Study of Nalbuphine HCl ER Tablets in Hemodialysis Patients With Uremic Pruritus: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Study of Nalbuphine HCl ER Tablets in Hemodialysis Patients With Uremic Pruritus (NCT02143648), a randomized phase 2, phase 3 study. The primary outcome is Change From Baseline to the Evaluation Period in Itch on the 0-10 Itch Numerical Rating Scale.

2. Clinical Question

3. Trial Design

This was a randomized, double-blind, placebo-controlled, parallel, 3-arm study. The registry record classifies its masking as triple. It does not specify which people or roles were included in that masking designation, so the meaning should not be expanded beyond the recorded classification. The study is listed as Phase 2 and Phase 3, with an enrollment of 373. Its status is completed; the recorded study start is 2014-06 and primary completion is 2015-07. The sponsor was Trevi Therapeutics.

The three regimens were nalbuphine HCl ER tablets 60 mg BID, nalbuphine HCl ER tablets 120 mg BID, and placebo tablets BID. The primary outcome concerned change in the 0-10 Itch Numerical Rating Scale. Its evaluation-period value was based on average itch scores during weeks 7 and 8 after treatment initiation. The stated primary-outcome population included participants with a baseline measurement and at least one post-baseline measurement for the evaluation-period average. The sample sizes displayed with the outcome are 82 for the 60 mg arm, 84 for the 120 mg arm, and 108 for placebo. These outcome-specific counts are not the same as the registry enrollment figure.

The posted arm summaries report least-squares means and standard deviations for the continuous endpoint. The record does not describe the model used to obtain those least-squares means, how any covariates were selected, or how the repeated observations were handled. It also does not report the original sample-size justification, planned allocation ratio, randomization procedure, treatment duration beyond the eight-week endpoint timeframe, or protocol deviations. These details should not be inferred from the randomized, parallel-group description.

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

Analysis population for the primary outcome, as defined in the registry: The sample sizes for each arm include participants who had a baseline value and at least one post baseline value for the average itch score during teh Evaluation 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.

Population: Of the initial 373 participants randomized, 4 were never treated and, therefore, are not included in baseline demographic or frequency tables of treatment emrgent adverse events (TEAEs). Thus, the number of treated particpants was 369.

6. Primary Endpoint

The registry lists the primary outcome as Change From Baseline to the Evaluation Period in Itch on the 0-10 Itch Numerical Rating Scale, measured over 8 weeks.

The primary endpoint was change from baseline to the evaluation period in itch on the 0-10 Itch Numerical Rating Scale. The evaluation period was defined as the average itch score over weeks 7 and 8 following initiation of treatment. The registry describes the endpoint as a least-squares mean, with standard deviation as the dispersion measure. Its direction is important: a negative change, calculated as evaluation-period score minus baseline, signified improvement according to the registry record.

A numerical rating scale converts a participant’s subjective symptom rating into a continuous measure. In general, repeated or averaged ratings can represent symptom burden over a specified interval rather than relying on a single momentary report. Averaging scores across the stated evaluation weeks is the registry’s way of defining the endpoint window; the record does not describe the precise daily or weekly assessment schedule.

Baseline change is useful because it expresses the outcome relative to each participant’s starting measurement. A group mean change describes average movement, not the experience of every participant, and the spread indicates that individual changes varied. Least-squares means are model-based adjusted means in general, but the model and adjustment variables are not reported in the registry record. Therefore, the posted label alone does not establish which factors, if any, were included in the adjustment. The outcome population also required baseline and post-baseline data, so the endpoint summaries apply to participants meeting that measurement criterion rather than automatically to everyone enrolled.

7. Results Posted in the Registry

• Nalbuphine HCl ER 120mg: mean -3.49 versus -3.10 on control; difference -0.39 (95% CI -1.11 to 0.33), standardized effect d = -0.17; z-test p = 0.287.
• Sugar Pill: mean -2.80 versus -3.10 on control; difference 0.30 (95% CI -0.36 to 0.96), standardized effect d = 0.13; z-test p = 0.372.

