Nebulized Sub-dissociative Dose Ketamine for Treating Pain: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Nebulized Sub-dissociative Dose Ketamine for Treating Pain (NCT03909607), a randomized phase 4 study. The primary outcome is Change in Pain Scores From Baseline to 30 Minutes.

2. Clinical Question

This is a dose-comparison question, not a comparison of ketamine with another treatment. The registry summary explains that the investigators sought to compare the 1.5 mg/kg dose with the lower doses and to assess whether lower doses were equally effective. The posted primary outcome is change in pain score, but the record does not specify how the direction of the change was coded. That matters when interpreting whether a higher mean represents a greater or smaller reduction in pain. The record also does not report a separate statistical comparison across all three groups as a single overall test.

3. Trial Design

The registry identifies a completed, randomized, parallel-group, quadruple-masked Phase 4 trial. It reports enrollment of 120 participants, with 40 assigned to each of the three ketamine dose groups. The listed arms are sub-dissociative ketamine at 0.75 mg/kg, 1.0 mg/kg, and 1.5 mg/kg. No non-ketamine arm is listed.

The trial’s primary outcome was change in pain scores from baseline to 30 minutes. Patients were to be assessed on an 11-point numeric rating scale when medication was given and again 30 minutes later. The registry states the scale range and its endpoints: 0 represents no pain and 10 represents very severe pain. The primary-outcome summary gives means and standard deviations for each group. It does not describe the analysis population or state how the change score was defined mathematically.

The registry lists the study start as 2019-04-16, primary completion as 2020-10-30, and status as completed. It does not report who was masked, how allocation was generated or concealed, or whether any participants were excluded after randomization. The original sample-size justification, intended statistical model, and full analysis plan are not reported in the registry record. Those omissions limit assessment of how closely the posted summaries follow the trial’s planned analysis. The record also lists one posted outcome measure and no posted secondary outcomes.

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 in Pain Scores From Baseline to 30 Minutes, measured over 30 minutes.

The primary endpoint is the change in pain score from baseline to 30 minutes after medication. The registry describes the score as an 11-point numeric rating scale, from 0 for no pain to 10 for very severe pain. A change score condenses the two assessments into a summary of how the measured score moved over the stated interval. The trial uses this measure to compare the three dose groups at a common follow-up time.

In general, a numeric rating scale provides an ordered, direct report of symptom intensity that can be summarized quantitatively. Comparing change rather than only the later score can account for where participants began, although it does not by itself explain how differences between groups were analyzed. The registry identifies the endpoint as a mean and reports standard deviations, which describe the average and variation of the change scores in each arm.

The arm means are 4.0 for 0.75 mg/kg, 4.2 for 1.0 mg/kg, and 4.1 for 1.5 mg/kg. The record does not state whether change was calculated as baseline minus follow-up or follow-up minus baseline. Therefore, the direction of a higher mean cannot be assigned a clinical interpretation from this record alone. The timing, scale, and summary measure are reported, but a threshold for a clinically important difference is not reported in the registry record.

7. Results Posted in the Registry

• SDK 1.0 mg/kg: mean 4.20 versus 4.00 on control; difference 0.20 (95% CI -0.68 to 1.08), standardized effect d = 0.10; z-test p = 0.655.
• SDK 1.5 mg/kg: mean 4.10 versus 4.00 on control; difference 0.10 (95% CI -0.73 to 0.93), standardized effect d = 0.05; z-test p = 0.814.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: it is a numeric change score, summarized with a mean and standard deviation. In general, a mean describes the center of a set of measurements, while a standard deviation describes how spread out individual measurements are around that mean. The registry reports these summaries for each dose group: 4.0 with a standard deviation of 1.9 for 0.75 mg/kg, 4.2 with a standard deviation of 2.1 for 1.0 mg/kg, and 4.1 with a standard deviation of 1.9 for 1.5 mg/kg.

The posted pairwise comparisons estimate the difference in mean change between each higher-dose group and the 0.75 mg/kg reference group. The estimate for 1.0 mg/kg is 0.2, and the estimate for 1.5 mg/kg is 0.1. In general, a mean difference is expressed in the original measurement units, so these estimates are in units on the pain scale’s change measure. The registry does not give the sign convention used to calculate change; a positive difference therefore cannot be labeled as favoring one dose on the basis of this record alone.

A confidence interval expresses uncertainty around an estimated effect. In general, intervals spanning zero include values consistent with no difference between groups, while also allowing for differences on either side of zero. Both posted intervals span zero. Their widths are substantial relative to the point estimates, so the estimates do not pin down a narrow range of plausible group differences. The confidence level used for the posted intervals is not reported in the registry record, so it should not be inferred from the interval values alone.

