Intraoperative Mean Arterial Pressure Variability and 30-day Mortality in Patients Having Noncardiac Surgery

ALTHOUGH the relationship between mean blood pressure and organ damage or death^1–4  is well established, there is also some evidence for a relationship between blood pressure variability and death or organ damage.^1,2,5–7  For example, in a study of approximately 9,000 ambulatory patients, Hansen et al.⁸  found that higher 24-h variability in systolic blood pressure (SBP) was significantly associated with long-term mortality and cardiovascular events after adjusting for mean blood pressure although including it did not substantially change predicted values for mortality. Control of variability in blood pressure is also thought to reduce morbidity or mortality, leading some investigators to suggest that longer-acting perioperative antihypertensive drugs may be preferable to shorter-acting drugs.^7,9 

A correlation between mean blood pressure and subsequent cardiovascular events has been observed in medical⁷  and surgical^10,11  patients. In addition, recent studies have found that intraoperative excursions in SBP outside of a targeted range (measured by magnitude × duration, i.e., area under the curve) were associated with 30-day mortality in cardiac surgery patients.^12,13  However, such hypotensive and hypertensive indices measure the average level of the blood pressure rather than reading-to-reading variability. The relationship between blood pressure variability per se (distinct from mean blood pressure) and mortality remains unclear in noncardiac surgical patients. In fact, some intraoperative variability may indicate healthy autonomic control. A constant blood pressure, either very high or very low, might indicate issues with perfusion of the patient, important fluid imbalances, or other problems.

We therefore tested the hypothesis that patient variability in mean arterial pressure (MAP), independent of time-weighted average MAP (TWA-MAP) and other confounding variables, is associated with 30-day postoperative mortality in patients having noncardiac surgery.

With institutional review board approval (Cleveland Clinic Institutional Review Board, Cleveland, Ohio), we extracted data on 140,312 adult patients with noncardiac surgery and American Society of Anesthesiologists physical status (ASA-PS) less than 5 between January 2005 and December 2012 from the Cleveland Clinic Perioperative Health Documentation System, which is an electronic medical record–based registry that pulls and merges data from various Cleveland Clinic electronic databases including EPIC (Epic Systems Corporation, USA), the anesthesia automated record keeping system (Talis Clinical, Inc., USA), billing data, laboratory data, pharmacy data, and others. Data are regularly scrutinized using range checks, cross-variable and table checks, and other data quality programs to assure good quality data for research.

Vital status was updated as of December 31, 2012. Only the longest lasting surgery was considered for patients who had more than one operation. Patients were excluded if their surgery duration (induction to emergence) was less than 60 min or missing baseline variables. We also excluded patients with inadequate information on blood pressure readings (periods of artifacts/unavailable data of >10 min or <6 measurements per hour). Thus, a total of 104,401 patients were included in the study.

Mean arterial pressure data from our monitors are stored in our automated record keeping system, in which MAP was recorded at 1-min intervals for patients with an arterial catheter and every 1 to 5 min for those with noninvasive blood pressure monitoring. Because electronic anesthesia records are known to contain considerable artifact, we removed artifacts using the following rules, in order: (1) blood pressure readings documented as artifacts; (2) out of range: values—if (a) SBP 300 mmHg or greater or SBP 20 mmHg or less, (b) SBP ≤ diastolic blood pressure (DBP) + 5 mmHg, or (c) DBP 5 mmHg or less or DBP 225 mmHg or more; and (3) abrupt change, defined as SBP change 80 mmHg or greater from last reading within 1 min in either direction, or abrupt SBP change 40 mmHg or greater within 1 min in both directions.

There is no definitive standard for evaluating blood pressure variability although within-patient SD is most commonly used.^5,14  Hansen et al.⁸  proposed an index of short-term reading-to-reading blood pressure variation called average real variability (ARV), calculated by the following formula (sum of the product of time between measurements and absolute change divided by total time):

where N is the number of blood pressure (BP) readings and t is the time interval between each set of readings, BP_k and BP_k+1.

