Remifentanil and Glycemic Response in Cardiac Surgery: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Remifentanil and Glycemic Response in Cardiac Surgery (NCT02349152), a randomized phase 4 study. The primary outcome is Blood Glucose Values (More Than One ) > 180 mg%.

2. Clinical Question

This is a question about a defined perioperative glucose outcome, not every aspect of glycemic response or variability. The registry also lists secondary outcomes concerning insulin use, glucose measurements, hemodynamic stability, cortisol, and inflammatory mediators. Those outcomes address related but separate questions and should not be substituted for the primary endpoint when interpreting the principal comparison.

3. Trial Design

The registry describes a prospective, randomized, open-label, parallel-group, phase 4 clinical trial. Participants were assigned to an intraoperative remifentanil group or an intermittent fentanyl group. The planned allocation is described as half of the participants in each group. Masking is listed as none, so the registry characterizes the study as open label.

The record lists enrollment as 116 and status as completed. The start date is 2016-01, and primary completion is listed as 2016-12. The posted primary-outcome groups include 54 participants in the remifentanil group and 52 in the fentanyl group. These are the group counts attached to the reported outcome, not a reconciliation of all enrolled participants. Reasons why the outcome counts differ from the enrollment figure are not reported in the registry record.

The comparison was between continuous intravenous remifentanil and intermittent intravenous fentanyl during cardiac surgery with cardiopulmonary bypass. Fentanyl is described as the institution's standard of care. The registry record does not report the treatment doses, the detailed administration schedule, adherence, or any changes to treatment during surgery.

The primary completion date concerns the primary outcome's listed study period; it should not be confused with the date on which results were posted. The record notes that the primary outcome was changed on 06/15/2015, with approval by the University of Pittsburgh IRB on 06/22/2015, before the first patient was enrolled in January 2016. The earlier endpoint and the reason for changing it are not reported in the registry record.

The registry lists 16 outcome measures and 60 analyses, and 15 secondary outcomes are posted. It does not report the trial's original sample-size justification or its detailed analysis plan. The statistical results therefore need to be read as the outcomes and analyses recorded, not as evidence about unreported design choices.

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.

Before assignment: No pre-assignment necessary for enrollment

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.

6. Primary Endpoint

The registry lists the primary outcome as Blood Glucose Values (More Than One ) > 180 mg%, measured over Intraoperative period.

The primary endpoint counts participants who had two or more intraoperative blood glucose levels greater than 180 mg/dl. It is a participant-level binary outcome: each participant either met this threshold-based definition or did not. The registry describes estimating the percentage in each group and using the difference between those percentages as the primary outcome measure.

This definition uses repeated glucose measurements to classify each participant, rather than treating every measurement as an independent observation. It focuses on whether elevated values occurred repeatedly during the intraoperative period. It does not, by itself, describe the exact glucose trajectory, the size of any elevation, or how long values remained above the threshold. Other listed outcomes address mean, peak, and trough intraoperative glucose, postoperative glucose, and insulin use.

A threshold-based endpoint can make a comparison easier to interpret because it expresses the outcome as the proportion of participants meeting a specified criterion. Its meaning nevertheless depends on the threshold, the requirement for repeated elevated values, and the period in which measurements were taken. The registry does not report the glucose measurement schedule, the handling of missing measurements, or further operational details about how the endpoint was assigned.

The posted counts are 17.0 participants in the remifentanil group and 33.0 in the fentanyl group, with group denominators of 54.0 and 52.0, respectively. These are counts, not percentages. The sponsor's analysis reports a risk ratio for the comparison, while the unadjusted recalculation expresses the comparison as a risk difference. Both concern the same endpoint but use different effect scales.

7. Results Posted in the Registry

• Fentanyl Group: 63.5% (33/52) versus 31.5% (17/54) on control; risk difference 32.0 percentage points (95% CI 14.0 to 50.0), risk ratio 2.02 (1.29–3.14); unadjusted two-proportion z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a risk ratio express?

