Intrathecal Hydromorphone for Pain Control After Cesarean Section: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Intrathecal Hydromorphone for Pain Control After Cesarean Section (NCT02096003), a randomized phase 2 study. The primary outcome is Post Operative Fentanyl PCA Consumption.

2. Clinical Question

3. Trial Design

The registry identifies NCT02096003 as a completed phase 2 randomized trial with a parallel-group design and quadruple masking. The sponsor is Icahn School of Medicine at Mount Sinai. The record lists an enrollment of 80. The start date is 2014-05, and primary completion is recorded as 2017-05-05.

The arms compared intrathecal morphine with intrathecal hydromorphone, each combined with 1.5 mg 0.75% bupivicaine for single-shot spinal anesthesia in primary cesarean sections. The morphine regimen is listed as 0.25mg ( 250mcg), and the hydromorphone regimen as 50mcg. The registry’s design fields specify quadruple masking; its study summary describes the planned comparison as double blind. The specific masking procedures and which roles were masked are not reported in the registry record.

The posted primary outcome summaries include 38 participants in the morphine arm and 37 in the hydromorphone arm. These are the arm counts accompanying the reported outcome, not an explanation of how all enrolled participants were handled. Reasons for any difference between enrollment and the outcome counts, participant flow, and the analysis population definition are not reported in the registry record.

The record lists four secondary outcomes: time to initial PCA use, pain score, patient satisfaction score, and a symptom scale for nausea and pruritus. Results for these outcomes are not reported in the registry record. The randomization sequence, allocation concealment, allocation ratio, eligibility details, and protocol deviations are also not reported in the registry record. Although the record says the trial is completed, completion status alone does not supply those design details.

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 Post Operative Fentanyl PCA Consumption, measured over at 24 hours.

The primary endpoint is total fentanyl patient-controlled analgesia consumption in the 24 hours after surgery, measured in µg. The posted summaries describe the mean and standard deviation for each arm. Fentanyl use is a measure of how much rescue analgesia participants used during the specified period, rather than a direct measurement of pain intensity.

In general, analgesic-consumption outcomes can complement pain scores: they describe medication use, while a pain scale describes reported pain at the time or times it is assessed. Consumption may reflect pain, but can also be affected by factors such as how the PCA is used and the study’s care procedures. Those details are not reported in the registry record. The registry lists pain score and time to initial PCA use as secondary outcomes, but their results are not reported in the registry record.

The primary comparison is a difference in arm means. The posted mean was 300.0 µg for intrathecal morphine and 446.0 µg for intrathecal hydromorphone. The reported difference is 146.0 µg, with hydromorphone as the compared arm relative to morphine. This measure addresses a specific postoperative period and outcome; it does not summarize all dimensions of analgesia or side effects.

7. Results Posted in the Registry

• Intrathecal Hydromorphone: mean 446.00 versus 300.00 on control; difference 146.00 (95% CI -51.40 to 343.40), standardized effect d = 0.33; z-test p = 0.147.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a mean difference express?

For a continuous outcome, a mean is the arithmetic average of the observed values in an arm. The registry reports a mean and standard deviation for fentanyl PCA consumption in each arm. A mean difference compares those arm averages on the original measurement scale, so the estimate is expressed in µg. In this comparison, the reported direction is hydromorphone relative to morphine: the estimate is 146.0 µg.

The mean difference answers a question about average consumption, not about every participant’s experience. Individuals may have used amounts above or below their arm’s average. The reported standard deviations, 432.0 µg for morphine and 440.0 µg for hydromorphone, describe variability among observations within each arm. Large variability relative to the mean difference makes the arm averages less precisely estimated. A group mean also does not show the distribution’s shape or whether a small number of large observations influenced the average.

What do the confidence interval and p-value address?

In general, a confidence interval gives a range of estimates that are reasonably compatible with the data and the method’s assumptions. The 95% interval for this comparison is -51.4 to 343.4 µg. It gives a sense of uncertainty around the estimated mean difference; it is not a range containing 95% of individual participants’ outcomes. Its inclusion of zero indicates that no difference is among the values compatible with this interval. The interval also includes positive values, so the data remain compatible with a higher mean in the hydromorphone arm over a broad range.

The unadjusted p-value is 0.147. In general, a p-value measures the extent to which data as or more inconsistent with a null hypothesis would arise under that null and the statistical model. Interpreting it depends on the chosen test and its assumptions. The registry does not report the test, model details, or whether an adjusted analysis was also conducted. The value should therefore be understood as the posted unadjusted p-value, without inferring an unreported analysis plan.

