Labetalol and Esmolol: Vital Signs and Post Operative Pain Management: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Labetalol and Esmolol: Vital Signs and Post Operative Pain Management (NCT01114971), a randomized phase 4 study. The primary outcome is Postoperative Pain.

2. Clinical Question

The study focuses on intraoperative management during laparoscopic surgery and whether the listed drug strategies are associated with differences in postoperative recovery outcomes. The registry describes the study as randomized, double-blinded, active-controlled, and Phase 4. It lists postoperative pain as the primary outcome, measured in the post-anesthesia care unit (PACU) using a verbal rating scale from 0 to 10, with measurement described over one day.

The comparison is between each active-control group and fentanyl: labetalol versus fentanyl, and esmolol versus fentanyl. The registry also lists outcomes related to opioid consumption, postoperative nausea and vomiting, return to feeling normal, satisfaction, and appetite. Numerical results are posted for opioid consumption, nausea and vomiting, and return to feeling normal. Results for satisfaction and low appetite are not reported in the registry record.

The registry's factorial model label does not, by itself, explain how factors or treatment combinations were specified. The detailed protocol structure and the rationale for the listed arm arrangement are not reported in the registry record. The clinical question can therefore be read from the posted treatment arms and outcomes, without assuming additional factorial comparisons.

3. Trial Design

The registry describes NCT01114971 as a completed, randomized, double-blinded, active-controlled Phase 4 study sponsored by Cedars-Sinai Medical Center. The listed enrollment is 75. The study concerns laparoscopic surgery and compares three groups: fentanyl, labetalol, and esmolol. Each posted arm contains 25 participants. The study start date is 2009-09-03, and the primary completion date is 2014-07-30.

Fentanyl, labetalol, and esmolol are listed as drug interventions. According to the arm descriptions, boluses were to be given at induction and before surgical incision, with additional boluses as needed during the intraoperative period. The stated hemodynamic criteria describe maintaining mean arterial pressure within 15% of the pre-induction baseline value, and/or heart rate > 80 bpm. The registry gives different concentrations for the listed drugs: fentanyl 50 micrograms/ml, labetalol 5 mg/ml, and esmolol 10 mg/ml.

The registry identifies the allocation as randomized and masking as double. It also gives the model as factorial, but does not report enough detail to establish the factorial factors, their levels, or the planned statistical handling of them. The trial's original allocation procedures, randomization method, concealment procedures, and blinding assessment are not reported in the registry record.

The primary outcome is postoperative pain, reported as a mean and standard deviation on a 0-to-10 scale. The registry lists a one-day timeframe and describes measurement in the PACU. Secondary outcomes include counts for opioid consumption and postoperative nausea and vomiting, days to return to feeling normal, satisfaction on a 0-to-10 verbal rating scale, and low appetite. Numerical results are posted for three of those secondary outcomes; satisfaction and low appetite results are not reported in the registry record.

The original sample-size justification, protocol-defined estimand, analysis population, and prespecified statistical analysis plan are not reported in the registry record. The numerical contrasts discussed for the posted primary and secondary outcome summaries should therefore be understood as unadjusted comparisons rather than as a complete account of a prespecified model.

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

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.

Population: ALL PARTICIPANTS = 75 PARTICIPANTS PER GROUP= 25

6. Primary Endpoint

The registry lists the primary outcome as Postoperative Pain, measured over one day.

The primary endpoint is postoperative pain measured in the PACU using a verbal rating scale from 0 to 10. The registry describes 0 as no pain at all and 10 as the worst imaginable pain. Participants verbally rate their pain on this eleven-point numerical scale. The reported summary is the mean score with its standard deviation, and the registry gives the measurement timeframe as one day.

A pain score is a continuous outcome in this analysis: the score can take values along the numerical scale, and group results can be summarized by an average and the spread of individual scores. The mean gives a measure of the group’s central score, while the standard deviation describes how much scores varied around that mean. This summarizes the group but does not show every participant’s experience or the distribution of scores.

