Comparison of Side Effects of Morphine and Hydromorphone Patient-Controlled Analgesia (PCA): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Comparison of Side Effects of Morphine and Hydromorphone Patient-Controlled Analgesia (PCA) (NCT00385541), a randomized phase 4 study. The primary outcome is Nausea Assessment by Patient.

2. Clinical Question

3. Trial Design

This completed Phase 4 study used randomized allocation, quadruple masking, and a parallel-group design. The registry records enrollment of 50 and lists Columbia University as the sponsor. The study dates are recorded as starting in 2003-11, with primary completion in 2007-10. Further details about recruitment sites, eligibility criteria, randomization procedures, or how masking was implemented are not reported in the registry record.

The comparison was between morphine PCA and hydromorphone PCA for postsurgical pain. The registry gives the dose per PCA dose, maximum hourly dose, and lockout interval for each regimen. These treatment details describe the arms; they do not establish how often participants used the PCA or how much medication they received in practice.

The primary outcome was patient-assessed nausea, recorded as a mean score with standard deviation. The outcome description calls the scale ordinal and gives its range as 0 to 10. The record lists assessment times of 1 hour after surgery and 8 hours after surgery. It does not specify the analysis method used to handle repeated assessments or how the reported summary relates to the two listed time points.

The primary outcome population is identified as intention to treat. The registry also lists four secondary outcomes: pruritus score, patient pain assessment, number of patients who vomited, and sedation score. Results are posted for the first three of these; a posted result for the sedation outcome is not included. The record lists no reported analyses. Details of the original statistical analysis plan, sample-size justification, missing-data procedures, and any interim analyses are not reported in the registry record.

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: Double blind randomized controlled trial. Patients under 18, with chronic pain or on pain medication before surgery were excluded.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Intention to treat (ITT)

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 Nausea Assessment by Patient, measured over 1 hour after surgery, 8 hours after surgery.

The primary endpoint is patient-assessed nausea on a scale from 0, meaning none, to 10, meaning the worst. The registry describes the outcome as ordinal but reports a mean and standard deviation for each group. A mean gives a group-level summary of scores, while the standard deviation describes how spread out the individual scores are around that mean. The score is measured in units on a scale.

Nausea is relevant to the stated comparison because the study was designed to assess side effects associated with the two PCA regimens. The registry lists assessments at 1 hour after surgery and 8 hours after surgery. It does not report whether the primary result reflects one time point, an average across time points, or a different summary. That missing detail limits how specifically the estimated difference can be tied to the timing of the assessments.

The posted group means are 4.6 for morphine PCA and 3.0 for hydromorphone PCA. The reported mean difference for hydromorphone compared with morphine is -1.6. This is a difference in group averages, not a description of every participant’s experience or of how many participants had nausea. The estimate and its confidence interval should therefore be read together: the mean difference gives the direction and size of the observed contrast, while the interval conveys uncertainty around that contrast.

7. Results Posted in the Registry

• Hydromorphone PCA: mean 3.00 versus 4.60 on control; difference -1.60 (95% CI -3.19 to -0.01), standardized effect d = -0.56; z-test p = 0.049.

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.

Mean Score on the Numeric Rating Scare (NRS) Pruritus Scale

• 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:
  • Hydromorphone PCA: mean 2.50 versus 2.00 on control; difference 0.50 (95% CI -0.01 to 1.01), standardized effect d = 0.54; z-test p = 0.054.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Hydromorphone PCA and the control. The interval gives the range of effects that remain compatible with the data.

Pain Assessment by Patient

• 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:
  • Hydromorphone PCA: mean 7.10 versus 7.90 on control; difference -0.80 (95% CI -2.10 to 0.50), standardized effect d = -0.34; z-test p = 0.229.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Hydromorphone PCA and the control. The interval gives the range of effects that remain compatible with the data.

The Number of Patients Who Vomited

• 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:
  • Hydromorphone PCA: 0.0% (0/25) versus 4.0% (1/25) on control; risk difference -4.0 percentage points (95% CI -11.7 to 3.7); unadjusted two-proportion z-test p = 0.312.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Hydromorphone PCA and the control. The interval gives the range of effects that remain compatible with the data.

The posted secondary outcomes cover pruritus, patient-assessed pain, vomiting, and sedation. Results are included for pruritus, pain, and vomiting, but a result for sedation is not reported. Across the posted comparisons, the directions are not uniform: some point toward lower scores or fewer events with hydromorphone, while the pruritus estimate points in the other direction. The secondary intervals include zero, so the estimates remain compatible with no difference as well as with effects in either direction.

The primary nausea estimate points toward a lower mean score in the hydromorphone group, but it should not be treated as a summary of all side effects or of pain. Each outcome measures a different experience and has its own scale and uncertainty. The secondary results therefore provide context rather than a direct confirmation of the primary comparison.