Hansen et al. showed that the ARV more reliably estimates variability for time-series data than the SD. But a limitation is that Hansen’s approach is only valid for equally distant blood pressure readings. For pressures at unequal intervals, this index overestimates the variability of steep changes. For example, consider five consecutive MAP readings of 50, 60, 70, 60, and 50 at 1-min intervals so that:

Now consider the same patient, but with data recorded at 1, 3, 4, and 5 min, so

or 50% more variability compared with the same patient with blood pressure recorded each minute.

To avoid incorrect estimates resulting from unequal measurement periods, we propose (and use) a better ARV index, generalized ARV, which does not require equally distant data. We calculate it simply as the sum of the absolute value of all changes across measurements divided by total time:

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:

and

The units for ARV-MAP are mmHg/min, so an ARV-MAP of 1 would mean that the MAP changes (either up or down) on average approximately 1 mmHg between consecutive minutes during the case for a given patient. Hereafter, we refer to our measure of variability (equation 2) as generalized ARV, and when referring to its use with MAP data, generalized ARV–MAP.

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.

For comparative purposes, we also report on the SD of MAP, or SD-MAP, as a measure of blood pressure variability. The difficulty with SD-MAP as a measure of variability is that it ignores the timing of the measurements. For example, SD-MAP for consecutive values of 60, 60, 80, 80, and 80 mmHg and 80, 60, 80, 60, and 80 mmHg has the same SD although the latter is obviously more variable. Generalized ARV analysis gives a value of 5 for the first set and 20 for the second set and thus clearly better estimating variability for the time series than the SD. Although we report SD-MAP as a measure of variability to facilitate comparisons with previous work, we do not consider it an optimal estimate of variability in sequential data.

Finally, to give more weight to steep changes (slope), we also consider a squared version of the generalized ARV called ARV_S, as follows:

In our example, we have for the 1-min data

and for the mixed distance data

Because of the squared term, this ARV measure does not give the same result with equal and unequal data intervals. However, it does penalize large jumps and is thus a generally intuitive variability measure.

We a priori selected generalized ARV-MAP as our primary estimate of MAP variability, with SD-MAP and squared ARV-MAP as secondary indices.

As a measure of mean MAP across a case, we also calculated TWA-MAP for each patient’s surgery. We assess its interplay with the relationship between blood pressure variability measures and 30-day mortality. TWA-MAP was calculated as the area under the curve of the MAP measurements divided by total measurement time (note that the area under the curve alone is insufficient because it ignores total time). TWA-MAP is equal to the mean of all measurements when all data are equidistant and is more accurate than a simple mean when the readings are not all equidistant,¹⁶  as in most intraoperative data. TWA-MAP is thus not an estimate of variability but rather a measure of patient severity or average level (see Discussion).

We first assessed the relationship between categories (for display purposes) of generalized ARV-MAP and all baseline characteristics, medical history, and important surgical factors by using chi-square tests and ANOVA.

In our multivariable models, we adjusted for all confounding variables in table 1. We defined preexisting medical conditions used International Classification of Diseases, Ninth Revision (ICD-9) billing codes and included only those fulfilling at least one of the following (1) appeared in the patient “problem list” with a date preceding the date of surgery, (2) appeared in an ICD-9 list before the index surgery, or (3) were flagged as a chronic ICD-9 condition based on the Healthcare Cost and Utilization Project definitions.¹⁷  Because there were many types of surgical procedures, we characterized each procedure code into 1 of 244 clinically meaningful categories using the Agency for Healthcare Research and Quality’s Clinical Classifications Software for Services and Procedures. We then aggregated low-frequency-event categories (N <5 death) into one group and used that as the reference group (a low-risk group). Pearson correlation coefficient was used to assess the correlations among the three variability measures (generalized ARV, SD, and squared ARV) and TWA of MAP. Discrimination (ability to discriminate events from nonevents) of models was assessed with the c-statistic; several model diagnostics were assessed as well.

We used univariable and multivariable logistic regression models to assess the relationship between 30-day mortality and each of generalized ARV-MAP, SD-MAP, squared ARV, and TWA-MAP. We assessed the linearity of the relationship between each exposure and 30-day mortality using a restricted cubic spline function with three knots (located at 10th, 50th, and 90th percentiles).¹⁸  Because all relationships were nonlinear, we used continuous versions of each exposure with a restricted cubic spline function (three knots) as our primary analyses. A restricted cubic spline function was used to obtain a smoothed relationship between selected predictor variables and response; this is a useful technique when a relationship appears quite nonlinear (i.e., not a straight line). Results in our logistic regression model setting were then interpreted by (1) simply observing the resulting curve and also by (2) reporting odds ratios for the outcome comparing certain values of the predictor (e.g., generalized ARV-MAP) to a reference value.