A risk ratio compares the frequency of an event in one group with the frequency in another. A value of 1 represents equal event frequencies on this scale; values on either side of 1 indicate different relative frequencies, with interpretation depending on which group is in the numerator. The sponsor reports a risk ratio of 1.9 and a 95% confidence interval from 1.3 to 3.0. Given the group counts, the ratio is expressed as the event frequency in the fentanyl group relative to the remifentanil group. The estimate is a relative comparison and does not directly state the absolute difference between group proportions.

What does a risk difference express?

A risk difference subtracts one group's event proportion from the other's. It is an absolute-scale comparison, unlike the relative comparison made by a risk ratio. The recalculated risk difference is unadjusted and based on the posted group counts. Its confidence interval excludes zero, the value that corresponds to no difference on this scale. The recalculated result is not the same statistic as the sponsor's reported risk ratio, so the estimates should not be compared as though they were interchangeable.

What does the chi-squared analysis test?

The sponsor identifies a chi-squared method for its reported analysis. In general, a chi-squared test assesses whether observed counts across groups are compatible with a specified null pattern of no association. Here, the endpoint is recorded as a count of participants meeting a binary definition. The reported p-value is 0.001. A p-value summarizes how unusual data at least as discrepant as those observed would be under the null model and the test's assumptions. It does not measure the probability that the null is true or provide a measure of clinical importance.

The registry does not report further details about the sponsor's calculation, including any continuity correction, covariate adjustment, or exact test procedure. Those details should not be inferred from the label “Chi-squared.” The unadjusted recalculation is based on summary counts; it does not add adjustment for participant characteristics or other factors.

How should confidence intervals be read?

A confidence interval describes uncertainty around an estimate under the method used to construct it. In repeated use of a correctly specified procedure, intervals constructed at a stated confidence level would cover the underlying value at that rate. For an individual study, the interval is not a probability statement that the true effect lies within its particular bounds. Its width reflects statistical precision, while its location indicates which effect values are more compatible with the data under the model. The sponsor's 95% interval is reported for the risk ratio. The recalculated interval is reported for the risk difference.

For a risk ratio, the null value is 1; for a risk difference, the null value is zero. Whether an interval includes its null value is one way to assess compatibility with no group difference under that analysis. It does not resolve concerns about study conduct, missingness, outcome measurement, or generalizability.

Why can the effect scale change the interpretation?

Relative and absolute measures emphasize different features of a comparison. A relative measure describes how event frequencies compare proportionally; an absolute measure describes the gap between the group proportions. When event frequencies differ, both can be informative, but each answers a distinct question. The registry's primary outcome description specifies a difference between group percentages, whereas the sponsor's reported analysis presents a risk ratio. The recalculated risk difference aligns with the outcome description's absolute comparison, but it remains an unadjusted calculation from posted counts.

Why does over-dispersion matter in general?

Over-dispersion is a general concern when a statistical model assumes a particular amount of variability but the observed data vary more than that assumption allows. If ignored, uncertainty estimates may be too small and inferential results can be misleading. It is especially relevant to some count or clustered-data models. The primary endpoint is a participant-level binary outcome, and the registry identifies a chi-squared analysis for the sponsor's reported comparison. Over-dispersion is not identified as a feature of this analysis, and the registry record does not report a model-based assessment of it. This general concept should not be mistaken for a claim about an analysis that was not reported.

What is and is not known about the analysis?

The record gives the endpoint definition, group counts, sponsor method, effect estimate, confidence interval, and p-value. It does not report a full statistical analysis plan, the handling of missing endpoint data, the analysis population definition, or any adjustment for multiple analyses. These omissions limit evaluation of whether the posted analysis follows a prespecified plan and how the reported result relates to the full set of outcomes and analyses.

10. Confidence Intervals and Precision

The sponsor reports a risk ratio of 1.9, with a 95% confidence interval from 1.3 to 3.0. The interval is compatible with a range of relative group differences rather than a single exact effect. Its lower and upper bounds are both above the risk-ratio null value of 1. The reported p-value is 0.001. Taken together, these statistics indicate that the sponsor's analysis identifies a group difference on the risk-ratio scale, while the interval also makes clear that the estimate is not exact.

