A Study Examining the Effects of Nebivolol Compared to Atenolol on Endothelial Function: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study Examining the Effects of Nebivolol Compared to Atenolol on Endothelial Function (NCT01522950), a randomized phase 2 study. The primary outcome is Change in Small Artery Elasticity.

2. Clinical Question

3. Trial Design

This was a randomized, parallel-group phase 2 study sponsored by the University of Minnesota. The registry describes quadruple masking and a placebo-controlled design. It lists an enrollment of 76 and a completed status. The registry record gives a start date of 2010-05 and a primary completion date of 2016-10. The brief summary describes follow-up for 9 months and says approximately 75 subjects were to be recruited.

Participants were allocated to nebivolol, atenolol or placebo. The summary says assignment used a block randomization scheme. The registry does not specify which groups of people were included in the quadruple masking, or provide details about concealment of allocation. The medication descriptions specify an initial dose period followed by titration; dose could be returned to initiation levels if side effects occurred. The placebo description also refers to dose titration.

The posted primary outcome summaries include 20 participants for nebivolol, 18 for atenolol and 22 for placebo. These are outcome-specific group counts and are not identical to the enrollment figure. The registry record does not explain the relationship between enrollment and the counts used for this outcome, or provide a participant-flow account. It also does not report the trial’s original sample-size justification or detailed statistical analysis plan.

Three secondary outcomes are listed: change in large artery elasticity, systolic blood pressure and diastolic blood pressure. The registry reports group summaries for these outcomes, but no separate analyses are listed as reported analyses.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Reasons for not completing this period:

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Change in Small Artery Elasticity, measured over baseline, 9 months.

The primary endpoint was change in small artery elasticity from baseline to 9 months after intervention initiation. The unit is ml/mmHg × 100. The registry describes this measure as a marker for endothelial function, so it was used to assess a vascular-function outcome rather than a clinical event endpoint.

The registry reports the mean change and standard deviation in each group. A mean describes the group’s average change, while the standard deviation describes the spread of individual measurements around that average. The posted mean changes were 2.4 for nebivolol, 1.0 for atenolol and 0.4 for placebo. These are group summaries; they do not show how every participant’s measurement changed.

The comparison of interest is the difference in mean change between an active-treatment group and placebo. The posted unadjusted recalculation estimates that difference as 2.0 for nebivolol versus placebo and 0.6 for atenolol versus placebo. The endpoint is a continuous measure, and the registry does not report a threshold defining a clinically important change. It also does not explain how missing measurements, if any, were handled.

7. Results Posted in the Registry

• Nebivolol: mean 2.40 versus 0.40 on control; difference 2.00 (95% CI 0.84 to 3.16), standardized effect d = 1.05; z-test p = <0.001.
• Atenolol: mean 1.00 versus 0.40 on control; difference 0.60 (95% CI -0.60 to 1.80), standardized effect d = 0.32; z-test p = 0.328.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Change in Large Artery Elasticity

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Nebivolol: mean 3.20 versus 0.20 on control; difference 3.00 (95% CI 0.40 to 5.60), standardized effect d = 0.72; z-test p = 0.024.
  • Atenolol: mean 2.90 versus 0.20 on control; difference 2.70 (95% CI 0.79 to 4.61), standardized effect d = 0.90; z-test p = 0.006.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for Nebivolol than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for Atenolol than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Change in Systolic Blood Pressure

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Nebivolol: mean -9.00 versus -3.20 on control; difference -5.80 (95% CI -13.47 to 1.87), standardized effect d = -0.46; z-test p = 0.138.
  • Atenolol: mean -13.00 versus -3.20 on control; difference -9.80 (95% CI -16.93 to -2.67), standardized effect d = -0.84; z-test p = 0.007.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Nebivolol and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Atenolol than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Change in Diastolic Blood Pressure

