Study of Nalbuphine HCl ER Tablets in Patients With Prurigo Nodularis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Study of Nalbuphine HCl ER Tablets in Patients With Prurigo Nodularis (NCT02174419), a randomized phase 2, phase 3 study. The primary outcome is Change From Baseline to the Evaluation Visit (Week 10) in Itch on the 0-10 Numerical Rating Scale.

2. Clinical Question

The registry describes a randomized, triple-masked, parallel-group study and gives the primary assessment timeframe as baseline to Week 10. The study’s primary objectives included evaluating the effects of the two doses on change from baseline in worst itch and evaluating safety and tolerability. The posted primary result is specifically the percentage meeting a reduction threshold. Further detail on how the registry outcome relates to the stated objective of evaluating change in worst itch is not reported in the registry record.

3. Trial Design

The registry record describes NCT02174419 as a randomized, triple-masked, parallel, placebo-controlled study of nalbuphine HCl ER tablets in patients with prurigo nodularis. It lists the study as phase 2 and phase 3. The three groups received nalbuphine HCl ER 90 mg BID, nalbuphine HCl ER 180 mg BID, or placebo tablets BID. The overall enrollment was 62.

The study began in 2015-03, reached primary completion in 2016-08, and is listed as completed. The registry record identifies Trevi Therapeutics as the sponsor. These details describe the registered study; they do not establish how many participants completed treatment or contributed to every outcome. The primary endpoint denominators are 22 in the 90 mg arm, 18 in the 180 mg arm, and 22 in the placebo arm. The registry outcome description specifies that the percentage is among participants in each group who were evaluated.

Randomization is intended to allocate participants to study groups by chance. A parallel-group design assigns participants to a group rather than having each participant receive each intervention in turn. Masking is reported as triple, but which people or roles were masked is not reported in the registry record. The allocation ratio, sequence-generation method, concealment method, treatment duration, and detailed visit schedule are also not reported in the registry record.

The study includes a primary outcome and one posted secondary outcome. The secondary outcome is change from baseline to the evaluation visit at Week 10 in mean itch on the 0-10 Numerical Rating Scale. Additional descriptions of the secondary result are not reported in the registry record. The record does not describe the original sample-size justification or its planned statistical analysis in enough detail to determine how the study was designed to address the primary comparison.

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.

6. Primary Endpoint

The registry lists the primary outcome as Change From Baseline to the Evaluation Visit (Week 10) in Itch on the 0-10 Numerical Rating Scale, measured over Baseline, Week 10.

The primary outcome is the percentage of evaluated participants who reported at least a 30% reduction from baseline to Week 10 in itch on the 0-10 Numerical Rating Scale. It represents a threshold response: participants are counted according to whether they met the specified reduction criterion. The posted results give the number meeting the criterion and the percentage within each arm: 6 of 22 participants in the 90 mg arm, 8 of 18 in the 180 mg arm, and 8 of 22 in the placebo arm. The corresponding percentages are 27.3%, 44.4%, and 36.4%.

A threshold-based endpoint can communicate how many participants reached a defined level of improvement, rather than describing only an average score. As a general statistical point, converting a continuous score change into a yes-or-no response can make the result easier to interpret against a prespecified threshold, but it also discards information about the size of changes above or below that threshold. The registry record does not report why this particular threshold was selected or whether it was prespecified in the protocol.

This outcome is not the same as the mean change in itch score. It also does not show the distribution of individual changes, the timing of any response before Week 10, or how many evaluated participants had missing measurements. Those details are not reported in the registry record. The record lists a secondary outcome for mean itch change at Week 10, but further result details for that outcome are not reported in the registry record.

7. Results Posted in the Registry

• Nalbuphine HCl ER 180 mg: 44.4% (8/18) versus 27.3% (6/22) on control; risk difference 17.2 percentage points (95% CI -12.4 to 46.7), risk ratio 1.63 (0.69–3.83); unadjusted two-proportion z-test p = 0.257.
• Sugar Pill: 36.4% (8/22) versus 27.3% (6/22) on control; risk difference 9.1 percentage points (95% CI -18.3 to 36.5), risk ratio 1.33 (0.55–3.21); unadjusted two-proportion z-test p = 0.517.

8. Statistical Interpretation

9. Statistical Methods Explained

What does the response percentage describe?

The primary result is a binary outcome: each evaluated participant either met the criterion of at least a 30% reduction in itch from baseline to Week 10 or did not. The arm percentage is the number meeting the criterion divided by the number evaluated in that arm, expressed as a percentage. This is why the outcome is described as a percentage of subjects rather than as a mean score. The posted denominators are 22, 18, and 22; the corresponding counts meeting the criterion are 6, 8, and 8.