8. Statistical Interpretation

9. Statistical Methods Explained

Continuous outcomes and group means

The itch outcome is continuous: each participant’s change can take values along a numerical scale rather than being limited to categories such as event or no event. A group mean summarizes the center of the recorded changes. It does not show the full distribution, the number of participants who improved, or whether individual experiences were similar. The posted summaries are described as least-squares means, which are commonly estimates from a statistical model. In general, model-based means may account for specified variables, but the registry record does not report the model specification or adjustment variables. It is therefore not possible to identify what makes these means “least squares” beyond the recorded label.

The standard deviation describes spread among measurements around a mean. A larger spread indicates more variation in individual values relative to the group mean. It is not the same as the standard error, which describes uncertainty in an estimated mean, nor is it a confidence interval. The posted arm summaries list standard deviations of 2.35, 2.37, and 2.22 for the 60 mg, 120 mg, and placebo groups, respectively. These values provide context for the variability of the endpoint but do not, on their own, show whether the groups differ statistically.

What is a mean difference?

A mean difference is a contrast between two group means, expressed in the original outcome units. Here, the recalculated contrasts use the 60 mg arm as reference. The 120 mg versus 60 mg contrast is -0.39 units on the itch scale; a negative value means the 120 mg group’s posted mean change is more negative than the reference group’s mean change. The placebo versus 60 mg contrast is 0.3 units, so the placebo group’s posted mean change is less negative than the reference group’s mean change. Because the endpoint is change from baseline and negative change signifies improvement, direction needs to be read using that definition, not simply by treating a positive or negative contrast as universally favorable.

What do the confidence intervals represent?

In general, a confidence interval gives a range of estimates compatible with the data and the method used, reflecting sampling uncertainty. It is not a range that contains every participant’s outcome, and it does not give the probability that a particular treatment effect is true. For the 120 mg versus 60 mg recalculated contrast, the interval is -1.108 to 0.328. Since zero lies within it, the posted summary statistics do not provide a clear separation from no mean difference under this unadjusted calculation. The placebo comparison’s interval also spans zero. A broad interval can accommodate a range of effects; it signals limited precision rather than proving that the true difference is exactly zero.

How should the p-values be read?

A p-value is a measure of how unusual data at least as discrepant as those observed would be under a specified null model and its assumptions. It is not the probability that the null hypothesis is true, the chance that the finding is due to chance, or a measure of clinical importance. The unadjusted recalculated p-values are 0.287 for 120 mg versus 60 mg and 0.372 for placebo versus 60 mg. They do not meet the conventional 0.05 threshold used in the planning illustration, but the registry record does not report that threshold as the trial’s own prespecified analysis rule. The original statistical plan and any adjustment for multiple comparisons are not reported in the registry record.

Why are the comparisons described as recalculated?

The pairwise estimates, intervals, and p-values are unadjusted recalculations from the posted arm summaries. The standard deviations are used as approximate inputs for the comparisons. Such calculations do not reproduce an unknown fitted model and should not be presented as the trial’s sponsor-reported adjusted analysis. The registry record does not report a primary inferential analysis for the endpoint. The distinction matters because model specification, covariate adjustment, missing-data handling, and the chosen analysis population can affect estimates and uncertainty.

Why can over-dispersion matter in other analyses?

General statistical context: over-dispersion occurs when observed variability in data exceeds what a model assumes. It is especially relevant for count outcomes, where a model that understates variability can produce standard errors that are too small and confidence intervals that are too narrow. The primary endpoint in this study is continuous, and the registry record does not report a count-model analysis. Over-dispersion is therefore a general concept rather than a stated feature of this trial’s primary analysis.

What do planning illustrations mean?

The sample-size illustrations use the observed contrast as a starting point and ask how many participants per arm would be needed to detect the stated fraction of that effect under stated assumptions. They are not a reconstruction of the trial’s original design. The registry record does not report the trial’s own sample-size justification or original design assumptions. In general, smaller target effects require more participants to distinguish them from random variation, all else held constant. The planning method and the resulting estimates do not establish the actual power of the completed study.