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Nebivolol: mean -8.50 versus -2.90 on control; difference -5.60 (95% CI -10.84 to -0.36), standardized effect d = -0.66; z-test p = 0.036.
  • Atenolol: mean -8.50 versus -2.90 on control; difference -5.60 (95% CI -10.57 to -0.63), standardized effect d = -0.72; z-test p = 0.027.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Nebivolol than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Atenolol than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The secondary outcomes cover large artery elasticity and systolic and diastolic blood pressure, all assessed as change from baseline to 9 months. Across these outcomes, the posted group means generally show a more favorable numerical change for active-treatment groups than for placebo, though the pattern is not identical across measures or comparisons. The secondary results add context to the primary small artery elasticity finding by describing other vascular and blood-pressure measurements, but they do not replace or independently validate the primary endpoint.

The registry includes unadjusted recalculated comparisons for each active-treatment group versus placebo. Some of those comparisons have intervals that exclude zero and smaller unadjusted p-values, while others do not. The registry does not list reported analyses for these outcomes, and it does not state whether these outcomes or contrasts were prespecified in a formal hierarchy.

Unadjusted secondary results carry less weight because several outcomes and contrasts create opportunities for apparently notable findings by chance. In general, a multiplicity procedure or a clearly prespecified testing hierarchy can control how evidence is interpreted across a family of analyses. The registry record does not report such a procedure. The secondary findings should therefore be regarded as exploratory descriptions of the posted data rather than as definitive independent confirmations of the primary result.

These endpoints remain continuous measures, and their group averages do not show the range of individual responses. No clinical importance threshold is reported for the secondary measures. The record also does not report adjusted models, missing-data methods, or analyses that link changes in these measures to cardiovascular events. Their relationship to the primary endpoint is consequently statistical and physiological in scope, not proof of a downstream clinical effect.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Change in Large Artery Elasticity
• Change in Systolic Blood Pressure
• Change in Diastolic Blood Pressure

9. Statistical Interpretation

10. Statistical Methods Explained

A continuous outcome is measured on a numerical scale, and a group mean summarizes its central value. For this trial, the reported endpoint is change in small artery elasticity from baseline to 9 months. The standard deviation is a measure of variability among the observations within a group; it is not the uncertainty around the mean itself. Greater spread makes a mean difference less precisely estimated when group sizes are otherwise similar.

What does a mean difference represent?

A mean difference compares the average change in one group with the average change in another. The primary comparisons use placebo as the reference. The posted unadjusted recalculation reports a mean difference of 2.0 for nebivolol versus placebo and 0.6 for atenolol versus placebo. A positive difference means the active-treatment group’s average change was numerically higher than placebo’s average change for this endpoint. The estimate is not an individual-level treatment effect and does not describe the distribution of outcomes for every participant.

The group summaries and recalculated differences are unadjusted. In general, an adjusted analysis can account for prespecified baseline measurements or other covariates, while an unadjusted comparison uses the summary outcome values without those adjustments. The registry record does not report a sponsor analysis or specify an adjustment model for the primary endpoint. The posted calculations therefore should be read as descriptive, unadjusted comparisons rather than as a substitute for a documented trial analysis.

How should the p-value be read?

In general, a p-value measures how compatible the observed data are with a specified null model, under the assumptions of the test. It does not measure the probability that a treatment effect is real, the probability that the null hypothesis is true, or the clinical importance of the estimate. For the primary endpoint, the unadjusted recalculated p-value for nebivolol versus placebo is < 0.001; for atenolol versus placebo it is 0.328. These values describe the respective unadjusted comparisons and do not account for the set of outcomes and contrasts considered.

A p-value is interpreted alongside the estimate and its confidence interval. A small p-value can occur with an estimate that is imprecise in practical terms, while a larger p-value does not establish that a meaningful effect is absent. The size and range of plausible effects matter, as does whether the analysis and outcome were prespecified. The registry does not report a detailed statistical analysis plan or identify a multiplicity procedure.

Why use a confidence interval?