We estimated odds ratios (95% CIs) from the spline models using the median of each exposure as the reference. In addition, we categorized the primary exposure of generalized ARV into five equal-distant groups (≤1, 1–2, 2–3, 3–4, and >4 mmHg/min) and used the lowest (≤1 mmHg/min) as the reference. A sensitivity analysis for the association between generalized ARV-MAP and 30-day mortality was conducted including only patients having minute-by-minute invasive blood pressure measurements. We further assessed the interaction between history of hypertension and the relationship between generalized ARV-MAP and 30-day mortality.

We conducted secondary analyses to assess the relationship between 30-day mortality and amount of time MAP is sustained below certain thresholds, independent of minute-to-minute variations in MAP (i.e., adjusting for generalized ARV-MAP). These analyses help to understand implications of the relationship between the overall mean (TWA-MAP) and 30-day mortality. Specifically, we assessed the relationship between 30-day mortality and minimum 10-min sustained MAP (i.e., the minimum MAP sustained continuously for ≥10 min) and cumulative time of MAP less than 50, 55, 60, 70, and 80 mmHg during surgery using multivariable logistic regression models. We adjusted for generalized ARV-MAP and baseline confounding variables (as in primary analyses).

We used a significance level of 0.05 for main effects and 0.10 for interaction effects. SAS software version 9.4 for Windows (SAS Institute, USA) was used for all statistical analyses and graphics.

Among 104,401 patients included in the study (fig. 1), the overall incidence of 30-day mortality was 1.3% (1,348). The overall mean (± SD) of TWA-MAP was 84 ± 10 mmHg, generalized ARV-MAP was 2.5 ± 1.3 mmHg/min, and SD-MAP was 12.2 ± 4.3 mmHg. Arterial line was used in 33% of patients and noninvasive measurement in 66%, whereas 1% used both.

Table 1 shows the characteristics of patients as a function of generalized ARV-MAP category. Patients with higher generalized ARV-MAP were more likely to be older, to have higher ASA-PS, to be designated as emergency cases, to have had arterial catheters inserted, to have a history of serious chronic disease, and to have higher SD-MAP and TWA-MAP.

Time-weighted average of MAP was only weakly correlated with variability measured by generalized ARV-MAP (Pearson correlation coefficient, 0.20; 95% CI, 0.19 to 0.21; P < 0.001) but moderately correlated with SD-MAP (0.41; 0.40 to 0.42; P < 0.001). A weak correlation between generalized ARV-MAP and TWA-MAP implies that variability as measured with ARV is fairly independent of a patient’s mean MAP during surgery. ARV-MAP was moderately-to-strongly correlated with SD-MAP (0.57; 0.567 to 0.574; P < 0.001) and highly correlated with squared ARV-MAP (0.92; 0.921 to 0.923; P = 0.001).

Univariably, 30-day mortality increased steeply as the generalized ARV-MAP increased to 3 mmHg/min but thereafter increased only slowly (P < 0.001; fig. 2A); conversely, there was a slight U-shaped univariable relationship between the SD-MAP and 30-day mortality (P < 0.001; fig. 2B); finally, 30-day mortality decreased steeply as the TWA of MAP increased up to approximately 80 mmHg and then slowly increased (P < 0.001; fig. 2C).