As a general statistical concept, binary outcomes are commonly compared using proportions or measures of difference and relative association. A risk difference describes the absolute difference between two proportions. A risk ratio compares one proportion with another as a ratio, while an odds ratio compares the odds of the event. These measures answer related but not identical questions. Their interpretation depends on which group is selected as the reference. The posted recalculations use the 90 mg arm as the reference for both pairwise contrasts.

What do the recalculated tests and intervals mean?

The reported recalculated p-values are unadjusted: 0.257 for the 180 mg arm compared with the 90 mg arm, and 0.517 for placebo compared with the 90 mg arm. A p-value measures how incompatible the observed data are with a specified null model, under the assumptions of the statistical test. It is not the probability that the null hypothesis is true, nor is it a measure of the size or importance of an effect. The registry record does not report sponsor analyses or a statistical plan specifying the intended test, so these recalculations should be understood as simple unadjusted analyses of the posted counts.

A confidence interval gives a range of estimates compatible with the data and the method used, in repeated-sampling terms. As a general explanation, a wide interval indicates that the data leave substantial uncertainty about the size and direction of an effect. Here, each recalculated interval for a risk difference crosses zero, so the compatible values include no difference as well as differences in either direction. That does not establish equivalence. Demonstrating equivalence would require a defined margin and an analysis designed for that question; neither is reported in the registry record.

Why are the recalculations unadjusted?

The recalculated comparisons are based on the posted counts and do not account for baseline characteristics, stratification factors, or other covariates. Whether the original trial used adjusted analyses, stratification, or another statistical model is not reported in the registry record. The recalculated pairwise results also do not account for testing multiple comparisons. As a general statistical concern, multiple testing can increase the chance of at least one apparently notable result when several hypotheses are examined. The registry record does not report a multiplicity strategy or a prespecified testing sequence.

There are three groups, but the recalculations compare each active or placebo group against the 90 mg group. Those are not direct comparisons of each nalbuphine dose with placebo. A study may have a different planned primary contrast from a simple recalculation, but the original contrast and analysis plan are not reported in the registry record. The distinction between the randomized design and the reference group used in a recalculation matters when interpreting the findings.

What cannot be inferred from the posted analysis?

The registry lists one secondary outcome, change from baseline to Week 10 in mean itch, but additional results for that outcome are not reported in the registry record. The primary posted endpoint does not provide the mean change, the spread of individual score changes, or participant-level trajectories. The record also does not identify the analysis population, how missing endpoint data were handled, whether any participants were excluded from the analysis, or whether there were protocol deviations. Without these details, the percentages should be read as the results among the evaluated participants described by the endpoint definition.

The number of outcome measures is listed as 3, while one secondary outcome is identified in the registry information. The record does not explain the relationship between these counts or provide detailed analyses for the other measures. It does not report an interim-analysis plan, stopping rule, covariate adjustment plan, or statistical analysis plan. Their absence from the registry record means the recalculations should not be presented as if they reproduce the trial sponsor’s intended analysis.

As a general principle, statistical significance and clinical relevance are different questions. A p-value alone does not establish that a difference is important, while a point estimate alone does not establish that it is dependable. Interpretation should consider the effect estimate, uncertainty, study design, endpoint definition, and completeness of reporting together. In this study, the modest arm sizes and intervals spanning both directions make precision an important consideration, and the registry does not provide enough methodological detail to resolve all analysis questions.

10. Confidence Intervals and Precision

The response percentages are based on 22 evaluated participants in the 90 mg arm, 18 in the 180 mg arm, and 22 in the placebo arm. Each observed percentage is therefore a summary of a relatively small group. A percentage can look quite different from the underlying count when the denominator is limited, so the counts are useful context for interpreting the displayed proportions.

The recalculated confidence intervals for the risk differences are broad and cross zero for both comparisons. The interval for 180 mg versus 90 mg includes both a negative and a positive risk difference; the interval for placebo versus 90 mg also includes both directions. Thus, the posted data are compatible with the comparison group having a lower response proportion, a higher response proportion, or little difference. These recalculated intervals do not support a precise estimate of the direction or magnitude of either contrast.

A confidence interval is not a guarantee that the true effect lies within a particular range. As a general statistical explanation, it describes the uncertainty generated by the data and the method under repeated sampling assumptions. The observed proportion is only one estimate, and the interval communicates that plausible values extend beyond that point estimate. The intervals are recalculations from summary counts, not intervals reported from the sponsor’s own analysis.

Precision is distinct from whether a result is statistically significant. A broad interval may include the null value while also allowing effects in either direction that could matter; it does not prove no effect. Conversely, an arm with the largest observed percentage does not necessarily have a reliably larger underlying response. Participant-level outcome data and details about missingness are not reported in the registry record, limiting further assessment of precision.