Why does variability matter?

In general, a standard deviation describes how dispersed individual observations are around the mean. When outcomes are highly variable, an estimated difference between group means can be imprecise unless the study has enough information to distinguish a real average difference from sampling variation. Here, the standard deviations are large, and the confidence interval is broad. That combination is consistent with limited precision for the mean-difference estimate.

General statistical methods also consider whether a continuous outcome is adequately represented by a mean-based analysis. Skewed data or influential extreme observations can affect means and standard deviations. Over-dispersion, in general, means that the observed variability exceeds what a model assumes; ignoring it can make uncertainty estimates unreliable. The registry does not report the outcome distribution, diagnostic checks, transformations, robust methods, or other modeling details. It is therefore not possible to tell from the registry record how these issues were assessed.

What is and is not documented about the analysis?

The registry identifies the primary measure as a mean with standard deviation and specifies the endpoint and timeframe. It also posts arm-level counts, means, standard deviations, a mean difference, confidence limits, and an unadjusted p-value. The statistical test, model specification, confidence-interval method, missing-data method, and analysis-population definition are not reported in the registry record. The reported values can be interpreted as posted, but their precise derivation cannot be reconstructed from the record alone.

There are four listed secondary outcomes: time to initial PCA use, pain score, patient satisfaction score, and symptoms of nausea and pruritus. Their results are not reported in the registry record. The record does not say whether testing of multiple outcomes was planned or adjusted for. In general, testing several outcomes can increase the chance of at least one apparently notable result if no multiplicity strategy is used. That general concern cannot be resolved for this trial from the registry record.

How should planning illustrations be distinguished from trial findings?

Planning calculations use assumptions to explore how many participants might be needed to detect an effect of a chosen size. The registry’s planning illustration uses the observed effect as its reference and evaluates smaller fractions of it. These figures are not part of the observed trial result and do not tell how much power the completed trial actually had. They are conditional illustrations, not a substitute for the trial’s original design documentation. The original sample-size rationale and assumptions are not reported in the registry record.

10. Confidence Intervals and Precision

Precision concerns how tightly the data estimate the mean difference. The posted estimate is 146.0 µg, and its 95% confidence interval extends from -51.4 to 343.4 µg. This is a wide range of compatible values: it includes a modest negative difference, no difference, and positive differences that are substantially larger than the point estimate. The interval therefore does not pinpoint the size or direction of the underlying mean difference.

In general, a confidence interval reflects both the observed data and the method used to quantify sampling uncertainty. It does not show the spread of individual fentanyl-consumption values; the standard deviations describe that within-arm variation. Nor does the interval guarantee that the true effect lies inside it. Its interpretation relies on the analysis method’s assumptions, and the specific method is not reported in the registry record.

The posted p-value is 0.147, but a p-value and confidence interval answer related, not identical, questions. The interval is particularly useful for seeing the range of effect sizes compatible with the estimate. Its inclusion of zero does not establish that the treatments are equivalent, and the positive estimates within it do not establish a precise increase. A conclusion of equivalence would require a prespecified margin and suitable analysis, neither of which is reported in the registry record.

Arm-level standard deviations are 432.0 µg and 440.0 µg, alongside outcome counts of 38 and 37. These describe substantial variability in relation to the reported mean difference. The registry record does not report whether missing observations, distributional features, or other factors were addressed in constructing the interval. The main precision message is therefore that the estimate is uncertain, with a range that permits materially different interpretations of the average contrast.

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 planning figures are expressed as participants per arm, not as total events. The calculation 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 a stated fraction of the observed effect. These are planning assumptions for an illustration based on the observed effect; the trial’s own original design assumptions are not reported in the registry record.

For planning for 100% of the observed effect, the illustration gives 140 participants per arm for 80% power and 188 participants per arm for 90% power. For planning for 75% of the observed effect, it gives 249 participants per arm for 80% power and 334 participants per arm for 90% power. For planning for 50% of the observed effect, it gives 560 participants per arm for 80% power and 750 participants per arm for 90% power.

In general, power is the probability that a study will detect an effect of a specified size under the assumptions used in the calculation. The 80% and 90% columns indicate different target probabilities for detecting the chosen effect, if the assumptions hold. Higher target power requires more participants for a given assumed effect. Likewise, smaller effects are harder to distinguish from random variation and therefore require more participants: the illustration’s smaller fractions correspond to larger planned group sizes.