The reported p-values are unadjusted: 0.655 for the comparison of 1.0 mg/kg with 0.75 mg/kg, and 0.814 for 1.5 mg/kg with 0.75 mg/kg. In general, a p-value measures how compatible the observed data are with a specified null hypothesis under the assumptions of the analysis. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The registry does not report the complete test specification or an adjustment for examining multiple dose comparisons.

Randomization is intended, in general, to reduce systematic differences between groups at the outset. The registry identifies the allocation as randomized and the design as parallel, with three groups. It does not report the sequence-generation or concealment procedures. Quadruple masking is recorded, but which people were masked and how masking was maintained are not reported in the registry record. These details are relevant to evaluating potential bias but cannot be reconstructed from the masking label.

Standard deviations are useful when considering whether group means are precise. In general, the standard error of a mean depends on both the variability of observations and the number analyzed. The posted summaries list 40 participants for each arm, but the number included in the outcome analysis and the handling of missing measurements are not separately described. The posted comparison estimates also include standard errors, but those values are not needed to conclude that the reported intervals cover zero.

The registry lists zero posted statistical analyses, while the record includes outcome summaries and pairwise comparison statistics. The exact statistical model, assumptions about the score distribution, adjustment variables, and analysis population are not reported in the registry record. As a general matter, model choice can affect standard errors and confidence intervals, especially if data depart from model assumptions. The posted record does not give enough detail to assess those choices or reproduce the analysis from participant-level data.

There are two listed comparisons against a shared reference group. In general, conducting multiple tests raises a multiplicity question: when several hypotheses are assessed, an adjustment may be used to control the chance of false-positive findings across the family of tests. The p-values are explicitly unadjusted, and no adjustment method is reported. The posted p-values should therefore be read as individual, unadjusted comparison results rather than as multiplicity-controlled evidence.

The registry’s endpoint description gives a measurement time and scale, but does not state whether a baseline score was included as a covariate, whether the analysis used raw change scores alone, or whether other adjustments were made. No additional statistical plan, interim-analysis details, or sample-size rationale are reported in the registry record. In general, these elements help distinguish planned analyses from analyses selected after seeing the data and help readers assess precision and risk of bias. Their absence does not invalidate the posted numbers, but it restricts independent evaluation of how they were obtained.

For a continuous outcome, over-dispersion is not the usual count-data concept, but the general issue of variability remains important: more variability makes a mean difference harder to estimate precisely at a fixed sample size. The observed standard deviations describe the spread in these groups. They do not demonstrate that a particular model was appropriate, and no model diagnostics or distributional details are reported.

10. Confidence Intervals and Precision

The point estimates are small in the scale’s change-score units: 0.2 for 1.0 mg/kg versus 0.75 mg/kg and 0.1 for 1.5 mg/kg versus 0.75 mg/kg. The confidence intervals for both comparisons extend to values below and above zero. This means the estimates do not isolate a single direction of difference; the data are also compatible with no mean difference. The intervals are wide in relation to the point estimates, indicating limited precision for distinguishing these groups.

In general, a confidence interval describes a range of effect estimates that are reasonably compatible with the data under the method used. It is not a range containing a known proportion of individual participants’ outcomes, and it does not mean that every value in the interval is equally likely. The confidence level for these posted intervals is not reported in the registry record. The registry also does not report a clinically important difference threshold, so the interval widths cannot be judged against a stated threshold for meaningful change.

The reported group standard deviations are 1.9, 2.1, and 1.9, with 40 participants listed in each arm. The standard deviations describe variation in scores, whereas confidence intervals describe uncertainty in estimated group differences. The distinction matters: similar group averages can coexist with considerable variation among participants. The registry does not report the number with observed outcome data separately from the number in each arm, or how missing data were addressed, which further limits a full assessment of precision.

Neither comparison is statistically distinguishable from zero on the posted unadjusted tests, but that does not establish equivalence. A conclusion of equivalence would depend on a clinically justified margin, adequate precision relative to that margin, and a suitable prespecified analysis. Those elements are not reported in the registry record.

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 participants per arm for the continuous-outcome comparisons, not total events. The illustration uses the observed comparison effect as a starting point and considers detecting 100%, 75%, or 50% of that observed effect. For each fraction, it gives a target number of participants per arm for 80% power and for 90% power. The figures are planning illustrations, not the number enrolled or analyzed in this trial.