The posted secondary comparisons are unadjusted. When several outcomes are examined, the chance of seeing at least one apparently notable result by chance can increase. Without a reported multiplicity plan, the secondary p-values should be interpreted cautiously and should not be treated as independent confirmatory tests. The registry also does not report a broader analysis plan explaining whether these outcomes were prespecified, how they were prioritized, or how missing observations were handled.

The combination of differing directions, uncertainty intervals that include zero, and absent multiplicity details means the secondary findings do not establish a consistent pattern across outcomes. They can identify questions for further study, but they carry less evidential weight than a result supported by a clearly reported analysis plan and appropriately accounted-for outcome testing.

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

• Mean Score on the Numeric Rating Scare (NRS) Pruritus Scale
• Pain Assessment by Patient
• The Number of Patients Who Vomited
• Mean Score on the Ramsey Scale of Sedation

9. Statistical Interpretation

10. Statistical Methods Explained

What does the mean difference represent?

The primary comparison is reported as a mean difference between hydromorphone PCA and morphine PCA. The sign is determined by the order of that comparison: a negative estimate means the hydromorphone group’s reported mean score is lower. Here, the means are 3.0 and 4.6, respectively, and the posted difference is -1.6. This estimate is a contrast between group averages. It does not say that every participant’s score changed by that amount, or that the same difference occurred at each listed assessment time.

The registry reports standard deviations of 2.5 for hydromorphone and 3.2 for morphine. Standard deviations describe variability among scores within each group, rather than uncertainty in the mean difference itself. The uncertainty in a comparison is represented by its confidence interval. A mean-and-standard-deviation summary is familiar for continuous outcomes, but the nausea scale is explicitly described as ordinal. A mean-based analysis can be useful as a summary, while still obscuring the distribution and ordering details of individual scores.

How should a confidence interval be read?

A confidence interval gives a range of values that are compatible with the observed estimate under the assumptions of the statistical procedure used to construct it. In general, a narrower interval indicates greater precision, while a wider interval indicates more uncertainty. The primary interval runs from -3.192 to -0.008. It lies just below zero at its upper end, so it includes estimates that are close to no difference as well as estimates reflecting a larger lower mean in the hydromorphone group.

The interval is not a range containing a fixed proportion of individual participants’ nausea scores. It concerns the estimated group difference. The registry does not report the method used to construct the interval, so details such as its exact distributional assumptions are not reported in the registry record.

What does the p-value add?

The primary unadjusted p-value is 0.049. In general, a p-value describes how unusual data at least as incompatible with a specified null hypothesis would be if that hypothesis and the analysis assumptions were true. It is not the probability that the null hypothesis is true, and it does not measure clinical importance. The unadjusted label matters because the record does not report adjustment for testing multiple outcomes or time points. The registry lists no reported analyses, so a fuller account of the inferential procedure is not reported in the registry record.

The p-value and confidence interval address related but different aspects of the comparison. The p-value summarizes evidence relative to a null value under an analysis, while the interval displays a range of plausible values for the effect under the interval procedure. Because the interval’s upper end is close to zero and the p-value is close to 0.05, the result warrants careful interpretation rather than a categorical conclusion.

Why can variation affect precision?

In general, greater variability in scores makes it harder to estimate a group mean or difference precisely, particularly when the amount of information is limited. The reported standard deviations show that scores varied within both groups. The registry does not provide participant-level data, so the shape of each score distribution, the frequency of individual scale values, and possible skewness cannot be assessed from these summaries.

For outcomes measured as counts or event indicators, the statistical scale differs from that of a mean score. The vomiting outcome is reported as the number of patients who vomited, and its comparison is given as a risk difference. A risk difference contrasts the proportions experiencing the event in the two groups. This is distinct from the mean difference used for nausea, pruritus, and pain. The posted methods for the binary outcome are not reported in the registry record.

What does over-dispersion mean in general?

For count outcomes, over-dispersion means that observed variability is greater than a model expects under its assumptions. It can make standard errors too small if a model does not accommodate that extra variability. This is a general statistical consideration, not a reported feature or analysis of this trial. The record does not provide a count-model analysis or enough detail to determine whether over-dispersion was assessed.

More broadly, the statistical analysis plan, model specifications, handling of repeated measurements, missing-data methods, and any adjustment for multiple comparisons are not reported in the registry record. Those details are important for evaluating how closely the posted summaries and comparisons follow the intended analysis.

11. Confidence Intervals and Precision

The primary mean difference is -1.6, with a 95% confidence interval from -3.192 to -0.008. The interval is informative because it shows that the estimate is not highly precise around a single value: values ranging from a difference near zero to a more substantial negative difference remain compatible with the result under the interval procedure. The upper limit is close to zero, so the distinction between a very small difference and no difference is not sharply resolved by the posted estimate.