In general, a confidence interval gives a range of values compatible with the observed data under the analysis assumptions. For a mean difference, it indicates uncertainty about the estimated difference. An interval entirely above zero indicates that the displayed range does not include no difference; an interval crossing zero includes both no difference and values on either side. This does not mean that every value in the interval is equally likely, nor does it address possible bias or missing data.

The primary nebivolol-versus-placebo interval is above zero, while the atenolol-versus-placebo interval includes zero. This difference in interval placement is consistent with the corresponding unadjusted p-values. The record does not report adjusted confidence intervals or a multiplicity correction.

What do the planning calculations represent?

The sample-size illustrations use the observed effect as a reference and consider smaller fractions of that effect. Their stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The figures for these continuous outcomes are participants per arm. These are planning illustrations based on the posted effect, not observed power and not a reconstruction of the trial’s original design assumptions.

In general, over-dispersion means that outcome variability is greater than a model assumes. If variability is understated, a calculation can suggest more precision or a smaller required sample than is warranted; if variability is appropriately represented, the calculation is more informative for planning. Here the outcome summaries include standard deviations, but the registry does not report a separate design assumption for variability, an original sample-size calculation, or a model for over-dispersion. The posted planning illustrations should therefore be treated as conditional on their stated assumptions rather than as evidence about the trial’s design adequacy.

Finally, the registry reports no analyses for the primary endpoint in its reported-analyses listing. That absence makes the recalculated summary comparison useful for understanding the posted values, but it leaves important analytical details unknown, including the analysis population, handling of incomplete measurements, and whether any prespecified covariate adjustment was intended.

11. Confidence Intervals and Precision

Precision concerns how narrowly the data locate the estimated mean difference. The primary nebivolol-versus-placebo estimate is 2.0, and its confidence interval lies above zero. This supports a positive difference in mean change within the assumptions of the unadjusted recalculation, while the interval’s width still represents uncertainty about the magnitude. The interval should not be read as a range of guaranteed effects or as a statement about each participant’s response.

For atenolol versus placebo, the estimate is 0.6 and the confidence interval includes zero. That interval leaves uncertainty about whether the mean difference is positive, absent, or negative. It does not establish equivalence, and the registry does not report an equivalence margin or a non-inferiority analysis.

Both comparisons use relatively small outcome groups, and individual measurements show variability, as reflected by the reported standard deviations. In general, larger group sizes and less outcome variability tend to produce more precise estimates, although precision also depends on the analysis and data structure. The registry does not explain the difference between its enrollment figure and the endpoint group counts, or report how missing outcome measurements were handled. Those omissions make it difficult to assess whether the posted intervals capture all relevant uncertainty.

The confidence intervals accompany unadjusted recalculated comparisons. They do not account for possible multiplicity across primary and secondary outcomes, nor can they address selection, measurement, or missing-data bias. Their statistical interpretation is conditional on the comparison and assumptions used to calculate them.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The sample-size table and curve are planning illustrations based on the observed effect for each comparison. The figures for this continuous endpoint are participants per arm, not total events. The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is expressed as the stated fraction of the observed effect. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the estimated participants per arm for a planning scenario designed to have an 80% chance of detecting the specified effect under the assumptions, if that effect and the model assumptions are correct. The 90% power column applies the same idea with a higher target chance of detection, which generally requires more participants per arm. These are hypothetical planning targets, not evidence about the probability that the completed trial detected an effect.