The stated 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 the stated fraction of the observed effect. These assumptions describe the illustration only. The trial’s original sample-size assumptions and justification are not reported in the registry record.

In general, 80% power means that a study designed under the stated assumptions would have an 80% chance of detecting an effect of the specified size if that effect were true. The 90% column applies the same idea with a higher target chance of detection. These are design targets, not guarantees for any particular study. The figures are not observed power.

Smaller effects require more participants because they are harder to distinguish from random variation. The planning values become larger when the target is a smaller fraction of the observed effect, and the 90% target requires more participants per arm than the 80% target for a given effect fraction. This illustration is based on the observed estimate, so it should not be treated as an independent estimate of the effect a future study would necessarily observe. It also does not incorporate design details that are not reported, such as a trial-specific adjustment plan or the handling of missing outcome data.

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 = 0.200; pooled standard deviation σ = 2.002.
2. n = 2 × (1.96 + 0.842)² × 2.002² / 0.200² = 1,573.7, rounded up to 1,574 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 <- 0.2                      # observed difference in means
sigma <- 2.00249843945008                     # 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(3909607)
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 = 1,574 (80% power), 2,107 (90% power)
 75% of observed effect: n per arm = 2,798 (80% power), 3,746 (90% power)
 50% of observed effect: n per arm = 6,295 (80% power), 8,427 (90% power)
power.t.test: 1574.7 
Simulated power at n = 1,574 per arm: 0.798 (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 primary endpoint is the change in pain score from baseline to 30 minutes. The record lists one posted outcome measure, no posted secondary outcomes, and no posted statistical analyses. It nevertheless includes two pairwise comparisons, each against the 0.75 mg/kg group. Their p-values are unadjusted. No method for controlling multiplicity across the comparisons is reported in the registry record.

In general, multiplicity arises when researchers conduct several tests or assess several outcomes. Without an adjustment or a clearly defined testing strategy, the chance of at least one false-positive result across a family of tests may be higher than for a single test. The record does not state whether the two comparisons were the only planned comparisons or whether another overall three-group test was conducted. An overall test result is not posted.

The registry reports 40 participants in each arm for the outcome summaries. It does not state whether all randomized participants contributed to the primary outcome, identify an intention-to-treat or per-protocol population, or report exclusions from analysis. Missing outcome counts, reasons for missingness, and the method used to handle missing data are not reported in the registry record. These omissions make it difficult to assess whether the available summaries reflect all randomized participants or a subset.

The record also does not report whether baseline score was included in an adjusted model, what statistical assumptions were checked, or whether any interim analyses were planned or conducted. The analysis model and complete statistical plan are not reported in the registry record. These items are important for understanding how the analyses were selected and whether the reported uncertainty reflects the design. The absence of these details should be distinguished from evidence that a particular analysis or procedure did or did not occur.

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 5% reporting threshold.

Most frequent non-serious adverse event terms

The registry reports serious adverse event counts of 0 in each group. Each group lists 40 participants at risk for serious adverse events. No serious adverse event terms are listed. Deaths are also reported as 0 in each group.

These figures describe the events recorded in the registry for the listed groups; they do not establish that the risk of a serious event is zero. In general, a count of zero events in a study group is compatible with some underlying risk, particularly when the number observed is limited. The record does not report the adverse-event observation window, definitions, or additional detail about ascertainment, so those aspects cannot be evaluated from the posted information.

The registry separately lists other adverse events affecting 5 participants in the 0.75 mg/kg group, 14 in the 1.0 mg/kg group, and 15 in the 1.5 mg/kg group, with 40 at risk in each group. These counts are not counts of serious adverse events. The record does not provide the event types in the safety summary used or a statistical comparison of these counts. They should be read as descriptive registry counts rather than as evidence of a causal difference between doses.

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

The posted primary-outcome summaries show mean change scores of 4.0, 4.2, and 4.1 for the 0.75 mg/kg, 1.0 mg/kg, and 1.5 mg/kg groups, respectively. The estimated mean differences against the 0.75 mg/kg group are 0.2 and 0.1. Both confidence intervals include zero, and the unadjusted p-values are 0.655 and 0.814. The results therefore do not provide precise evidence of a difference between either higher-dose group and the reference group in this measured outcome.

That interpretation is not the same as demonstrating that the doses are equivalent. The confidence intervals allow differences in either direction, and no equivalence margin or noninferiority criterion is reported in the registry record. The small observed point estimates alone cannot establish that clinically meaningful differences have been ruled out. Nor can the results establish that any of the doses is superior, because the posted comparisons do not show a clear difference and the direction of score change is not defined in the record.