In a multivariable model using cubic splines, we found no interaction between generalized ARV-MAP and TWA-MAP on 30-day mortality (P = 0.36). Both continuous ARV-MAP (P = 0.033) and continuous TWA-MAP (P< 0.001) were independently associated with 30-day mortality (fig. 3). Compared with the univariable analysis, TWA-MAP had a similarly shaped but attenuated relationship with mortality (fig. 3C). However, generalized ARV-MAP (fig. 3A) was only weakly associated with mortality (nearly flat curve) after adjusting for covariates as well as TWA-MAP. A plot of odds ratios using the multivariable spline fit (from fig. 3) showed that an ARV-MAP of approximately 3.8 had the lowest risk of 30-day mortality (fig. 4A). A generalized ARV-MAP of 1 mmHg/min indicates that the MAP changes (either up or down) an average of 1 mmHg between consecutive minutes during the case for a given patient. The odds ratio (95% CI) at the 25th percentile for a 1-mmHg/min increase in generalized ARV-MAP versus the median ARV-MAP (2.3) was 1.14 (1.03 to 1.25, P = 0.01) and at the 75th percentile was 0.94 (0.88 to 0.99, P = 0.02) (table 2). The c-statistic for this model was 0.93, indicating very good discrimination. In contrast, odds ratios of mortality for SD of MAP had a more U-shaped relationship (fig. 4B).

Because the relationship between generalized ARV-MAP and mortality was nonlinear, we also assessed the multivariable association using evenly spaced categories of ARV-MAP and mortality. We observed a decreasing trend of mortality (P = 0.015, test for linear trend) from low to high generalized ARV-MAP category (0.30 to 0.21%). However, none of the categories of generalized ARV-MAP differed significantly from the reference (lowest) category in their relationship with 30-day mortality (table 2).

Sensitivity analyses using only patients who had minute-by-minute invasive blood pressure measurements (N = 34,547) gave the same conclusions for the association between 30-day mortality and generalized ARV-MAP (both continuous and categorized ARV-MAP) as when using all data. Squared ARV also gave the same conclusions. A sensitivity analysis to the primary results including only the subset of patients (58% of the total sample) for whom history of cardiovascular medications was available (and thus adjusted for as confounding factors) gave very similar results (appendix 1 and table 3), with no differences in trends or conclusions but a slightly stronger relationship between ARV-MAP and 30-day mortality. Finally, using Hansen’s version of the ARV-MAP, shown above only to be intuitive for equally spaced data, we found a similarly shaped relationship between ARV-MAP and 30-day mortality (overall P value of 0.004); however, odds ratios were weaker, and no difference was found between high ARV and the median.

In a separate multivariable model, both continuous SD-MAP (P < 0.001) and continuous TWA-MAP (P < 0.001) were independently associated with 30-day mortality. The interaction between SD-MAP and TWA-MAP was significant using three knots (P = 0.026) but not using 4 or 5 (P > 0.10), so only the main effects model is reported. As in the univariable model, a U-shaped multivariable relationship between SD-MAP and mortality was found (fig. 3B). However, the relationship between SD-MAP and mortality was small compared with TWA-MAP (fig. 3C). The odds ratio (95% CI) of the 25th percentile versus the median SD-MAP (reference) was 1.09 (1.03 to 1.16, P = 0.006), and for the 75th percentile was 1.05 (1.01 to 1.10, P = 0.033) (table 2).

The confounder-adjusted relationship between minimum MAP sustained for 10 min or more and 30-day mortality was J-shaped with the low point at 75 mmHg (fig. 5A). Minimum MAPs greater than 75 mmHg were associated with only slightly greater mortality. In contrast, the estimated odds of dying by 30 days was 32% higher (95% CI, 25 to 39) for a 5-mmHg reduction in the minimum MAP value sustained for 10 min when that minimum was less than the median of 70 mmHg (P < 0.001; table 2). Corresponding odds ratios for a range of minimum MAP value sustained for 10 min compared with 70 mmHg are given in figure 5B. Finally, cumulative time of MAP less than 50, 55, 60, 70, or 80 mmHg was each associated with higher odds of 30-day mortality (all P < 0.001; table 2).

For the primary model of ARV-MAP and 30-day mortality and other models, diagnostics in the form of DFBETAs, Pearson residuals, and leverage statistics were good, and no issues were found (see details for primary model in appendix 2 and figs. 6 and 7).

Mean arterial pressure variability, measured as the sum of consecutive jumps or drops across a surgery (generalized ARV-MAP), was independently associated with 30-day mortality, consistent with our hypothesis.⁸  TWA-MAP was also independently associated with 30-day mortality, consistent with that reported in previous literature.¹⁹  However, the relationship between mean MAP and mortality was much stronger than that for variability and mortality. Interestingly, the relationship between MAP variability and 30-day mortality did not depend on TWA of MAP in any substantial way, such that low variability was weakly associated with higher mortality regardless of the patient’s mean MAP for the case. Likewise, TWA of MAP was independently associated with 30-day mortality irrespective of the level of variability.