For the posted comparison, the clinical interpretation depends on the difference in mean scores between each drug group and the fentanyl group. Because lower values on the scale indicate less reported pain, the direction of a mean difference must be read with the group order in mind. The posted estimates are given as the treatment-arm mean minus the fentanyl-arm mean: a negative estimate means the treatment-arm mean was lower, while a positive estimate means it was higher.

The PACU measurement is intended to capture postoperative pain near the recovery period. It is one outcome at the stated assessment timeframe, not a complete measure of pain over the entire recovery course. The registry does not report additional details about repeated pain measurements, the handling of missing scores, or whether the scale was administered at more than one point during the stated timeframe.

7. Results Posted in the Registry

• Labetalol: mean 3.00 versus 3.20 on control; difference -0.20 (95% CI -1.61 to 1.21), standardized effect d = -0.08; z-test p = 0.782.
• Esmolol: mean 3.90 versus 3.20 on control; difference 0.70 (95% CI -0.55 to 1.95), standardized effect d = 0.31; z-test p = 0.274.

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.

Number of Participant With Opioid Consumption

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Labetalol: 56.0% (14/25) versus 60.0% (15/25) on control; risk difference -4.0 percentage points (95% CI -31.3 to 23.3), risk ratio 0.93 (0.58–1.50); unadjusted two-proportion z-test p = 0.774.
  • Esmolol: 52.0% (13/25) versus 60.0% (15/25) on control; risk difference -8.0 percentage points (95% CI -35.4 to 19.4), risk ratio 0.87 (0.53–1.42); unadjusted two-proportion z-test p = 0.569.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Labetalol and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Esmolol and the control. The interval gives the range of effects that remain compatible with the data.

Postoperative Nausea and Vomiting

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Labetalol: 16.0% (4/25) versus 36.0% (9/25) on control; risk difference -20.0 percentage points (95% CI -43.7 to 3.7), risk ratio 0.44 (0.16–1.26); unadjusted two-proportion z-test p = 0.107.
  • Esmolol: 28.0% (7/25) versus 36.0% (9/25) on control; risk difference -8.0 percentage points (95% CI -33.8 to 17.8), risk ratio 0.78 (0.34–1.76); unadjusted two-proportion z-test p = 0.544.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Labetalol and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Esmolol and the control. The interval gives the range of effects that remain compatible with the data.

Return to Feeling Normal

• 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:
  • Labetalol: mean 10.00 versus 11.00 on control; difference -1.00 (95% CI -5.99 to 3.99), standardized effect d = -0.11; z-test p = 0.694.
  • Esmolol: mean 12.00 versus 11.00 on control; difference 1.00 (95% CI -4.27 to 6.27), standardized effect d = 0.11; z-test p = 0.710.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Labetalol and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Esmolol and the control. The interval gives the range of effects that remain compatible with the data.

The secondary outcomes provide a broader but incomplete view of recovery. The registry lists opioid consumption, postoperative nausea and vomiting, return to feeling normal, patient satisfaction, and low appetite. Numerical summaries are posted for the first three, while satisfaction and low appetite results are not reported in the registry record. The secondary outcomes also use different timeframes and measurement types, so they do not all describe the same aspect of recovery.

Across the outcomes with numerical results, the observed contrasts do not form a uniform pattern that clearly reinforces or contradicts the primary pain result. Some group summaries are numerically lower than the fentanyl comparison, while others are higher, and the uncertainty around the posted comparisons is substantial. These results are better viewed as exploratory descriptions than as a single coherent secondary finding.

Secondary outcomes can add context to a primary endpoint, but they do not substitute for it. Opioid consumption and nausea and vomiting are related to postoperative care, while return to feeling normal concerns a broader recovery experience. None directly changes what the primary pain-scale comparison estimates. The registry does not report an analysis that combines these outcomes or specifies how much weight each should receive.