These numbers are not observed power for the completed trial. They are conditional planning illustrations tied to the observed effect estimate, which itself is uncertain. They should not be read as proof that the trial could or could not detect any particular true effect, and they are not evidence about the trial’s original planning process.

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, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 146.000; pooled standard deviation σ = 435.964.
2. n = 2 × (1.96 + 0.842)² × 435.964² / 146.000² = 140.0, rounded up to 140 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 <- 146                      # observed difference in means
sigma <- 435.963552579894                     # 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(2096003)
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 = 140 (80% power), 188 (90% power)
 75% of observed effect: n per arm = 249 (80% power), 334 (90% power)
 50% of observed effect: n per arm = 560 (80% power), 750 (90% power)
power.t.test: 140.9 
Simulated power at n = 140 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.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary endpoint, total fentanyl PCA consumption at 24 hours, and four secondary outcomes: time to initial PCA use, pain score, patient satisfaction score, and a symptom scale for nausea and pruritus. The primary comparison has a posted unadjusted p-value of 0.147. Results for the secondary outcomes are not reported in the registry record.

Multiplicity is the issue that arises when several hypotheses or outcomes are examined. In general, the more statistical tests conducted, the greater the opportunity for a result to appear notable by chance if all tests are treated as independent confirmatory tests. A prespecified testing hierarchy or adjustment can address this, but the record does not report whether either was planned or used. The unadjusted p-value should not be interpreted as accounting for the listed secondary outcomes.

The registry record does not report the statistical analysis plan, whether analyses were prespecified in a protocol, or whether interim analyses took place. It also does not describe an adjustment for multiple endpoints or subgroup analyses. These details should be regarded as unavailable rather than assumed to have been absent or performed.

Missing-data handling and analysis populations are also not reported in the registry record. The primary outcome summaries list 38 participants for morphine and 37 for hydromorphone, while the registry reports enrollment of 80. The record does not explain the relationship between enrollment and these outcome counts, identify any excluded or missing observations, or state whether the analysis was intention-to-treat, per-protocol, or another population. Without that information, the consequences of missing data or post-randomization exclusions cannot be assessed.

The trial is described as randomized, but the randomization procedure, allocation concealment, and handling of protocol deviations are not reported. These omissions limit assessment of the full analysis process. They do not alter the arithmetic meaning of the posted estimate, but they constrain how confidently it can be interpreted as an unbiased comparison under the intended trial design.

14. 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 registry’s serious adverse-event figures list zero affected participants in each arm, with 40 at risk in each arm. It also records zero deaths in both arms. These are the posted serious-event counts; they do not mean that no non-serious adverse events occurred.

For the category labeled as other adverse events, the record lists 36 affected participants among 40 at risk in the morphine arm and 35 affected participants among 40 at risk in the hydromorphone arm. These counts should be read as registry-reported affected participants in that category, not as counts of individual event episodes. The registry does not provide the event terms or severity breakdown for those other events in the information recorded.

In general, a zero count of serious events is not proof that an event is impossible or that two regimens have identical safety profiles. The ability to characterize uncommon harms depends on the amount and duration of observation, among other factors. Follow-up duration for adverse events, definitions used, and detailed event narratives are not reported in the registry record. Safety counts are descriptive and should be considered alongside the trial’s limited scope and the absence of detailed secondary-outcome results.

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

The posted result describes a difference in average fentanyl PCA consumption during the 24 hours after surgery. The morphine-arm mean was 300.0 µg, and the hydromorphone-arm mean was 446.0 µg. The estimated hydromorphone-minus-morphine difference was 146.0 µg. This is a numerical contrast in the observed arm means, not a complete account of postoperative pain or treatment experience.

The confidence interval, -51.4 to 343.4 µg, shows that the data leave considerable uncertainty about the underlying average difference. Because the interval includes zero and a range of positive and negative values, the posted result does not establish a precise difference. The unadjusted p-value is 0.147. Neither the p-value nor the point estimate demonstrates equivalence, non-inferiority, or a clinically important difference. The registry does not report a threshold for clinical importance or a prespecified equivalence margin.

The result also does not answer every question posed in the trial description. The study was intended to compare analgesia and side effects, but the primary endpoint is fentanyl consumption, and the listed secondary outcomes do not have posted results in the registry record. Consequently, this primary result cannot establish how the arms compared on time to first PCA use, pain scores, satisfaction, nausea, or pruritus.