The unadjusted recalculation reports a risk difference with a confidence interval that excludes zero. Zero is the null value for an absolute difference. The interval's exclusion of that value is consistent with the recalculated p-value of <0.001. The numerical bounds and estimate use more than three decimal places in the registry's calculated results, so they are not repeated. The important distinction is that this interval quantifies uncertainty for an absolute difference, whereas the sponsor's interval quantifies uncertainty for a ratio.

Confidence intervals describe statistical precision under the calculation's assumptions; they do not incorporate every source of uncertainty. They do not account for unreported outcome missingness, potential measurement issues, or the effect of decisions made in the analysis. Nor do they establish the importance of the endpoint difference for other outcomes or settings.

The group counts are modest in size, and the precision of a binary-outcome estimate depends on both the number of participants and how many meet the endpoint. The registry does not report a formal precision target or original sample-size rationale. The available intervals should therefore be interpreted as uncertainty around the posted analyses, not as evidence that all relevant uncertainty has been captured.

11. 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 display is a planning illustration based on the observed primary-outcome effect, not the trial's original design calculation. The displayed figures are participants per arm, not total event counts. Its assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The planning scenarios use the stated fraction of the observed effect as the effect to detect. The original sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm that the calculation associates with an 80% chance of detecting the specified effect, if the planning assumptions and effect are correct. The 90% power column gives the corresponding per-arm planning number for a 90% chance. Power is a design probability under an assumed effect and analysis, not a guarantee that a study will detect an effect or that a result will be true.

The rows describe planning for the full observed effect, 75% of the observed effect, and 50% of the observed effect. Smaller effects are harder to distinguish from random variation, so the planning illustration requires more participants per arm for the smaller-effect scenarios. The associated curve visualizes the relationship between the assumed effect fraction and the calculated planning requirement; it does not show outcomes from additional participants or a new trial.

These figures are not observed power. They are not a retrospective measure of whether this completed trial had a high chance of finding its observed result. Because the observed effect itself is uncertain, planning directly from it is illustrative and should not be treated as a definitive sample-size recommendation. The registry record does not report the assumptions used to plan the actual trial.

12. 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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.315; treatment proportion p₁ = 0.635; average p̄ = 0.475.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7062 = 1.3841.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6690 = 0.5631.
4. n = (1.3841 + 0.5631)² / (0.3198)² = 37.1, rounded up to 38 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
p0 <- 0.314814814814815                          # control proportion
p1 <- 0.634615384615385                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(2349152)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 38 (80% power), 50 (90% power)
 75% of observed effect: n per arm = 66 (80% power), 88 (90% power)
 50% of observed effect: n per arm = 146 (80% power), 195 (90% power)
power.prop.test: 37.1 
Simulated power at n = 38 per arm: 0.816 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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.

13. Analyses Reported by the Sponsor

The sponsor's own analysis reports a chi-squared comparison with a risk ratio of 1.9, a 95% confidence interval from 1.3 to 3.0, and p = 0.001. The recalculated analysis uses the posted group counts to produce an unadjusted risk difference and its interval, with an unadjusted p-value of <0.001. These are distinct effect scales: the sponsor's result is relative, while the recalculation is absolute.

The posted risk-ratio estimate and the recalculated risk ratio are not identical. They arise from different reported calculation pathways and may reflect differences in method or rounding. The registry does not provide enough detail to determine the exact reason for that difference. The discrepancy flag is false, so the registry does not identify a discrepancy requiring the sponsor's result to supersede the recalculation. The sponsor's analysis remains the analysis reported by the trial; the recalculation is a separate, simple analysis of the posted summary counts.

Both approaches compare the same primary endpoint and point in the same direction, with fewer participants meeting the endpoint in the remifentanil group than in the fentanyl group. Their numerical estimates should not be mixed or treated as though they were the same statistic. The sponsor's analysis is the appropriate reference for what the trial reported, while the recalculation offers a complementary unadjusted absolute-scale description. Neither provides information absent from the registry record about missing data, adjustment, or the full analysis plan.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 16 outcome measures, 60 analyses, and 15 posted secondary outcomes. It also identifies one primary endpoint: the proportion of participants with two or more intraoperative blood glucose levels greater than 180 mg/dl. With multiple outcomes and analyses, the chance of observing apparently notable results can increase if many comparisons are examined. Statistical approaches to multiplicity can address that issue, but the registry record does not report whether any adjustment was planned or applied. It also does not describe a hierarchy among the secondary outcomes or state which analyses were prespecified.