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 figures are planning illustrations based on the observed effect, not the original trial’s design calculations. They assume a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. For each comparison, the table considers detecting the full observed effect and smaller fractions of that effect. The original study’s own sample-size assumptions and justification are not reported in the registry record.

For these binary outcome comparisons, the listed figures are participants per arm, not total events. The 80% power column gives the planned number of participants per arm for a hypothetical design with an 80% chance of detecting the stated effect under the planning assumptions, if that effect were the true effect. The 90% power column describes the corresponding per-arm number for a hypothetical design with a 90% chance. These are design-planning concepts, not guarantees about what a future study will find.

The table shows planning for the full observed effect, 75% of the observed effect, and 50% of the observed effect. Smaller effects need more participants to detect under otherwise unchanged assumptions. The participant counts also differ across the comparisons because the observed effect used for each planning illustration differs. These figures should not be interpreted as proof that the observed study had a particular probability of success; this is not observed power. The planning values are illustrations, not evidence about treatment effect or the original trial’s statistical design.

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 = 0.273; treatment proportion p₁ = 0.444; average p̄ = 0.359.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6782 = 1.3293.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6673 = 0.5616.
4. n = (1.3293 + 0.5616)² / (0.1717)² = 121.3, rounded up to 122 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 <- 0.272727272727273                          # control proportion
p1 <- 0.444444444444444                          # 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(2174419)
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 = 122 (80% power), 162 (90% power)
 75% of observed effect: n per arm = 211 (80% power), 282 (90% power)
 50% of observed effect: n per arm = 459 (80% power), 614 (90% power)
power.prop.test: 121.3 
Simulated power at n = 122 per arm: 0.812 (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. Multiplicity, Missing Data and Analysis Populations

The registry record does not report a multiplicity adjustment, a hierarchy of hypotheses, or a prespecified sequence for testing outcomes. The posted recalculated pairwise p-values are unadjusted. Because the study has three arms and multiple outcome measures are listed, it is important not to treat each nominal comparison as if it were necessarily the sole planned test. Whether the original analysis controlled for multiple testing is not reported in the registry record.

The record identifies a primary outcome and one secondary outcome, but it does not provide a full statistical analysis plan. It does not report how the primary outcome was analyzed by the sponsor, which contrasts were prespecified, or whether any model or covariate adjustment was planned. It also lists three outcome measures without detailing all their results. As a result, the posted summary does not establish whether the recalculated contrasts align with the original inferential objectives.

Missing-data handling is not reported in the registry record. The primary endpoint description refers to the percentage among participants evaluated in each arm, and the denominators differ across the three groups. The record does not explain why some enrolled participants may not be represented in a given endpoint denominator, whether measurements were unavailable, or how any missing values were treated. It also does not state whether the analysis followed an intention-to-treat principle, a per-protocol approach, or another population definition.

The record does not report an interim-analysis plan, stopping rules, protocol deviation summaries, or the analysis population for the primary endpoint. These omissions do not show that such procedures were absent from the trial; they mean that their details are not reported in the registry record. Without them, readers cannot determine how the sponsor’s planned handling of multiple outcomes and incomplete data might affect interpretation.

14. 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.

Most frequent serious adverse event terms

Serious events with the highest arm-level rate: road traffic accident (4.5%), thoracic vertebral fracture (4.5%), leukocytosis (4.5%).

The serious adverse event figures are reported for the same three groups. One serious adverse event is listed among 22 participants at risk in the 90 mg group, none among 18 participants at risk in the 180 mg group, and one among 22 participants at risk in the placebo group. The record lists zero other adverse events in each group. Deaths are not reported in the registry record.

These are event counts and group denominators, not estimates that establish whether one group is safer than another. With these group sizes, the counts alone provide limited information about the range of possible underlying event rates. No comparative safety analysis or confidence intervals for adverse events are reported in the registry record. The listed serious event terms are Road traffic accident, Thoracic vertebral fracture, and Leukocytosis, each shown as 4.5%. The registry summary does not provide the group attribution or further context for those terms.

The primary efficacy endpoint and the serious adverse event summary are different types of information. The adverse event figures should be read as descriptive counts for this study, rather than as a complete assessment of safety or as evidence about risks outside the trial.

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

The results describe how many evaluated participants in each group met the primary itch reduction threshold at Week 10. The observed proportions were 27.3% in the 90 mg arm, 44.4% in the 180 mg arm, and 36.4% in the placebo arm. They show variation across the three groups, but the counts and recalculated intervals indicate substantial uncertainty about the pairwise differences.