For context, the group means are 4.6 for morphine PCA and 3.0 for hydromorphone PCA, with standard deviations of 3.2 and 2.5. These standard deviations describe variation in scores, whereas the confidence interval describes uncertainty in the between-group estimate. The summaries do not reveal the full distribution of scores or how the estimates differ between the two listed assessment times.

Confidence intervals for the secondary comparisons also convey uncertainty. The intervals for the posted secondary comparisons include zero, so those data do not sharply distinguish a difference from no difference under the reported comparisons. The registry does not report adjusted confidence intervals or a multiplicity plan. As a result, interval interpretation should account for the fact that several outcomes are listed and that the posted comparisons are unadjusted.

In general, a confidence interval is not a guarantee that the true effect lies within its endpoints, and it does not express the range of individual responses. It quantifies uncertainty about an estimated group contrast under the method used. The record does not identify that interval method, and the limited summary information means precision should be considered alongside the missing analysis details.

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 planning figures are participants per arm, not a total across both arms. The registry’s 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 as the stated fraction of the observed effect. The registry’s original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column describes the planned number of participants per arm under which a study would have an 80% chance of detecting the chosen effect, given the stated assumptions. The 90% power column describes the corresponding planning target for a 90% chance. These are conditional planning calculations, not guarantees: actual results depend on the true effect, variability, and whether the assumptions hold.

Rows planning for 100% of the observed effect use the full observed estimate as the target effect. Rows planning for 75% or 50% of the observed effect use smaller targets. Smaller effects are harder to distinguish from random variation, so the planning calculations require more participants per arm as the target effect gets smaller. This pattern is a general feature of power planning, not a result about what the trial actually achieved.

These figures are planning illustrations based on the observed effect and the stated assumptions; they are not observed power. They do not show that the completed study had a particular probability of finding an effect after its results were known. The actual trial enrollment was 50, with 25 participants reported in each arm, but the registry does not report that its original design used the displayed planning assumptions or targets.

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 = -1.600; pooled standard deviation σ = 2.871.
2. n = 2 × (1.96 + 0.842)² × 2.871² / -1.600² = 50.6, rounded up to 51 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 <- -1.6                      # observed difference in means
sigma <- 2.87141080307225                     # 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(385541)
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 = 51 (80% power), 68 (90% power)
 75% of observed effect: n per arm = 90 (80% power), 121 (90% power)
 50% of observed effect: n per arm = 203 (80% power), 271 (90% power)
power.t.test: 51.5 
Simulated power at n = 51 per arm: 0.797 (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 a primary nausea outcome and several secondary outcomes, with assessments recorded at 1 hour after surgery and 8 hours after surgery. Testing several outcomes or time points creates a multiplicity issue: even when there is no underlying effect, repeated testing can increase the chance of at least one result appearing noteworthy. The record does not report a plan for controlling this issue, such as a prespecified hierarchy, adjustment method, or designation of selected results as exploratory.

The primary comparison is labeled with an unadjusted p-value. That label is important because the reported value does not communicate whether multiplicity was accounted for. The secondary comparisons are also presented without reported adjustment. The record lists no reported analyses, and the statistical analysis plan is not reported in the registry record. It is therefore not possible to determine whether the posted comparisons match a prespecified analysis or how the investigators intended to interpret multiple outcomes.

The primary outcome population is identified as intention to treat. This identifies the stated analysis population, but the registry does not describe how participants with missing outcome measurements were handled or whether all randomized participants contributed to each time point. Missing-data procedures, exclusions after randomization, and the number of observations available for each assessment are not reported in the registry record.

The record also does not explain how repeated nausea measurements were analyzed, or whether the posted mean represents one assessment or a combined summary. These omissions affect interpretation of both the point estimate and its uncertainty. In general, transparent reporting of multiplicity, missing data, and analysis populations helps readers distinguish planned confirmatory comparisons from exploratory ones and assess whether the estimates may be affected by incomplete observations.

15. Safety Results

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

Other (non-serious) adverse events

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

The registry records 0 serious adverse events in the morphine PCA group and 0 in the hydromorphone PCA group. For other adverse events, it also records 0 in each group. The number at risk is reported as 25 for each group. These entries describe the posted adverse-event counts; they do not establish that no adverse events occurred beyond the categories or reporting period represented in the record.

Deaths are not populated in the adverse-event fields, so death counts are not reported in the registry record. The record does not provide event descriptions, severity definitions, attribution procedures, or further detail about how adverse events were collected. Zero recorded events should therefore be read as the registry’s posted count, not as proof that a treatment has no safety risks.