Unadjusted secondary results carry less weight when many outcomes and comparisons are examined, because the chance of obtaining apparently notable results by chance can increase across multiple tests. The registry does not report a multiplicity adjustment or a hierarchy among secondary outcomes. Nor does it report whether these outcomes were designated as confirmatory or exploratory in the analysis plan. Their estimates and p-values should therefore be interpreted cautiously and alongside the primary result, rather than treated as independent proof of a treatment effect.

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

• Number of Participant With Opioid Consumption
• Postoperative Nausea and Vomiting
• Return to Feeling Normal
• Patient Satisfaction Using a Verbal Rating Scale From 0 to 10
• Low Appetite

9. Statistical Interpretation

10. Statistical Methods Explained

What does a mean difference describe?

For a continuous outcome such as the pain score, a mean difference compares the average score in one group with the average score in another. The posted comparisons use fentanyl as the reference group. The contrast is expressed as the treatment-arm mean minus the fentanyl-arm mean. A negative value means the treatment-arm average was lower; a positive value means it was higher. Since lower scores on the stated pain scale indicate less reported pain, direction matters when interpreting the estimate.

A mean difference is a group-level summary. It does not mean every participant in the group had a score equal to that difference, and it does not describe the full range of individual outcomes. The group means and standard deviations give a concise account of the central values and variability, while the confidence intervals quantify uncertainty in the estimated contrasts.

What does a confidence interval add?

A confidence interval gives a range of values compatible with the data under the assumptions of the analysis. It communicates the precision of an estimate: a narrower interval indicates greater precision, while a wider interval leaves more uncertainty about the possible size and direction of the contrast. A confidence interval that includes zero is compatible with no average difference, but it may also include nonzero differences. It does not demonstrate equivalence or prove that an effect is absent.

The intervals for both posted primary comparisons include zero. Their widths also show that the estimates are uncertain: plausible values extend to either side of zero. A point estimate alone can make an uncertain contrast look more settled than it is, so the interval should be considered alongside the estimated difference and the group summaries.

What do the p-values say?

The posted p-values for the primary contrasts are unadjusted. A p-value measures how unusual data at least as incompatible with a specified null model would be if that model and the analysis assumptions were correct. It is not the probability that the null hypothesis is true, nor is it a measure of the size or clinical importance of an effect. A p-value should be interpreted with the estimate, interval, study design, and analysis plan rather than as a stand-alone decision rule.

The registry record does not report a prespecified significance threshold or an adjustment for the number of outcomes and comparisons. The displayed p-values therefore do not account for multiplicity. The statistical plan, including whether other analyses were intended, is not reported in the registry record.

Why does variability matter?

The standard deviation describes the spread of individual values around a group mean. The pain-score standard deviations are 2.0 in the fentanyl group, 3.0 in the labetalol group, and 2.5 in the esmolol group. Greater variability makes it harder to estimate a group mean difference precisely when the sample size is unchanged. The registry reports the means and standard deviations, but not participant-level observations or distributions, so the shape of the outcome within each group cannot be assessed from these summaries alone.

For outcomes expressed as counts, the posted comparisons use risk differences. A risk difference is the difference between the proportions with an outcome in two groups, expressed in the posted estimates as a decimal. A negative estimate means a lower observed proportion in the treatment group than in the fentanyl group; a positive estimate means a higher observed proportion. The interval represents uncertainty in that comparison. The posted count summaries do not replace a protocol-defined model or analysis plan.

What is and is not reported about analysis?

The registry lists randomized allocation and double masking, but detailed procedures for randomization, concealment, and blinding are not reported in the registry record. The record labels the model as factorial but does not give a full description of the factors, interaction terms, or planned analysis. It also does not report the analysis population, missing-data methods, covariate adjustment, or a prespecified statistical analysis plan.

