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    (1)
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    (2)
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    where T is the total time from first to last BP reading (equivalent to in equation 1 ). In our example, generalized ARV is the same for both sets of the above data, demonstrating that the new measure is robust to varying distances between readings:
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    Mena et al. 15 proposed an earlier version of the ARV that was calculated as the sum of absolute differences divided by the number of readings minus 1 or . Although they found that it predicted cardiovascular events better than the SD index, the difficulty with this version of the ARV, as with the SD index (see next paragraph), is that it ignores the distance between the consecutive readings, and thus does not have a “change per minute” interpretation as does our generalized ARV.
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    (3)
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    Table 1. Baseline Characteristics and Intraoperative Factors by Generalized Average Real Variability of MAP
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    Fig. 1. Study population. Consort diagram showing study population. ASA = American Society of Anesthesiologists; BP = blood pressure.
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    Fig. 2. Univariable association between 30-day mortality and measures of mean arterial pressure (MAP) variability and location. Univariable association between 30-day mortality and ( A ) generalized average real variability (ARV) of MAP, ( B ) SD of MAP, and ( C ) time-weighted average (TWA) of MAP. Curves derived from univariable logistic regression smoothed by restricted cubic spline with 3 degrees of freedom and knots at 10th, 50th, and 90th percentiles of predictor. Shaded areas represent estimated 95% point-wise CIs. Results: ( A ) 30-day mortality increases steeply with increasing ARV of MAP to approximately 3 mmHg/min and then more slowly; ( B ) SD of MAP has slight U-shaped relationship with 30-day mortality; and ( C ) 30-day mortality decreases steeply up to TWA of MAP of approximately 90 mmHg and then increases. See figure 3 for multivariable results—that is, the independent association of each factor with 30-day mortality.
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    Table 2. Multivariable Association between 30-day Mortality and Primary and Secondary Outcomes (N = 104,401)
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    Fig. 3. Multivariable association between 30-day mortality and measures of mean arterial pressure (MAP) variability and location. Multivariable association between 30-day mortality and ( A ) generalized average real variability (ARV) of MAP, ( B ) SD of MAP, and ( C ) time-weighted average (TWA) of MAP. ( A and B ) Mild multivariable relationship between 30-day mortality and both generalized ARV of MAP and SD of MAP. ( C ) Estimated 30-day mortality decreases steeply up to TWA of MAP approximately 85 mmHg and then flattens. Estimated 30-day mortality curves derived from multivariable logistic regression smoothed by restricted cubic spline with 3 degrees of freedom and knots at 10th, 50th, and 90th percentiles of given variable. A and C are from the same model; B is from a separate multivariable model (with TWA-MAP relationship similar to C ). Both models adjusted for all variables in table 1. Shaded areas represent estimated 95% point-wise CIs.
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    Fig. 4. Multivariable odds ratios for relationship between 30-day mortality and mean arterial pressure (MAP) variability measures. Spline plot of odds ratios from separate multivariable logistic regression models for generalized average real variability (ARV) of MAP ( A ) and SD of MAP ( B ). The reference category for each odds ratio is the median value of the respective variability measure. Dashed lines represent estimated 95% point-wise CIs. There is no variability (and hence no CI) at the median, where odds ratio = 1.0. Whereas odds ratios for the relationship between SD-MAP and mortality are symmetric around the median, odds ratios for ARV-MAP remain flat above the median because predicted mortality did not increase for higher ARV-MAP.
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    Table 3. Subset Analysis of Patients for Whom Information on History of Cardiovascular Medications Was Available (Multivariable Association between ARV-MAP* and 30-day Mortality; N = 60,616)
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    Fig. 5. Multivariable association between minimum 10-min sustained mean arterial pressure (MAP) and 30-day mortality. ( A ) Spline plot of multivariable probability of 30-day mortality as function of 10-min sustained MAP. ( B ) Spline plot of multivariable odds ratios (Y-axis) for relationship between minimum 10-min sustained MAP and 30-day mortality. The reference category for each odds ratio is the median value of the predictor (70 mmHg). There is no variability (and hence no CI) at the median, where odds ratio = 1.0. Curves derived from multivariable logistic regression smoothed by restricted cubic spline with 3 degrees of freedom using 10th, 50th, and 90th percentiles of minimum 10-min sustained MAP as knots.