10. Confidence Intervals and Precision

The precision of a group contrast is reflected in the range of values that remain compatible with the data and the calculation method. For the recalculated 120 mg versus 60 mg mean difference, the estimate is -0.39 and the confidence interval extends from -1.108 to 0.328. Its inclusion of zero means the interval is compatible with no mean difference as well as with differences in either direction. The estimate alone should not be read as a precise measurement of the underlying effect.

The placebo versus 60 mg estimate is 0.3, and its recalculated confidence interval also spans zero. This indicates uncertainty around the direction and magnitude of that contrast. The exact interval limits are not repeated because the key interpretive point is that the range includes both negative and positive values. Neither interval is a prediction range for individual participants, and neither establishes equivalence. Demonstrating equivalence would require a prespecified margin and an appropriate analysis; such a margin and analysis are not reported in the registry record.

Standard deviations of 2.35, 2.37, and 2.22 indicate spread in the arm-level outcome values. The amount of spread, outcome-specific sample sizes, and the interval estimates all contribute to uncertainty in comparisons. The registry record does not report the fitted model behind the least-squares means, adjusted confidence intervals, or an analysis accounting for any design features beyond the recorded parallel randomized structure. The displayed unadjusted recalculations use approximate standard deviations and should be read accordingly.

Confidence intervals are useful because they show a range of plausible effect estimates under the calculation’s assumptions, while a p-value compresses evidence into a single measure. Neither replaces consideration of the endpoint definition, analysis population, missing data, and possible multiplicity. The registry record does not report a clinical threshold for interpreting the size of a change on this scale, so statistical precision cannot be translated into a claim about clinical importance from these data alone.

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 values are participants per arm, not total event counts. They are illustrations based on the observed contrast, not the trial’s original design calculation. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is the stated fraction of the observed effect. The trial’s own original sample-size assumptions and justification are not reported in the registry record.

For the 120 mg versus 60 mg contrast, planning for 100% of the observed effect gives 575 participants per arm for 80% power and 770 participants per arm for 90% power. Planning for 75% of the observed effect gives 1,023 participants per arm for 80% power and 1,369 participants per arm for 90% power. Planning for 50% of the observed effect gives 2,300 participants per arm for 80% power and 3,079 participants per arm for 90% power.

For placebo versus 60 mg, planning for 100% of the observed effect gives 905 participants per arm for 80% power and 1,211 participants per arm for 90% power. Planning for 75% of the observed effect gives 1,608 participants per arm for 80% power and 2,153 participants per arm for 90% power. Planning for 50% of the observed effect gives 3,618 participants per arm for 80% power and 4,843 participants per arm for 90% power.

In plain terms, the 80% column gives the estimated participants per arm for a design with an 80% chance of detecting the assumed effect under the stated model, and the 90% column does the same for a design with a 90% chance. Smaller effects need more participants to detect under otherwise identical assumptions. These are planning illustrations, not observed power.

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 = -0.390; pooled standard deviation σ = 2.360.
2. n = 2 × (1.96 + 0.842)² × 2.360² / -0.390² = 574.9, rounded up to 575 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -0.39                      # observed difference in means
sigma <- 2.36014313331969                     # 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(2143648)
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 = 575 (80% power), 770 (90% power)
 75% of observed effect: n per arm = 1,023 (80% power), 1,369 (90% power)
 50% of observed effect: n per arm = 2,300 (80% power), 3,079 (90% power)
power.t.test: 575.9 
Simulated power at n = 575 per arm: 0.804 (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 record describes one posted primary outcome measure and lists zero analyses. It lists zero posted secondary outcomes. That is different from evidence that the study measured only one outcome or conducted only one analysis; the registry record does not report a full analysis inventory. It also does not report a prespecified hierarchy among doses, endpoints, time points, or contrasts.