Rows that plan for a smaller fraction of the observed effect require more participants per arm. This reflects a general statistical principle: smaller differences are harder to distinguish from random variation when the outcome has the same level of spread. The illustrations are sensitive to the observed estimate, which can be unstable in a small study. They should not be treated as a recommendation for a future trial without considering the intended effect, analysis plan, outcome variability, and other design assumptions. This is not observed power.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 2.000; pooled standard deviation σ = 1.901.
2. n = 2 × (1.96 + 0.842)² × 1.901² / 2.000² = 14.2, rounded up to 15 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- 2                      # observed difference in means
sigma <- 1.90052624291274                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(1522950)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 15 (80% power), 19 (90% power)
 75% of observed effect: n per arm = 26 (80% power), 34 (90% power)
 50% of observed effect: n per arm = 57 (80% power), 76 (90% power)
power.t.test: 15.2 
Simulated power at n = 15 per arm: 0.796 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary endpoint and three secondary outcomes, with comparisons of each active-treatment group against placebo. Considering multiple outcomes and contrasts raises a multiplicity issue: even when each test is conducted at a conventional significance level, the chance of at least one apparently notable finding across a family of tests can increase. In general, multiplicity can be addressed through prespecified outcome hierarchies, adjusted testing, or a clearly exploratory interpretation. The registry record does not report a multiplicity adjustment, testing hierarchy, or detailed statistical analysis plan.

The posted comparison p-values are unadjusted recalculations. They should not be interpreted as if they accounted for the full set of outcomes and comparisons. The record also does not identify whether a particular analysis was designated confirmatory, or report any interim analyses. Those details are not reported in the registry record.

Missing-data handling is also not reported. The registry gives an enrollment figure and outcome-specific group counts, but does not describe participant flow, withdrawals, reasons for missing measurements, or the analysis population. The record does not say whether analyses used complete cases, imputation, or another method. No assumptions about missing outcomes can therefore be verified.

In general, missing data can affect a group comparison if the likelihood of having an observed outcome is related to participant characteristics or outcomes. An analysis based only on observed measurements may not represent all randomized participants when such differences exist. This is a general concern, not a claim that missingness occurred in a particular way in this trial. The record’s lack of detail prevents assessment of whether missingness could influence the estimates.

The registry also does not report whether the primary endpoint analysis adjusted for baseline values, how protocol deviations were handled, or whether an intention-to-treat population was used. These are distinct analysis choices, and their absence should be understood as a limit on interpretation rather than evidence that any particular method was or was not used.

15. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent non-serious adverse event terms

The safety summary reports serious adverse events attributed to study interventions as zero in each group. The group counts at risk for serious events were 20 for nebivolol, 18 for atenolol and 22 for placebo. The registry lists one death in the atenolol group and one in the placebo group, with none in the nebivolol group. It does not identify these deaths as intervention-attributed serious adverse events.

Other adverse events affected 6 participants in the nebivolol group, 4 in the atenolol group and 7 in the placebo group, using the posted groups at risk of 20, 18 and 22. These are counts of participants affected, not event counts or rates. No serious adverse-event terms are listed.

These figures are descriptive and do not establish that groups had equivalent safety profiles. The record does not provide event-level descriptions, timing, duration, severity details for the other events, or an analysis comparing safety outcomes. Small group counts and incomplete reporting limit interpretation; the posted counts should not be used alone to make individual treatment decisions.

16. What the Result Does, and Does Not, Mean

The primary posted summaries show that mean small artery elasticity increased from baseline in all three groups, with the largest mean change in the nebivolol group. The unadjusted recalculated comparison with placebo has an estimated mean difference of 2.0 and a confidence interval above zero. The corresponding atenolol comparison is less precise and its interval includes zero. These findings describe the posted continuous endpoint over 9 months.

They do not establish the clinical importance of the measured difference. The registry does not report a threshold for a meaningful change in small artery elasticity, and the measure is described as a marker of endothelial function rather than a clinical event. The study title and summary refer to cardiovascular risk, but the posted outcome summaries do not demonstrate a change in cardiovascular events.

The comparisons are unadjusted recalculations from posted group summaries, not reported sponsor analyses. The registry does not state the analysis population, missing-data approach, multiplicity plan, or baseline-adjustment strategy. This missing information limits confidence in treating the nominal p-values as confirmatory evidence. The observed means and intervals also do not describe how much individual outcomes varied beyond the group standard deviations.

