect a higher arterial cross-sectional area and subsequently smaller lumen when the vessel wall is hypertrophied. Indeed, such structural arterial changes underlie an increased risk in hypertension.36 Thus, the relationship between arterial structural and functional properties, and BP reactivity to different stressors, which defines BP variability, rest on sound physiological grounds. In other words, a greater variation of ambulatory BP during systole than during diastole may be an integrated reflection of arterial structural and functional properties that can be captured by ambulatory BP-derived variables such as the s.d. of BP.

An important observation is that, although the s.d. of both systolic and diastolic BP is tightly related to R (the correlation coefficient of the systolic vs. diastolic BP), the ratio of systolic-to-diastolic BP variability (BPVR) is much less dependent on R and hence less influenced by outliers (see Figure 2).

The waning of the prediction of mortality with time may seem as a weakness of BPVR and AASI (the validity of the Cox proportional hazards assumption was not explicitly reported in some of the earlier AASI outcome studies, for example, Dolan et al.5 and Kikuya et al.29). Prediction was strong up to 18 months, fair up to 7 years and nonsignificant thereafter. However, during these periods of time, many aspects may change, including BP control and the use of medications that may affect arterial structure. Changes in structure would affect BP reactivity, and hence its variability, during the varying stresses of the awake and asleep periods. Indeed, in the largest hypertension study to date,26 the effect of antihypertensive medications on congestive heart failure outcome was also blunted with time. As the relationship of BP to heart failure is indisputable, similarly the blunting over time of the BPVR prediction of all-cause mortality should not be an argument to nullify its importance. This limitation of our study is related to the known regression dilution bias.37 Introduction of follow-up measurements, had they been available, may have altered this trend. Obviously, a better understanding of the underlying physiology represented by BPVR will enhance the understanding of this phenomenon.

Our study has several other limitations. It reflects a referred population and may not represent the hypertensive or general population. More than 50% of the patients were treated for hypertension, and antihypertensive therapy is known to reduce BP variability.17, 38 We used the 24-h s.d. of BP, which incorporates in it the circadian variation, and BPVR might be improved by appropriate weighing of awake and asleep measurements.39 However, as we consider that the 24-h association between systolic and diastolic BP yields a reliable property that incorporates the extremes of circadian BP changes, we used the simple s.d. This may underestimate the predictive power of BPVR. Baseline cardiovascular comorbidities and risk factors were largely unavailable for outcome analyses. Their absence does not allow an accurate estimation of the prognostic information depicted in BPVR. However, a comparison of BPVR with AASI and blood pressure variability is still valid.

In conclusion, although the physiological meaning of the slope relating systolic to diastolic ambulatory BP is not well understood, the potential of BPVR and the other slope-related parameters to reveal vascular properties deserves exploration. Indeed, some readily available slope-related indices, including the BPVR, which may be viewed also as a derivation of BP variability, should be further evaluated as practical measures of vascular health.40 We should consider such predictors at a time when individual global risk assessment is becoming incorporated in hypertension guidelines.41