A Comparison of Proprietary Formulations of Oral Ketamine + Aspirin and Oral Ketamine Alone for Musculoskeletal Pain: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Comparison of Proprietary Formulations of Oral Ketamine + Aspirin and Oral Ketamine Alone for Musculoskeletal Pain (NCT04860804), a randomized phase 4 study. The primary outcome is Change in Pain Score at 60 Minutes.

2. Clinical Question

3. Trial Design

This was a phase 4, randomized, open-label, parallel-group clinical trial. The registry record lists the study status as completed, an enrollment of 60, a start date of 2021-04-22, and a primary completion date of 2021-11-30. Participants were assigned to one of two oral-drug groups: a proprietary formulation of 0.5mg/kg ketamine plus 324mg aspirin, or a proprietary formulation of 0.5mg/kg ketamine alone. The record describes no masking, meaning the trial is listed as open-label.

The primary outcome was change in pain score at 60 minutes. The record lists 28 participants in each arm for this outcome. It does not explain how those outcome counts relate to the enrollment of 60, or report the characteristics of participants included in the outcome summaries. The registry record also does not report further details about how randomization was generated or implemented, whether allocation was concealed, or the clinical setting beyond the stated adult emergency-department population with acute musculoskeletal pain.

One primary outcome measure is listed, and no secondary outcomes are posted. Although the outcome measure is reported by arm and a between-group comparison is posted, the record lists no analyses. It does not describe a prespecified statistical analysis plan, the analysis population, or any adjustments beyond the reported comparison. These omissions limit what can be established about how the posted summary statistics were produced. The study design supports a comparison of the two assigned groups, but the registry information alone does not establish the details needed to assess every aspect of conduct or analysis.

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 Score at 60 Minutes, measured over 60 minutes.

The primary endpoint is change in pain score from baseline to 60 minutes, measured using the numeric rating scale (NRS). The registry describes the NRS as an 11 item Likert scale ranging from 0, meaning no pain, to 10, meaning very severe pain, with 5 indicating moderate pain. The endpoint is expressed in units on that scale, and the registry identifies the summary measure as a mean with standard deviation.

Change from baseline is used to describe how a participant’s score at a follow-up time differs from their starting score. In general, this can focus a comparison on movement over the treatment period rather than only on scores at the later time. However, the registry record does not specify the subtraction order or otherwise define the sign convention for the change score. Therefore, the reported positive values and the between-group difference can be described numerically, but the direction should not be interpreted as improvement or worsening without that definition.

The 60-minute measurement is the stated primary time point. The registry record does not describe why this particular time point was selected, whether other measurements were collected but not posted, or how baseline and follow-up pain scores were obtained. The outcome is a patient-reported rating, and the open-label design means participants and study personnel were not masked to group assignment. These features are relevant context for interpreting a self-reported endpoint, but the record does not quantify their influence on the observed values.

7. Results Posted in the Registry

• OK Group: mean 4.01 versus 2.18 on control; difference 1.83 (95% CI 0.73 to 2.93), standardized effect d = 0.87; z-test p = 0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The posted primary outcome is continuous: it is a numeric pain-score change summarized as a mean and standard deviation. The registry reports one group mean for each arm and a mean difference comparing the OK Group with the AOK Group. The displayed comparison is unadjusted, and the record lists no analyses. The statistical concepts below explain how these kinds of summaries are generally interpreted; they do not establish details of an analysis plan that the registry does not report.

What does a mean summarize?

In general, the mean is the arithmetic average of observed values. It provides a compact description of the center of a group’s measurements, but it does not show how individual participants’ values were distributed. Here, the arm-level means are 2.18 for the AOK Group and 4.01 for the OK Group. Because the endpoint is a change score and the registry does not define its sign convention, the means should be read as reported numerical summaries rather than labeled as pain reduction or worsening.

The standard deviation describes the spread of individual measurements around a group mean. The reported standard deviation is 2.1 in each arm. It is not the same as the standard error, which describes the estimated variability of a sample statistic such as a mean. In general, standard errors are used to quantify the sampling uncertainty of an estimate, while standard deviations describe variability among observations. The record does not provide participant-level values, so the shape of the outcome distribution and the presence of unusual observations cannot be assessed from the group summaries alone.

What does the mean difference represent?