The outcome is a change in a pain rating between baseline and 30 minutes, measured on a scale from 0 to 10. The registry does not specify the arithmetic sign convention for that change, and it does not report a clinically important difference threshold. The numerical results can therefore be described, but their clinical direction and importance cannot be resolved from the record alone.

The trial compares three ketamine doses and has no listed non-ketamine group. Its results do not estimate ketamine’s effect against placebo, usual care, or another treatment. The registry also does not provide other follow-up outcomes, a detailed analysis population, missing-data handling, or an adjusted analysis plan. Conclusions should remain focused on the posted, short-term dose comparisons and not extend to unreported outcomes or populations.

16. Why This Trial Matters Statistically

This trial poses a statistical question that is different from a simple test of whether a treatment changes a score. Its listed arms compare three doses of the same drug, and the reported pairwise contrasts share the 0.75 mg/kg group as a reference. That structure makes it important to distinguish a dose comparison from a treatment-versus-control comparison and to note that there is no non-ketamine arm.

The outcome is measured as change on a bounded 0-to-10 numeric rating scale over a stated 30-minute interval. Summarizing change with means and standard deviations is straightforward to read, but the registry does not report the change-score sign convention, the statistical model, or whether baseline scores were adjusted for. Those details affect how the reported numerical contrasts should be understood. The lack of an explicit clinically important difference threshold also means that statistical uncertainty cannot be directly translated into a threshold-based judgment about importance.

The trial enrolled 120 participants, with 40 listed in each group. Against that scale of enrollment, the posted comparisons have confidence intervals spanning zero and point estimates of 0.2 and 0.1. This makes precision central: a failure to distinguish the estimates from zero is not proof of equality, and an equivalence conclusion would need a prespecified margin and suitable design. Neither is reported.

Finally, the record illustrates why registry transparency matters. The results include group summaries and unadjusted comparisons, while details on multiplicity, missing outcomes, analysis populations, and the original sample-size rationale are not reported. Readers can describe the posted findings, but cannot fully reconstruct the analysis or judge whether every planned comparison is represented.

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 primary-outcome change score is not given a sign convention. Without knowing whether change was calculated as baseline minus follow-up or the reverse, the direction represented by a higher mean cannot be established. The registry also does not report a clinically important difference threshold, making it difficult to judge whether the estimated contrasts could matter clinically.

Only the primary outcome is posted, and the registry lists no secondary outcomes. The record provides two pairwise comparisons against the 0.75 mg/kg group but no reported overall test across all three groups. The p-values are unadjusted, and a multiplicity plan is not reported. The original sample-size justification and full statistical plan are also not reported in the registry record.

The number listed in each arm is 40, but the record does not report the number with measured outcomes, exclusions after randomization, reasons for missing data, or the method used to address missingness. It does not identify an analysis population or say whether an adjusted model was used. These gaps limit assessment of how representative the outcome summaries are of all randomized participants.

The registry records quadruple masking but does not identify the masked roles or describe how masking was maintained. It also does not report allocation-generation or concealment details. For safety, serious adverse event counts and deaths are listed, but the observation period, event definitions, and ascertainment procedures are not reported. The safety counts therefore cannot characterize risk beyond the information in the record.

The trial compares doses only; no non-ketamine arm is listed. Its posted results cannot determine how these dose groups compare with another treatment or with no ketamine. The endpoint is measured at 30 minutes, and additional follow-up outcomes are not reported in the registry record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Nebulized Sub-dissociative Dose Ketamine for Treating Pain — NCT03909607.
• Registry record last updated 2022-06-15; status last verified 2022-04.
• Results first posted 2022-05-03.
• 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

The registry record describes a completed, randomized, parallel-group, quadruple-masked Phase 4 trial with enrollment of 120 participants. It compares nebulized sub-dissociative ketamine at 0.75 mg/kg, 1.0 mg/kg, and 1.5 mg/kg, with 40 participants listed in each arm.

The primary endpoint is change in pain score from baseline to 30 minutes on an 11-point numeric rating scale. The reported group means are 4.0, 4.2, and 4.1, respectively. The two posted comparisons against the 0.75 mg/kg group have estimated mean differences of 0.2 and 0.1, with unadjusted p-values of 0.655 and 0.814. Both confidence intervals include zero.

The record lists zero serious adverse events and zero deaths in each arm. The direction of the change-score calculation, the analysis population, missing-data methods, multiplicity plan, original sample-size rationale, and detailed statistical plan are not reported in the registry record.