No reported analyses are listed in the registry record. The estimates and p-values associated with the posted summaries can be read as unadjusted comparisons, but they should not be confused with a documented sponsor analysis or a complete reconstruction of the original analysis plan. The registry record does not report whether interim analyses were planned or conducted.

How should planning calculations be understood?

Sample-size calculations can illustrate how many participants might be needed under stated assumptions to detect an effect of a chosen size. Those calculations depend on the assumed effect, variability or event rates, allocation, significance level, and statistical method. They are planning illustrations rather than observations about what the completed study could or could not detect. The trial's original design assumptions and its sample-size justification are not reported in the registry record.

For the posted planning illustrations, the stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set as a stated fraction of the observed effect. The calculations use the observed effect as their starting point, which makes them sensitive to the uncertainty in this small study's estimates. The planning results should not be interpreted as evidence of observed power or as proof about the reliability of the original trial design.

11. Confidence Intervals and Precision

The precision of a treatment comparison is conveyed most directly by its confidence interval. For postoperative pain, the labetalol-versus-fentanyl estimate is -0.2, with a 95% confidence interval from -1.613 to 1.213. The esmolol-versus-fentanyl estimate is 0.7, with a 95% confidence interval from -0.555 to 1.955. Each interval spans zero, so the posted data are compatible with no average difference as well as with differences in either direction.

The interval endpoints also show why the point estimates should not be treated as precise conclusions. The labetalol estimate is close to zero, but its interval extends to both lower and higher scores. The esmolol estimate is positive, while its interval includes negative values as well as positive ones. Neither interval pins down a single direction or a narrow range of possible effects.

In general, confidence intervals reflect both the observed data and the assumptions used to calculate them. They are not guarantees that the true effect lies within a particular interval, and they do not measure the probability that a specific treatment is better. Their width is a practical indication of uncertainty under the analysis method. Here, each group contains 25 participants, while the standard deviations indicate variation in the observed pain scores.

The registry does not report a clinically important difference threshold for the pain scale. Consequently, the posted intervals cannot be categorized by whether they exclude differences considered important by the study team. The registry also does not report adjusted confidence intervals or a multiplicity procedure. The intervals should therefore be read as uncertainty around the unadjusted comparisons, not as definitive bounds for all possible analyses.

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 planning illustrations are estimates of participants per arm for 80% power and participants per arm for 90% power under the stated assumptions. They are not total event counts: the event-count convention applies to time-to-event outcomes, and the posted outcomes in these calculations are not time-to-event measures. The original trial enrolled 25 participants in each group, while the planning figures illustrate larger hypothetical studies under selected effect assumptions.

The stated 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 set to 100%, 75%, or 50% of the observed effect. These are planning scenarios based on the observed estimates, rather than the trial's original design assumptions; the original sample-size justification is not reported in the registry record.

In plain terms, the 80% power column gives the estimated participants per arm for a hypothetical design with an 80% chance of detecting the specified effect under the assumptions if that effect were real. The 90% column uses a higher target chance and generally requires more participants per arm. For each comparison, the scenarios using a smaller fraction of the observed effect require more participants, because smaller differences are harder to distinguish from random variation.

These calculations are not observed power. They do not measure the probability that the completed trial's findings are correct, and they are not evidence that the trial did or did not have an adequate original sample size. Because the observed effects are estimated from a small study, the planning figures can be especially sensitive to how large those estimates happen to be.

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 = -0.200; pooled standard deviation σ = 2.550.
2. n = 2 × (1.96 + 0.842)² × 2.550² / -0.200² = 2,550.9, rounded up to 2,551 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 <- -0.2                      # observed difference in means
sigma <- 2.54950975679639                     # 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(1114971)
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 = 2,551 (80% power), 3,415 (90% power)
 75% of observed effect: n per arm = 4,535 (80% power), 6,071 (90% power)
 50% of observed effect: n per arm = 10,204 (80% power), 13,660 (90% power)
power.t.test: 2551.8 
Simulated power at n = 2,551 per arm: 0.799 (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 outcome and five secondary outcomes, and the posted numerical results include comparisons of each active treatment with fentanyl. This creates multiple opportunities to examine differences across endpoints and treatment contrasts. A multiplicity strategy can specify how to control the increased chance of false-positive findings when multiple statistical tests are conducted. No such strategy is reported in the registry record.