A between-group mean difference compares the two group means on the endpoint’s scale. The posted comparison is oriented as OK Group relative to AOK Group: 4.01 versus 2.18, producing a reported mean difference of 1.83 units. That orientation communicates which group’s reported mean is numerically higher. It does not settle whether a higher change score reflects a beneficial or unfavorable direction because the registry does not state how change was calculated. The comparison is unadjusted, so the record does not indicate that the estimate accounts for covariates or other factors.

Random assignment is generally used to create groups that are comparable in expectation, helping support a causal comparison of assigned interventions. But that general property does not verify how randomization was implemented in a particular trial. The registry identifies the study as randomized, but details such as sequence generation and allocation concealment are not reported in the registry record. In addition, the trial is described as open-label, so participants and study personnel were not masked to assignment. For a self-reported endpoint, awareness of assignment is relevant context; the registry record does not measure or quantify any resulting influence.

How should the p-value be read?

The unadjusted p-value is 0.001. In general, a p-value is calculated under a null hypothesis and model assumptions; it indicates how unusual the observed data, or more extreme data, would be if those assumptions and the null hypothesis held. It is not the probability that the intervention has no effect, and it does not indicate the size or importance of the difference. Interpretation also depends on which comparison and analysis were planned. The registry record does not provide the full statistical plan, so it is not possible to verify whether this was the prespecified test or whether other analyses were considered.

Multiplicity refers generally to testing more than one outcome, comparison, subgroup, or time point. When many tests are performed, the chance of finding at least one apparently notable result can increase unless the analysis plan accounts for that testing. One primary measure is listed, and no secondary measures are posted, but the registry record does not establish how many analyses were planned or conducted. It does not report a multiplicity adjustment. Thus, the posted unadjusted p-value should be described as such, without assuming that all possible testing has been accounted for.

What do the interval and model assumptions add?

A confidence interval gives a range of values that are compatible with the observed data under a specified statistical procedure and its assumptions. It conveys uncertainty around the estimated mean difference and helps readers assess the range of effect sizes consistent with the analysis. The reported 95% interval is 0.73 to 2.93 units. General interpretation of such an interval relies on the method’s assumptions; the registry record does not state the exact interval procedure or the assumptions checked.

For a continuous outcome, an analysis may rely on assumptions about the sampling distribution and variability of measurements. In general, substantial skew, outliers, or unequal variances can affect the suitability of some methods. The two reported standard deviations are both 2.1, but this alone does not establish the full distributions or validate any model. The registry record does not report diagnostic checks, transformations, a robust method, or handling of outliers. No analysis details are posted beyond the group summaries and comparison, so the statistical method cannot be reconstructed fully from the record.

The record also does not describe missing-data handling or identify the population used for the primary analysis. Those details matter because incomplete outcome data can affect group summaries and comparisons, depending on why measurements are unavailable and how the analysis treats them. With the available information, the appropriate reading is limited to the reported 60-minute summaries and unadjusted comparison, accompanied by the stated uncertainty and the reporting gaps.

10. Confidence Intervals and Precision

The reported mean difference is 1.83 units, comparing the OK Group with the AOK Group. Its 95% confidence interval extends from 0.73 to 2.93 units. The interval conveys uncertainty about the estimated contrast: values across that range are compatible with the observed data under the interval method and its assumptions. It is not a range containing 95% of individual participants’ changes, and it does not indicate that every plausible value is equally likely.

The interval is entirely on the positive side of zero, consistent with the posted comparison’s numerical direction: the OK Group’s reported mean change is higher. As with the point estimate, the registry record does not define whether positive change means an increase or decrease in pain. The interval therefore describes precision in the numerical difference, not the clinical direction or desirability of that difference.

Precision is also distinct from clinical importance. The registry record does not provide a threshold for a meaningful difference on the NRS or explain how such a threshold would be interpreted. The interval alone cannot establish whether the contrast is important to patients. The unadjusted p-value is 0.001, but statistical evidence against a null model does not replace consideration of the estimate’s scale, uncertainty, and clinical context.

Each arm-level outcome summary includes 28 participants. The record does not explain how these counts relate to the enrollment of 60 or report the number and handling of missing measurements. That absence limits assessment of how representative the reported estimates are of all enrolled or randomized participants. The confidence interval quantifies uncertainty as calculated for the posted comparison; it does not account for reporting limitations that cannot be evaluated from 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, not total events. They are an illustration based on the observed mean difference, rather than the trial’s original design calculation. The stated 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 to a stated fraction of the observed effect. The registry record does not report the trial’s own original sample-size assumptions or justification.