Several studies have shown that low heart rate variability is a marker of autonomic dysfunction among patients with congestive heart failure²⁰  or recovering from a myocardial infarction,²¹  as well as among patients without clinical evidence of heart disease.²²  Because physiological parameters such as blood pressure and heart rate are autonomic functions, it is possible that decreased variability in blood pressure may be associated with increased mortality and cardiovascular events due to autonomic dysfunction as seen with heart rate. We also saw that blood pressure variability was moderately correlated with TWA-MAP. It thus follows that patients with low TWA-MAP are more likely to have lower variability of MAP, and so the higher mortality for those patients with low variability may reflect the lower mean blood pressure.

Our work differs from previous literature in that we distinguish and isolate blood pressure variability from blood pressure per se. For example, Aronson et al.¹²  found that mean duration of systolic excursion (outside a range of 105–130 mmHg) was weakly associated with 30-day mortality and referred to this exposure as “variability.” However, this is not actually a measure of variability but rather of mean pressure. For example, a patient could spend much time with systolic pressure less than 105 mmHg and yet have low variability because all measurements were similar. In other studies, duration of intraoperative hypotension was not associated with mortality²³  or stroke^24,25  under various definitions, but such durations measure extreme values and not specifically the measure-to-measure variability we were interested in. We thus focused on pure measures of variability, that is, those directly assessing changes in consecutive measurements over time, independent of the mean. We adjusted for the mean blood pressure in all models (e.g., Hansen et al.⁸  adjusted for 24-h blood pressure in their “full” model) as well as a host of other baseline confounding variables, allowing an assessment of the independent contribution of variability per se.

Anesthesiologists consider mean, systolic, and diastolic pressures—and each provides valuable information. However, diastolic and especially systolic pressures are subject to considerable distortion depending on vasomotor status, measurement site, and general anesthesia.^26,27  In contrast, MAP generally very nearly equals aortic pressure over a wide variety of clinical conditions and with both oscillometric and radial artery measurements. As might thus be expected, our results were essentially unchanged when analysis was restricted to radial arterial pressures.

There is no recognized standard for measuring blood pressure variability. We considered three measures of mean arterial pressure variability, and our conclusions did not differ markedly across the approaches. However, ARV seems preferable to the commonly used SD because it measures consecutive changes in blood pressure, whereas the SD ignores timing of the measurements.⁸  We enhance this approach by proposing a generalized version of ARV that remains valid when measurements are recorded at nonequidistant times—as is typical in clinical practice. We also considered a squared version of the ARV to give more weight to more steep jumps but found little difference compared with generalized ARV in the relationship with 30-day mortality. Our generalized ARV thus appears to provide a good estimate of intraoperative variability in blood pressure.

Walsh et al.¹⁹  identified 55 mmHg as a number below which the odds of acute kidney injury and myocardial infarction begin to noticeably increase, with the target of 55 mmHg based on the apparently univariable relationship between minimum MAP (single MAP value per patient) and outcome. Our results on MAP should not be directly compared with those of Walsh et al. for several reasons, but mainly because we focused on 30-day mortality, whereas they focused on acute kidney injury and myocardial infarction. We observed a U-shaped relationship between TWA-MAP and mortality, such that the odds of mortality decreased as TWA-MAP increased from 40 up to approximately 85 mmHg and then increased for TWA-MAP greater than 85 mmHg. We also found positive relationships between mortality and cumulative minutes of MAP less than 50, 55, 60, 70, and 80 mmHg, such that longer exposure was worse for each threshold. Finally, we found that decreasing the minimum value of MAP that was sustained for more than 10 min was associated with higher odds of mortality when that minimum was less than 70 mmHg, but no association when greater than 70 mmHg. Each of our analyses adjusted for MAP variability and a host of confounding variables and thus represents an estimate of the isolated contribution of MAP level.