The record does not report whether the primary outcome was tested using a prespecified hierarchy, whether secondary outcomes were intended to be confirmatory, or whether any adjustment to p-values or confidence intervals was planned. The posted p-values are unadjusted. They should not be read as though each were the only statistical test conducted, and isolated secondary findings would be particularly difficult to interpret without a stated analysis hierarchy.

Missing-data handling is not reported in the registry record. The posted arm summaries give 25 participants in each group, but that alone does not establish whether every randomized participant contributed data to every endpoint. The registry does not describe how unavailable pain scores, incomplete follow-up, withdrawals, or other missing outcome information were handled. It also does not report imputation methods, sensitivity analyses, or a missingness assessment.

The analysis population is also not reported in the registry record. It is therefore not possible to determine from the posted information whether results follow an intention-to-treat, per-protocol, or other analysis population. Detailed participant flow, protocol deviations, and exclusions from each endpoint analysis are not reported in the registry record. Those details matter because excluding participants or handling missing outcomes differently can affect estimates and uncertainty.

The record does not report a statistical analysis plan, model specifications, covariate adjustments, or interim analyses. Although the study is labeled factorial, the planned handling of factors and potential interactions is not described. Without these details, the unadjusted contrasts are interpretable as descriptive comparisons of the posted group summaries, but they do not establish how the original investigators intended to address multiplicity, missing data, or the analysis population.

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.

The registry reports zero serious adverse events in each posted group, with 25 participants at risk in the fentanyl group, 25 in the labetalol group, and 25 in the esmolol group. It also reports zero deaths in each group. The serious adverse event term list is empty. These are the counts recorded in the registry; they do not establish that no adverse events could occur or that the treatments have identical safety profiles.

The registry also records zero other adverse events in each group. As with the serious-event figures, a zero count in a group of this size provides limited information about uncommon events or risks that may not be captured in the posted record. The registry record does not provide a detailed adverse-event description, event timing, severity breakdown, or causal assessment.

Safety counts should be interpreted alongside the number of participants at risk and the way events were collected. The posted figures describe the recorded events among the listed groups; they do not establish comparative safety beyond these observations. No medical conclusion or treatment recommendation follows from these counts alone.

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

The posted primary summaries show mean postoperative pain scores of 3.2 for fentanyl, 3.0 for labetalol, and 3.9 for esmolol on the stated 0-to-10 verbal rating scale. The unadjusted contrasts are -0.2 for labetalol versus fentanyl and 0.7 for esmolol versus fentanyl. Both confidence intervals include zero and extend to values on either side of it. The data therefore do not precisely establish the direction or size of the group differences.

That uncertainty does not mean the treatments are equivalent, nor does it establish that there is no difference. Equivalence requires a prespecified margin and an analysis designed to assess whether the confidence interval excludes differences beyond that margin. A margin is not reported in the registry record. Similarly, a nonsignificant unadjusted p-value is not proof of no effect.

The findings also do not establish that one treatment works or does not work. This record reports group-level outcome summaries and unadjusted comparisons, not a complete causal analysis with all protocol and analysis details. Randomization and masking are recorded, but implementation details, analysis populations, missing-data methods, and the original analysis plan are not reported in the registry record.

Secondary outcomes offer limited additional context because results are posted for only three of the five listed secondary outcomes, and their comparisons are unadjusted. The record does not state how the multiple endpoints were handled or whether secondary results were confirmatory. The overall interpretation should therefore center on the uncertainty in the primary outcome and treat secondary patterns as descriptive.