For each effect-size scenario, the 80% power column gives the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting that specified effect under the stated assumptions, if the assumptions hold. The 90% power column gives the corresponding per-arm planning estimate for a 90% chance. Power is a property of a planned design under specified assumptions; it is not a probability that a particular result is true.

The displayed scenarios use 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For 100% of the observed effect, the estimate is 21 participants per arm for 80% power and 28 for 90% power. For 75% of the observed effect, the estimates are 37 and 50 participants per arm. For 50% of the observed effect, they are 83 and 111 participants per arm. Smaller effects need more participants to detect under the same assumptions, which is why the planning estimates rise as the target effect becomes smaller. These are planning illustrations, not observed power.

The calculation is anchored to the effect seen in this trial and should not be treated as an independent estimate of the effect that a future study would observe. The registry record does not state that these were the assumptions used to design or enroll the trial. Differences in the target effect, outcome variability, analysis method, or other design choices would change planning requirements; the registry record does not provide a trial-specific justification to evaluate.

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 = 1.830; pooled standard deviation σ = 2.100.
2. n = 2 × (1.96 + 0.842)² × 2.100² / 1.830² = 20.7, rounded up to 21 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 <- 1.83                      # observed difference in means
sigma <- 2.1                     # 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(4860804)
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 = 21 (80% power), 28 (90% power)
 75% of observed effect: n per arm = 37 (80% power), 50 (90% power)
 50% of observed effect: n per arm = 83 (80% power), 111 (90% power)
power.t.test: 21.7 
Simulated power at n = 21 per arm: 0.782 (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 lists one primary outcome measure: change in pain score at 60 minutes. It lists no secondary outcomes and no analyses. This describes what is posted in the registry record; it does not establish that no other outcomes or analyses were planned, collected, or considered. The record does not report a statistical analysis plan, analysis populations, or whether any adjustment for multiple testing was prespecified or performed.

Multiplicity is a general concern when statistical testing covers multiple outcomes, comparisons, time points, subgroups, or analytic choices. If many tests are examined, a nominal p-value can overstate the strength of evidence for a finding unless the testing strategy is addressed. Here, the posted p-value is explicitly unadjusted. Because the record does not detail the full set of planned or conducted tests, it is not possible to determine whether multiplicity was relevant or how it was handled. The p-value should therefore be read as the unadjusted result for the posted comparison, not as evidence that all possible testing has been controlled.

The outcome summaries include 28 participants in each arm, while enrollment is listed as 60. The registry record does not explain the difference, state whether all randomized participants were included in the primary analysis, or report how missing outcomes were addressed. It also does not say whether the analysis followed assignment regardless of treatment received, or whether another analysis population was used. These are important distinctions when assessing how closely an analysis preserves the randomized comparison and how incomplete data may influence results.

In general, missing-data methods rely on assumptions about why measurements are missing and how the missing values relate to observed data. No such assumptions or methods are reported in the registry record. There is also no reported sensitivity analysis to show how alternative handling might affect the result. These omissions do not negate the posted estimates, but they constrain evaluation of their robustness and the scope of inference that can be drawn from them.

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.

The adverse-event record lists 28 participants at risk for serious adverse events in each group. It reports zero serious adverse events in the AOK Group and zero in the OK Group. It also reports zero other adverse events in each group and zero deaths in each group. No serious adverse-event terms are listed.

These are the counts posted in the registry record for the groups and at-risk totals shown. A count of zero means no event of that listed type was reported for those participants in this record; it does not establish that an event is impossible or that a larger or longer observation would produce the same counts. The record does not report further details about safety definitions, collection procedures, follow-up duration for adverse events, or whether events were assessed as related to an intervention.

The trial’s listed primary endpoint is a 60-minute pain-score change, and the registry record does not give a separate safety follow-up timeframe. Therefore, the adverse-event counts should be read alongside the limited safety information posted, without inferring more about duration or completeness of surveillance than the record states. These counts are descriptive and do not provide a basis for broad safety conclusions.

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

The result describes a short-term comparison of mean pain-score change at 60 minutes between two randomized groups of adults presenting to an emergency department with acute musculoskeletal pain. The reported mean was 2.18 units in the AOK Group and 4.01 units in the OK Group, each based on 28 participants. The posted mean difference, oriented as OK Group relative to AOK Group, was 1.83 units, with a 95% confidence interval from 0.73 to 2.93. The unadjusted p-value was 0.001.