The primary outcome description notes that the endpoint changed on 06/15/2015 and that the change was approved by the University of Pittsburgh IRB on 06/22/2015. The record says the first patient was enrolled in January 2016. This timing places the recorded change before enrollment, but the earlier endpoint, the reason for the amendment, and whether other outcome or analysis changes occurred are not reported in the registry record.

Missing-data handling is not reported in the registry record. The primary-outcome results give group counts and denominators, but do not explain why the outcome counts may not account for every participant listed as enrolled. The record does not describe missing glucose measurements, exclusions, imputation, or sensitivity analyses. It is therefore not possible to assess from the posted information whether missingness could have affected the comparison.

The analysis population is also not reported in the registry record. The record does not specify whether the analysis followed randomized assignment, included all randomized participants, or used another population definition. Details about adherence and protocol deviations are likewise not reported. These omissions do not prove that the analysis was biased or that data were missing; they identify limits on what can be evaluated from the posted results.

There is no reported interim-analysis plan or stopping rule in the registry record. The original statistical analysis plan, including any prespecified covariate adjustments, is also not reported. As a result, readers can describe the recorded comparison but cannot verify its relation to unreported analysis decisions or to the full set of analyses undertaken.

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 serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: pleural effusion (5.8%), pneumonia (1.9%), pericardial effusion/tamponade (1.9%), stroke (1.9%).

The registry lists serious adverse events for 1 participant in the remifentanil group and 5 participants in the fentanyl group. It lists other adverse events for 28 participants in the remifentanil group and 27 in the fentanyl group. Deaths are listed separately as 3 in the remifentanil group and 6 in the fentanyl group. These are reported event counts; they do not establish that an event was caused by a study drug.

The registry identifies pleural effusion at 5.8% as the most frequent listed serious-event term, followed by pneumonia, pericardial effusion/tamponade, and stroke, each at 1.9%. These terms are presented as top serious-event terms. The record does not state in this listing how the percentages were calculated, whether terms overlap within participants, or how events were judged to be related to treatment.

Adverse-event counts need context, including the observation period, event definitions, severity criteria, and completeness of reporting. Those details are not reported in the registry record. Differences in the listed counts should therefore be read descriptively, not as a causal comparison or a definitive assessment of comparative safety.

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

The posted primary-outcome results show fewer participants meeting the endpoint in the remifentanil group than in the fentanyl group. The endpoint was defined as having two or more intraoperative glucose levels greater than 180 mg/dl. The sponsor's risk-ratio estimate and the unadjusted recalculation both indicate a difference between the groups on their respective effect scales. Their confidence intervals convey statistical uncertainty, and their p-values summarize evidence under the assumptions of their analyses.

This result does not establish the cause of the observed difference. Randomization is a design feature intended to support a fair comparison, but the registry's limited reporting does not allow evaluation of every feature of implementation, missing data, adherence, measurement, or analysis. The study is open label, and further details about glucose measurement and endpoint adjudication are not reported in the registry record.

The endpoint captures whether a participant crossed a repeated-value threshold during the intraoperative period. It does not fully describe the timing or duration of elevated readings, overall glucose variability, postoperative glucose, or insulin use. Those are distinct outcomes listed in the registry and require their own results and interpretation. The primary endpoint should not be taken as a result for every glycemic or perioperative outcome.

The results also do not by themselves show how the finding applies beyond this study's cardiac-surgery setting, or how it relates to outcomes not reported in the registry. The record describes the trial's intervention and comparator, but does not provide detailed participant characteristics or broader evidence from other settings. The statistical comparison is evidence about the posted endpoint in this trial, not a universal conclusion about treatment.