The result applies to the participants and outcomes represented in the registry record. It is not a complete description of every aspect of recovery, pain over time, or safety. The registry's posted summaries do not show participant-level distributions or the full protocol. They also do not provide a stated threshold for a clinically important difference. These limits constrain the conclusions that can be drawn from the numerical estimates.

17. Why This Trial Matters Statistically

This study is statistically instructive because it places modest group differences alongside substantial uncertainty. The primary mean differences are close to zero for labetalol and positive for esmolol, but the confidence intervals span zero and extend in both directions. Looking at estimates, intervals, and group variability together gives a more complete picture than relying on the point estimates or p-values alone.

The study also illustrates the difference between a lack of clear evidence for a difference and evidence of equivalence. The posted comparisons are not precise enough to rule out differences in either direction, and the registry does not report a prespecified equivalence margin. A nonsignificant test cannot answer an equivalence question by itself.

Multiple outcomes add another important statistical issue. The registry lists several aspects of postoperative recovery, but it does not report a multiplicity plan or designate a hierarchy among the secondary outcomes. Unadjusted results across multiple measures can be useful for description, but they should not be treated as a collection of independent confirmatory findings.

Finally, the planning illustrations make clear how sample-size requirements depend on the effect size being targeted. Smaller effects need more participants under the stated assumptions. Because these illustrations are based on the observed effects, they demonstrate planning sensitivity rather than the original trial's design rationale. The original sample-size justification and statistical plan are not reported in the registry record, so those planning calculations should remain distinct from the design of the completed study.

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 follow from the registry record. Each posted group contains 25 participants, and the primary comparisons have broad confidence intervals. The estimates are consequently uncertain, and the results do not establish a narrow range for the possible differences in postoperative pain.

The registry describes a factorial model but does not specify its factors, planned contrasts, or interaction analysis. Three separate arms are listed, but the record does not explain how the factorial label relates to those arms. It is not possible to infer a more detailed design or analysis from that label alone.

The registry does not report the original sample-size calculation, the target effect used in planning, or the statistical analysis plan. It also does not report the analysis population, participant flow, missing-data methods, or whether there were interim analyses. These omissions limit assessment of how closely the posted comparisons reflect the trial's original analytic intentions.

Only three of the five listed secondary outcomes have numerical results posted. Satisfaction and low appetite outcomes are not reported in the registry record. The record also does not describe adjustment for multiple comparisons, so the secondary results should be treated cautiously.

The outcomes reflect particular measures and timeframes: pain in the PACU with a one-day timeframe, opioid consumption and return to feeling normal over one month, and nausea and vomiting over one day. These do not constitute a complete account of recovery. The registry does not report the pain-score distribution, a clinical-importance threshold, or detailed safety event descriptions. These limitations constrain interpretation of both the size and practical meaning of the posted results.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Labetalol and Esmolol: Vital Signs and Post Operative Pain Management — NCT01114971.
• Registry record last updated 2020-02-20; status last verified 2020-02.
• Results first posted 2020-02-20.
• 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

NCT01114971 is a completed, randomized, double-blinded, active-controlled Phase 4 study of intraoperative fentanyl, labetalol, and esmolol during laparoscopic surgery. The registry lists 75 participants, with 25 in each group. The primary outcome is postoperative pain measured in the PACU on a 0-to-10 verbal rating scale.

Mean pain scores were 3.2 in the fentanyl group, 3.0 in the labetalol group, and 3.9 in the esmolol group. The unadjusted mean differences versus fentanyl were -0.2 for labetalol and 0.7 for esmolol; both confidence intervals include zero and are broad. The posted data therefore leave uncertainty about the direction and size of the differences.

Numerical results are also posted for opioid consumption, postoperative nausea and vomiting, and return to feeling normal. Satisfaction and low appetite results are not reported in the registry record. The original sample-size justification, analysis plan, missing-data methods, and analysis population are not reported in the registry record.