A confidence interval crossing zero does not prove that a treatment and placebo have the same effect, while an interval excluding zero does not by itself demonstrate clinical relevance or freedom from bias. Similarly, the presence of a positive group mean does not mean every participant improved. The result is a statistical comparison of group averages, interpreted in light of the study’s limited reporting and the fact that the endpoint is a surrogate-like vascular measure.

The registry’s adverse-event counts are also descriptive. They do not establish relative safety, and the posted death counts are not, by themselves, evidence that an intervention caused or prevented a death. The overall record supports a cautious reading of reported changes and uncertainty, not a treatment recommendation.

17. Why This Trial Matters Statistically

This trial illustrates why an estimated effect, its uncertainty and its analysis context should be read together. The nebivolol-versus-placebo estimate is positive and its confidence interval excludes zero, whereas the atenolol-versus-placebo interval includes zero. Looking only at whether a p-value crosses a threshold would conceal the difference in precision and the range of effects still compatible with the data.

It also highlights the distinction between a statistically detectable change in a continuous vascular measure and a change in a clinical outcome. Small artery elasticity is identified as a marker of endothelial function, but the registry does not report a clinically meaningful threshold or cardiovascular-event results. Statistical evidence about the marker cannot alone establish the importance of the change for patients.

The outcome group counts are smaller than the registry enrollment figure, and the record does not explain the relationship or describe missing-data handling. This makes participant flow and analysis-population reporting important for interpreting a trial’s results. The lack of reported analyses, multiplicity methods and original sample-size assumptions further separates the posted unadjusted recalculations from a fully documented confirmatory analysis.

Finally, planning illustrations based on observed effects demonstrate how required sample size depends on the effect targeted and the assumptions used. They are useful for understanding planning sensitivity, but cannot establish the adequacy of this study’s original design when that justification is not reported.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

Several trial-specific limitations arise from the registry reporting. The primary outcome summaries use groups of 20, 18 and 22, while the registry enrollment is 76. The record does not explain the difference, provide a participant-flow diagram, or state whether the outcome counts reflect all randomized participants. It is therefore not possible to determine from the record how many participants lacked the primary endpoint or why.

The registry does not report the sponsor’s primary or secondary analyses, a complete statistical analysis plan, baseline-adjusted results, or a multiplicity strategy. The posted comparisons are unadjusted recalculations from summary statistics. They are informative about the group means, but cannot resolve whether the original analysis used other prespecified methods.

The primary outcome is a continuous measure described as a marker of endothelial function. The record does not provide a threshold for clinical importance or show whether the observed change corresponds to a patient-important outcome. Cardiovascular risk is part of the study description, but the posted results do not report cardiovascular events.

The record also gives limited safety detail. It lists counts for serious events, deaths and other affected participants, but does not provide event descriptions or a comparative safety analysis. The summary describes a quadruple-masked study, but does not identify the masked roles or provide details on allocation concealment. These reporting gaps constrain interpretation without establishing that the methods were inadequate.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: A Study Examining the Effects of Nebivolol Compared to Atenolol on Endothelial Function — NCT01522950.
• Registry record last updated 2020-07-17; status last verified 2020-07.
• Results first posted 2020-01-21.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

The registry describes a completed, randomized, quadruple-masked, parallel-group phase 2 study of nebivolol, atenolol and placebo in patients with early vascular disease. The primary endpoint was change in small artery elasticity from baseline to 9 months. Posted group means were 2.4 for nebivolol, 1.0 for atenolol and 0.4 for placebo.

Unadjusted recalculated comparisons versus placebo show a mean difference of 2.0 for nebivolol and 0.6 for atenolol. The nebivolol interval excludes zero; the atenolol interval includes zero. Three secondary outcomes and descriptive adverse-event counts are also reported. The registry does not report formal analyses, multiplicity handling, missing-data methods, or the original sample-size justification, so the comparisons require cautious interpretation.