Likewise, the adverse-event figures should be read narrowly. Serious adverse events and deaths are recorded as zero in both arms, while other adverse events affected 36 participants in the morphine arm and 35 in the hydromorphone arm. Without event details and fuller follow-up information, these counts cannot characterize the nature, timing, or severity of the reported other events.

Overall, the registry supports a cautious description of the observed primary endpoint and its uncertainty. It does not support a broad claim about which regimen is preferable, nor does it resolve differences in safety or other patient-reported outcomes. The design is specific to the stated cesarean setting and regimens, and important analysis and participant details are not reported in the registry record.

16. Why This Trial Matters Statistically

This trial is statistically informative because its primary endpoint is a continuous measure with a direct, interpretable scale: the amount of fentanyl PCA used during a defined postoperative period. A mean difference expressed in µg can be related to the observed arm means without converting the result into an abstract standardized score. The comparison also illustrates why an estimate should be read together with its uncertainty.

The arm means differ numerically, but the 95% confidence interval spans -51.4 to 343.4 µg. That interval makes clear that the point estimate alone gives an incomplete picture. The trial’s result is not a precise estimate of a single effect size, and a non-significant-looking or small-sample p-value interpretation cannot replace consideration of the full interval and the clinical meaning of the endpoint.

Variation is central to this example. The arm standard deviations are 432.0 µg and 440.0 µg, while the posted mean difference is 146.0 µg. In general, variability affects how precisely group averages can be compared. Planning for a smaller effect consequently requires more participants in the registry’s illustration, emphasizing that studies designed around large effects may not provide precise estimates of more modest differences.

The record also highlights the value of complete reporting. The trial lists secondary questions about analgesia and side effects, but does not report their results. Missing analysis details, including the analysis population, missing-data approach, and multiplicity strategy, further limit statistical interpretation. Such information matters because readers need to know which outcomes were evaluated, how uncertainty was estimated, and whether the presented analyses reflect the intended plan.

For researchers, the key lesson is not a treatment recommendation. It is the importance of aligning the endpoint, estimand, sample-size planning, analysis plan, and reporting. A clear mean difference is useful, but precision and transparency determine how much can be concluded from it.

17. 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 constrain interpretation. The primary endpoint captures total fentanyl PCA consumption at 24 hours, rather than pain intensity across time or the full postoperative analgesic experience. Although pain score, time to initial PCA use, satisfaction, and nausea and pruritus are listed as secondary outcomes, their results are not reported in the registry record.

The outcome counts accompanying the primary summaries are 38 for morphine and 37 for hydromorphone, while enrollment is listed as 80. Reasons for this relationship, participant flow, missing observations, and any exclusions are not reported in the registry record. The definition of the analysis population and the method for handling missing data are also not reported, so their possible influence on the estimate cannot be evaluated.

The registry gives arm means and standard deviations, but does not report the statistical test, model, distributional assessment, or method used to obtain the confidence interval and p-value. Whether the analysis was adjusted for baseline factors, whether an interim analysis occurred, and whether multiple testing was addressed are not reported in the registry record. The record also does not provide the original sample-size calculation or its assumptions.

Detailed eligibility criteria, participant characteristics, care procedures beyond the listed regimens, adherence, and protocol deviations are not reported in the registry record. The registry specifies quadruple masking, while the study summary uses the term double blind; the operational details are not reported. These limits prevent a detailed assessment of applicability, potential deviations, and analysis robustness. They do not change the posted numerical result but narrow the conclusions that can be drawn from it.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Intrathecal Hydromorphone for Pain Control After Cesarean Section — NCT02096003.
• Registry record last updated 2019-08-20; status last verified 2019-07.
• Results first posted 2019-08-20.
• 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.

21. Record Summary

NCT02096003 is a completed phase 2 randomized parallel-group comparison of intrathecal morphine and intrathecal hydromorphone for postoperative analgesia after cesarean delivery. The registry lists quadruple masking and enrollment of 80. Primary completion is recorded as 2017-05-05.

The primary outcome is fentanyl PCA consumption at 24 hours. The posted means are 300.0 µg for morphine and 446.0 µg for hydromorphone. The hydromorphone-minus-morphine mean difference is 146.0 µg, with a 95% confidence interval from -51.4 to 343.4 µg and an unadjusted p-value of 0.147.

Four secondary outcomes are listed, but their results are not reported in the registry record. Serious adverse events and deaths are recorded as zero in both arms. Other adverse events affected 36 participants in the morphine arm and 35 in the hydromorphone arm. Important details about analysis methods, missing data, and the original sample-size rationale are not reported in the registry record.