In our multivariable modeling of the relationship between blood pressure variability and 30-day mortality, we adjusted for a host of baseline potentially confounding variables, including surgical procedure and a wide range of baseline comorbidities. Although we adjusted for numerous cardiovascular comorbidities, a limitation of our analysis is that we were not able to adjust for history of receiving cardiovascular drugs in the primary analysis due to current limitations of our database. However, adjusting for the reasons for being on the cardiovascular drugs (i.e., the comorbidities) may remove much or most of the confounding due to those drugs on the relationship between blood pressure variability and 30-day mortality. In fact, we were able to verify that adding cardiovascular drugs in a subset of patients (58% of total) for which the information was available only minimally affected our results and did not change any conclusion (appendix 1).

Patients with higher MAP variability had higher levels of many baseline variables known to be risk factors for mortality. Our multivariable models thus included demographics, emergency surgery, medical history, use of an arterial catheter, procedure, ASA-PS, and more. It would be challenging to randomly vary MAP, especially in the most interesting range (approximately <75 mmHg); and it probably would be even more challenging to control blood pressure variability. An analysis of observational data is thus the best practical approach to the questions we addressed in this study. It remains possible that results would differ in other populations or surgical environments. In particular, the observed relative effects might well be clinically important if observed in settings with higher overall 30-day mortality because the absolute differences in mortality across levels of blood pressure variability would be higher. But given the overall limited association between blood pressure variability and mortality, it seems unlikely that blood pressure variability provides much additional predictive information.

In conclusion, MAP and mean pressure variability were nonlinearly related to 30-day mortality in our noncardiac surgery population. After adjusting for TWA-MAP and other important covariables, low blood pressure variability was still associated with higher 30-day mortality, but the differences were not clinically important in our population. Anesthesiologists might thus pay more attention to overall trends in the mean blood pressure for a case than in the minute-to-minute variation.

Support was provided solely from institutional and/or departmental sources.

The authors declare no competing interests.

Table 3 shows that when we adjusted for history of taking specific cardiovascular medications on the patients in whom this information was available (58% of total), results are almost identical to our primary analysis on all patients—odds ratios are very similar and all conclusions are the same. We conclude that the primary analysis (table 2) did not include any noticeable bias due to data on cardiovascular medications not being available.

For the primary analysis model assessing the association between generalized average real variability of mean arterial pressure (ARV-MAP) (see equation 2 in Materials and Methods), we report on observations that might cause instability in the parameter estimates using DFBETAs. The DFBETA diagnostic for an observation is the standardized difference in the parameter estimate due to deleting the observation and can be used to assess the effect of an individual observation on an estimated parameter of the fitted model. For small to medium datasets, values greater than 1 may be considered large. For larger datasets, a conservative calculation indicating large values of DFBETA is an absolute value or 0.006 in our data.

Figure 6, A and B, reports DFBETA values for the linear and nonlinear spline terms for generalized ARV-MAP, respectively, whereas figure 6, C and D, reports the same statistics for time-weighted average mean arterial pressure. Figure 6, A–D, had 1.5, 1.6, 1.7, and 1.7% beyond the recommended cutoff point (i.e., DFBETA > 0.006), indicating that the model fit the data well with relatively very few values that might cause instability in the respective regression parameters.

An outlier data value is traditionally defined as a response variable Y (here, 30-day mortality), for which the standardized Pearson residual is greater than 2 in absolute value, shown in the figure with the horizontal line.

A conservative definition for an extreme value for an independent variable X (here, the parameter corresponding to the linear portion of the ARV-MAP spline function) for a large dataset is when the leverage calculation is greater than (2k + 2)/n, where k is the number of parameters in the model (k = 96). In our dataset, a leverage value greater than 0.0018 suggests an extreme value, as shown in the figure by the vertical line. However, experts report that leverage values are not very reliable when the predicted probability is less than 0.10 as is the case for most of our data (Hosmer and Lemeshow²⁷ ).

As displayed in figure 7, only approximately 1% of observations had a Pearson residual outside of ±2, indicating good model fit. Only 0.3% of data points were both outliers and with high leverage, as shown in the figure 7B and representing only 0.5% of observations. Figure 7C (neither abnormal residual nor high leverage) contains 90.2% of all observations. Figure 7A (high Pearson residual but normal leverage) had 0.3% and figure 7D (normal Pearson residual but abnormal leverage) had 8.8% of the data points, respectively.