Multiplicity arises when several hypotheses or comparisons are assessed. If each is evaluated separately without an adjustment, the chance of obtaining at least one apparently unusual result can increase. General methods for addressing this include defining a primary contrast in advance or adjusting the decision threshold across comparisons. The registry record does not report whether any such method was planned or used. The recalculated p-values are unadjusted, so they should not be read as multiplicity-controlled results. The comparison structure available for these calculations uses 60 mg as reference for both 120 mg and placebo; direct active-dose-versus-placebo inferential results are not reported.

The outcome population was described as participants who had a baseline value and at least one post-baseline value for the evaluation-period average itch score. The registry record does not report how missing values were handled, whether observations were imputed, or whether sensitivity analyses assessed alternative assumptions about missingness. It also does not report reasons for missing endpoint data or the number of participants excluded from the endpoint summaries for each reason. The stated measurement criterion therefore describes who contributed to the posted endpoint summaries, but not a complete missing-data strategy.

The registry record does not report whether the primary analysis was intention-to-treat, per-protocol, or another analysis population. It does not specify a modified intention-to-treat definition beyond the endpoint measurement criterion, or describe exclusions after randomization. The outcome-specific group counts should consequently be interpreted as the reported endpoint sample sizes, not as proof of a particular analysis principle. Additional details on protocol deviations, adherence, and treatment discontinuation are not reported in the registry record.

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 serious adverse event terms

Serious events with the highest arm-level rate: cardiac failure congestive (3.2%), gastrointestinal haemorrhage (3.2%), hyperkalemia (2.4%), fluid overload (1.6%), syncope (1.6%).

The registry lists serious adverse events for groups at risk of 126 in the nalbuphine HCl ER 60mg group, 120 in the nalbuphine HCl ER 120mg group, and 123 in the Sugar Pill group. Serious adverse events affected 16, 8, and 19 participants in those groups, respectively. There were 0 deaths in each group. These counts describe the posted safety record and should not be directly compared with the smaller outcome-specific sample sizes, because the populations recorded for safety and the primary itch endpoint differ.

The registry lists serious-event terms including Cardiac failure congestive (3.2%), Gastrointestinal haemorrhage (3.2%), Hyperkalemia (2.4%), Fluid overload (1.6%), Syncope (1.6%), and Anaemia (1.6%). The denominator and method behind these percentages are not reported in the registry record. The percentages should therefore be read as the registry’s listed figures, not recalculated rates or arm-specific risks.

Serious adverse event counts do not establish that a treatment caused an event, and an event count does not measure severity beyond the registry’s serious-event classification. The record does not provide enough detail to assess event timing, exposure duration, relatedness judgments, or comparative statistical uncertainty. The safety figures are descriptive and do not by themselves determine the overall benefit-risk profile.

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

The posted primary outcome describes average change in itch-score values over a defined evaluation period among participants with the required baseline and post-baseline measurements. The negative arm means indicate decreases from baseline under the endpoint definition, where negative change was designated as improvement. The arm summaries and recalculated comparisons provide information about the direction and uncertainty of these average changes in the recorded analysis population.

The unadjusted recalculated mean differences are small relative to their uncertainty intervals in the sense that both intervals include zero; no new standardized or relative effect is calculated. These comparisons do not establish that the groups were equivalent, nor do they prove there was no difference. They also do not establish that any observed within-group change was caused by treatment. Between-group comparisons, not just change within each arm, are needed to distinguish treatment contrasts from other influences over time.

The registry record does not report the primary inferential analysis, its model, a prespecified clinically important difference, multiplicity handling, or the missing-data strategy. Without those details, the posted summaries cannot support a complete assessment of the trial’s planned statistical conclusions. Similarly, the listed serious adverse events and deaths are descriptive record entries; they do not establish causation or provide a full comparative safety analysis.

These results are specific to the registry’s study population, endpoint definition, recorded analysis samples, and follow-up period. They do not by themselves answer how results would generalize to people with other clinical characteristics or under different care conditions. Statistical results also do not replace clinical judgment. The record’s findings can be described as observed group summaries and uncertain unadjusted contrasts, rather than a definitive statement that a regimen does or does not work.