Finally, statistical evidence and clinical importance are different questions. A p-value does not measure the size or importance of an effect, and a confidence interval does not determine whether a difference matters to patients or clinicians. The registry record does not report a threshold for clinical importance for this endpoint. The findings should therefore be described as a statistical comparison of the recorded endpoint, without turning it into medical advice or a claim about treatment benefit.

17. Why This Trial Matters Statistically

This trial illustrates why a precise endpoint definition matters in clinical research. The primary outcome is not simply an average glucose value: it is the proportion of participants with at least two intraoperative readings above a stated threshold. That definition determines who counts as having an event and shapes the interpretation of the group comparison. It also distinguishes the primary endpoint from listed measures such as mean, peak, and trough glucose or insulin requirements.

The result can be expressed on more than one statistical scale. The sponsor reported a risk ratio, while the recalculation uses a risk difference. The relative scale describes how event frequencies compare proportionally; the absolute scale describes the gap between group proportions. Reading both carefully helps prevent a relative estimate from being mistaken for an absolute change, or an absolute difference from being interpreted as a relative one.

The record also highlights the importance of prespecification and transparent reporting. The primary endpoint was changed before enrollment, but the earlier endpoint and rationale are not reported. A large number of outcomes and analyses are listed, while the approach to multiplicity is not reported. Without the analysis plan, missing-data details, and population definition, readers cannot fully assess how the posted primary result fits within the trial's complete analytical process.

Finally, the sample-size illustration demonstrates a general planning principle: smaller effects require more participants to detect under the same assumptions. Because it is based on the observed effect and not the original design rationale, it is a planning aid rather than evidence of the study's achieved power. Together, these issues show why an effect estimate, its interval, and the quality of reporting all matter when interpreting clinical trial statistics.

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 of interpretation follow from details not reported in the registry record. The study is open label, but the record does not explain whether outcome assessment was blinded or how glucose measurements were handled. It also does not give participant characteristics, detailed eligibility criteria, or information about how representative the enrolled participants were of other cardiac-surgery populations.

The primary endpoint depends on repeated measurements during the intraoperative period, yet the measurement schedule, device or laboratory procedures, and handling of missing readings are not reported. The posted counts do not explain the relation between the enrollment figure and the outcome denominators. Without a stated analysis population or missing-data method, the effect of exclusions or unavailable measurements cannot be assessed.

The registry reports that the primary outcome changed before enrollment, with an approval date, but does not describe the prior endpoint or the reason for changing it. It lists many analyses and secondary outcomes, but does not report a complete statistical analysis plan or a multiplicity strategy. That makes it difficult to evaluate prespecification and the risk that reported results were selected from a broader set of analyses.

The sponsor reports a chi-squared analysis, but additional computational details are not reported. The recalculation is unadjusted and uses summary counts; no participant-level covariate adjustment is possible from those counts. The record also does not report adherence, treatment crossover, protocol deviations, or detailed adverse-event observation procedures. These limitations constrain assessment of precision, bias, and generalizability; they do not show that any particular problem occurred.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Remifentanil and Glycemic Response in Cardiac Surgery — NCT02349152.
• Registry record last updated 2020-04-21; status last verified 2020-04.
• Results first posted 2018-05-14.
• 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, open-label, parallel-group phase 4 trial of continuous intraoperative remifentanil versus intermittent fentanyl during cardiac surgery with cardiopulmonary bypass. Enrollment is listed as 116, with a start date of 2016-01 and primary completion in 2016-12.

The primary endpoint was the proportion of participants with two or more intraoperative blood glucose levels greater than 180 mg/dl. Posted counts meeting the endpoint were 17.0 in the remifentanil group and 33.0 in the fentanyl group. The sponsor reported a risk ratio of 1.9, a 95% confidence interval from 1.3 to 3.0, and p = 0.001. An unadjusted recalculation reports an absolute risk difference with a confidence interval excluding zero.

The record lists multiple secondary outcomes and analyses. Details about the original sample-size rationale, missing-data handling, analysis populations, multiplicity, and the complete statistical plan are not reported in the registry record. Results should be understood as the posted comparison for the defined endpoint, with those reporting limits in view.