These results do not establish that a dose caused a difference in response. The recalculated comparisons use the 90 mg arm as the reference and are unadjusted; they are not direct comparisons of each dose with placebo. The p-values do not demonstrate equivalence, and the confidence intervals crossing zero do not prove that the groups have identical outcomes. The registry record does not provide sponsor-reported inferential analyses or enough detail to determine the intended primary contrast.

The endpoint also has a specific scope. It counts participants meeting a defined threshold rather than describing the average change in itch, the full distribution of responses, or how symptoms changed over time. The listed secondary outcome concerns mean itch change at Week 10, but further results are not reported in the registry record. The reported outcome should therefore not be used as a substitute for those missing descriptions.

More broadly, the registry summary does not report the analysis population, handling of missing data, multiplicity procedures, or original sample-size justification. These limitations constrain how confidently the results can be interpreted. The trial’s results characterize the recorded Week 10 threshold responses in the study groups; they do not alone establish a general conclusion about effects in other populations or settings.

16. Why This Trial Matters Statistically

This trial illustrates why arm percentages need to be read alongside denominators and uncertainty. The percentages differ, but they come from groups of 22, 18, and 22 evaluated participants. The recalculated confidence intervals span values on both sides of no difference, making the apparent ordering of the point estimates an uncertain guide to the underlying contrasts.

It also highlights how the comparison chosen affects interpretation. The study is placebo-controlled, yet the available recalculated comparisons use the 90 mg group as the reference. Those comparisons answer a different question from comparing each dose with placebo. Naming the reference group clearly is essential when reading any relative effect or p-value.

The endpoint further demonstrates the trade-off involved in threshold outcomes. A percentage meeting a defined response criterion can be readily understood, while it omits information about the amount of change for participants who do and do not cross the threshold. The registry lists a mean-change secondary outcome, but its detailed results are not reported in the registry record.

Finally, the registry’s missing details on analysis populations, missing-data handling, multiplicity, and the original statistical plan limit what can be inferred from recalculated tests. Statistical interpretation depends not only on the observed percentages but also on how outcomes were defined and analyzed. Here, the posted summary supports a careful descriptive account, while leaving important questions about the planned inferential analysis unresolved.

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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The primary outcome denominators are smaller than the overall enrollment of 62, and the registry record does not explain the difference or provide participant flow by group. It specifies that the percentages apply to participants evaluated, but does not report why other enrolled participants are not included in those denominators or how missing measurements were handled. This makes it difficult to assess the potential influence of missing outcome data.

The group sizes are limited, and the recalculated confidence intervals are broad. The point estimates therefore have substantial uncertainty. The available pairwise calculations use the 90 mg group as the reference, rather than comparing each dose directly with placebo. No sponsor-reported analysis is listed in the registry record, so it is not possible to establish whether these recalculations correspond to the original analysis plan.

Other methodological details are also not reported in the registry record, including eligibility criteria, baseline participant characteristics, allocation procedures, treatment duration, the roles masked under triple masking, and analysis population definitions. The original sample-size justification, multiplicity approach, covariate adjustment, interim analysis plans, and statistical analysis plan are not reported. These omissions limit assessment of the trial’s design assumptions and the robustness of the posted results.

The primary result is a threshold response percentage rather than a complete account of itch-score change. The registry record lists a mean-change secondary endpoint, but does not provide its detailed results. Safety information is limited to the posted event counts and terms; deaths are not reported in the registry record. These limitations define the scope of what can be concluded from the posted summary.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Study of Nalbuphine HCl ER Tablets in Patients With Prurigo Nodularis — NCT02174419.
• Registry record last updated 2025-05-21; status last verified 2025-05.
• Results first posted 2020-08-21.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

NCT02174419 is a completed randomized, triple-masked, parallel, placebo-controlled phase 2 and phase 3 study sponsored by Trevi Therapeutics. It enrolled 62 participants and evaluated nalbuphine HCl ER 90 mg BID, nalbuphine HCl ER 180 mg BID, and placebo tablets BID. The study began in 2015-03 and reached primary completion in 2016-08.

The primary posted outcome was the percentage of evaluated participants reporting at least a 30% reduction from baseline in itch on the 0-10 Numerical Rating Scale at Week 10. The percentages were 27.3%, 44.4%, and 36.4% in the 90 mg, 180 mg, and placebo groups, respectively. Unadjusted recalculations compare each of the latter two groups with the 90 mg group; the registry record does not report sponsor analyses or the original statistical plan.

The record lists one secondary outcome concerning mean itch change at Week 10, but detailed secondary results are not reported in the registry record. Serious adverse events were recorded in the 90 mg and placebo groups, and deaths are not reported in the registry record.