16. Why This Trial Matters Statistically

This trial illustrates why the direction of a continuous endpoint must be understood before interpreting contrasts. A negative change in itch score was defined as improvement, so a negative between-group difference represents a more negative mean change in the compared group than in its reference group. That interpretation depends on the endpoint definition and would not transfer automatically to another scale or outcome.

It also highlights the distinction between within-group change and between-group evidence. Each arm had a negative mean change, but that pattern alone does not show that the treatment groups differed from one another. The recalculated contrasts make the comparisons explicit, while their intervals convey uncertainty. The intervals include zero, so the estimates do not precisely distinguish the groups under these unadjusted calculations.

The record also illustrates how different analysis populations can appear within one trial. Endpoint sample sizes are based on participants with specified itch measurements, whereas the safety counts use different at-risk populations. Treating those denominators as interchangeable would misstate what each statistic describes. Likewise, interpreting a registry’s least-squares mean without model details can lead to unwarranted assumptions about adjustment.

Finally, planning illustrations derived from observed effects are not the same as the study’s original design justification, and they are not observed power. Their values depend on assumptions about allocation, significance level, distributional approximation, and target effect. The trial’s original design assumptions are not reported in the registry record. Recognizing these distinctions helps keep the conclusions proportional to the posted information and separates descriptive results from confirmatory inference.

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.

The main limitation for interpreting this trial statistically is the lack of registry-posted primary inferential analysis details. The record lists zero analyses, while the posted outcome summaries and recalculated pairwise results do not disclose the original model, covariate adjustment, or prespecified comparison hierarchy. The comparisons therefore remain unadjusted recalculations rather than a substitute for the trial’s planned analysis.

The endpoint summaries include participants with a baseline and at least one post-baseline value for the evaluation-period average. The registry record does not report the reasons for missing endpoint data, the missing-data method, or sensitivity analyses. This prevents assessment of whether the endpoint sample represents all randomized participants or whether missingness could affect the group estimates. The stated enrollment and the endpoint-specific sample sizes describe different counts; the record does not detail the disposition of participants across follow-up.

The outcome is a least-squares mean, but the fitted model and adjustment factors are not reported. The registry also does not report a clinically important difference for the itch scale, so statistical uncertainty cannot be mapped to a registry-defined threshold of clinical importance. The recalculated comparisons use approximate standard deviations and have no reported multiplicity adjustment. Direct inferential comparisons of each active dose with placebo are not posted in the available analysis details.

For safety, the serious-event risk populations differ from the endpoint sample sizes, and the denominator for the listed event-term percentages is not reported. Event attribution, timing, and comparative uncertainty are also not described in these figures. The registry record does not report further details sufficient to interpret those percentages as arm-specific incidence rates or to draw causal conclusions. These limitations constrain interpretation of both efficacy and safety summaries without negating the descriptive information that is recorded.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Study of Nalbuphine HCl ER Tablets in Hemodialysis Patients With Uremic Pruritus — NCT02143648.
• Registry record last updated 2025-05-21; status last verified 2025-05.
• Results first posted 2020-09-07.
• 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

NCT02143648 is a completed randomized, triple-masked, parallel, 3-arm study listed as Phase 2 and Phase 3. It enrolled 373 participants and evaluated nalbuphine HCl ER tablets 60 mg BID, nalbuphine HCl ER tablets 120 mg BID, and placebo tablets BID in hemodialysis patients with moderate to severe uremic pruritus. The recorded study start was 2014-06 and primary completion was 2015-07.

The primary endpoint was change from baseline in itch on the 0-10 Itch Numerical Rating Scale, using the average itch score over weeks 7 and 8 as the evaluation period. Negative change signified improvement. The posted arm means were -3.1, -3.49, and -2.8 for 60 mg, 120 mg, and placebo. Recalculated unadjusted comparisons against the 60 mg arm had intervals that included zero. The registry record does not report the original sample-size justification, primary inferential analysis details, multiplicity handling, or missing-data approach. Safety entries include serious adverse events and 0 deaths in each group.