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

The primary result describes a difference in average patient-reported nausea scores between the two randomized PCA groups. The posted mean was 4.6 with morphine and 3.0 with hydromorphone, and the reported mean difference was -1.6. The confidence interval extends from -3.192 to -0.008, while the unadjusted p-value is 0.049. Together, these results show an estimated difference favoring a lower average nausea score in the hydromorphone group, but with uncertainty that includes values very close to no difference.

This estimate does not show that all participants in one group experienced less nausea, nor does it describe each individual’s score. Group means can conceal variation and differences in the distribution of responses. The registry describes the scale as ordinal, and it does not report the full score distribution. It also lists two assessment times without explaining how they contribute to the reported primary estimate.

The result does not establish clinical importance. The registry does not report a threshold for what patients or clinicians would consider a meaningful change on this scale. The p-value is not a measure of treatment benefit, and a result near a conventional threshold is not a substitute for evaluating the estimate, its uncertainty, and the trial’s analysis limitations.

Nor does the primary outcome settle the comparison across all outcomes. The secondary estimates vary in direction and have intervals that include zero. The record does not report a multiplicity plan, detailed missing-data methods, or the original analysis plan. The safety entries record no serious or other adverse events in either group, but the registry does not provide enough detail to infer absence of risk.

These findings apply to the trial’s recorded groups, regimens, and outcome reporting. The registry does not give enough information to establish how the results generalize to other populations or settings. The appropriate interpretation is a posted, uncertain group-level comparison, not a universal claim about the medicines or their effects.

17. Why This Trial Matters Statistically

This trial is statistically instructive because a point estimate, confidence interval, and p-value tell related but distinct parts of the story. The estimated mean difference is -1.6, and the interval reaches from a value close to zero to a more negative value. The unadjusted p-value is 0.049. Reading only the p-value can make a borderline result seem more decisive than the interval and analysis context support.

The outcome also illustrates the importance of matching summaries to measurement scales. Nausea is described on an ordinal scale, yet the registry reports means and standard deviations. Those summaries are compact and familiar, but they do not show how responses were distributed across the scale. Reporting scale distributions or a clear analysis rationale would help readers understand what the mean comparison captures.

The listing of multiple outcomes and assessment times makes analysis transparency especially important. Without a reported multiplicity plan, missing-data procedures, or analysis plan, readers cannot fully evaluate how the primary and secondary findings were selected and interpreted. This is not a claim that the analysis was inappropriate; it identifies information that is needed to assess the evidence.

Finally, the record distinguishes observed estimates from planning illustrations. The planning calculations are based on the observed effect and stated assumptions, while the trial’s original design assumptions are not reported. Keeping those roles separate prevents planning numbers from being mistaken for evidence about the trial’s achieved power or design rationale.

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.

The registry provides limited detail about the primary outcome’s timing and analysis. It lists assessments at 1 hour after surgery and 8 hours after surgery, but does not explain whether the reported mean is based on one time point or combines measurements. It also does not report how repeated observations were modeled. This makes it harder to connect the estimated difference to a specific postoperative time.

The nausea scale is described as ordinal, while results are summarized with means and standard deviations. The record does not include the score distributions, so readers cannot assess concentration at particular values, skewness, or the prevalence of high scores. The reported group summaries are not a substitute for those details.

Although the primary population is identified as intention to treat, missing-data handling and the number of available observations at each assessment are not reported in the registry record. The record also lacks a reported statistical analysis plan, multiplicity strategy, and original sample-size justification. These omissions limit assessment of whether the posted comparisons were prespecified and how robust they are to analysis choices.

The study enrolled 50, with 25 participants reported in each arm. The resulting estimates may be imprecise, as reflected in the primary confidence interval. The planning illustrations do not resolve this limitation because they use the observed effect rather than documenting the original design. Further limitations include the absence of a posted sedation result and limited adverse-event detail. The registry does not report additional information that would clarify generalizability, recruitment settings, or participant characteristics.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Comparison of Side Effects of Morphine and Hydromorphone Patient-Controlled Analgesia (PCA) — NCT00385541.
• Registry record last updated 2018-08-14; status last verified 2018-07.
• Results first posted 2010-08-31.
• 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 records a completed, randomized, quadruple-masked, parallel-group Phase 4 comparison of morphine PCA and hydromorphone PCA for postsurgical pain. Enrollment is 50, and the primary outcome is patient-assessed nausea on a 0-to-10 scale, with assessments listed at 1 hour and 8 hours after surgery.

The posted mean nausea scores are 4.6 for morphine and 3.0 for hydromorphone. The reported mean difference is -1.6, with a 95% confidence interval from -3.192 to -0.008 and an unadjusted p-value of 0.049. Secondary results are posted for pruritus, pain, and vomiting; a sedation result is not reported. The registry lists no reported analyses and does not report the original statistical plan, multiplicity approach, or missing-data procedures.