These values show a numerical difference between the posted group summaries. They do not, on their own, establish which group had a greater reduction in pain. The registry describes the endpoint as change from baseline but does not specify the sign convention. Nor does it state a threshold for a clinically meaningful difference. Accordingly, the result can be described statistically as a higher reported mean change in the OK Group, but its clinical direction and importance cannot be determined from the record alone.

The findings also do not resolve how the comparison would look at other times, in other populations, or in settings outside the stated adult emergency-department population with acute musculoskeletal pain. No secondary results are posted, and the registry record does not report longer-term outcomes. The open-label design is relevant context for a self-reported outcome, although the record does not establish what influence, if any, awareness of assignment had.

Important analysis details are absent: the registry record does not explain the difference between enrollment of 60 and outcome summaries of 28 participants per arm, report missing-data handling, identify the analysis population, or provide the full statistical plan. The posted estimate and interval are informative descriptions of the available summary comparison, but they cannot answer these unreported questions. They should not be expanded into a general claim about treatment effects beyond the population, measure, and time point recorded.

16. Why This Trial Matters Statistically

This trial illustrates why statistical interpretation needs more than a p-value. The reported mean difference of 1.83 units is paired with a 95% confidence interval from 0.73 to 2.93, giving a range of estimates compatible with the analysis rather than only a single point estimate. The unadjusted p-value of 0.001 is another summary, but it does not describe effect size, clinical importance, or the direction of change on the pain scale.

The endpoint’s sign convention is especially consequential. The registry reports change from baseline but does not define the order used to calculate it. Without that definition, even a clear numerical contrast cannot be translated confidently into which group had more improvement. This is a reminder that a statistical estimate must be interpreted using the outcome’s coding and measurement definitions, not only its magnitude or sign.

Reporting completeness also matters. Enrollment is listed as 60, while 28 participants per arm appear in the outcome summaries; the relation between these figures is not explained. The record does not report missing-data methods, analysis populations, or a full statistical plan. These details help readers assess how the estimates relate to the randomized sample and whether analytic choices may affect interpretation.

Finally, the study is randomized but open-label, and the endpoint is self-reported. Randomization is an important design feature for comparative inference, while lack of masking remains relevant context for measurement and conduct. The registry record does not quantify such effects. Considered together, the estimate, interval, design, endpoint definition, and reporting gaps show why careful statistical reading distinguishes what the posted results establish numerically from what remains uncertain.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

Several limitations specific to this trial follow from the registry information. The primary outcome is described as change from baseline, but the calculation’s sign convention is not stated. This prevents a clear interpretation of whether a higher reported change represents more or less pain. The record gives the NRS scale’s range and anchors but does not report a threshold for a clinically meaningful difference, so the practical importance of the 1.83-unit contrast cannot be assessed from the registry information alone.

The trial is listed as open-label, and the primary outcome is a self-reported pain score. Awareness of group assignment is therefore relevant context, but the record does not describe measures to address possible influence or quantify its effects. Details of randomization and allocation procedures are also not reported in the registry record.

The enrollment is 60, while the primary outcome summaries include 28 participants in each group. The record does not explain this difference, identify the analysis population, describe missing observations, or state how missing data were handled. It also does not provide participant characteristics, baseline pain summaries, or the full statistical analysis plan. The posted summaries do not permit independent assessment of these aspects.

Only one outcome measure is listed, and no secondary results or analyses are posted. The record does not establish whether additional outcomes, time points, or analyses were planned or conducted, or whether the unadjusted p-value was adjusted for any multiplicity. Safety reporting lists zero events for the posted categories, but further information about definitions and follow-up is not reported. Together, these gaps narrow interpretation to the posted short-term outcome comparison and descriptive safety counts.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: A Comparison of Proprietary Formulations of Oral Ketamine + Aspirin and Oral Ketamine Alone for Musculoskeletal Pain — NCT04860804.
• Registry record last updated 2024-07-17; status last verified 2024-06.
• Results first posted 2023-04-07.
• 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

The registry record describes a completed phase 4, randomized, open-label, parallel-group trial with enrollment of 60. It compared a proprietary oral formulation of 0.5mg/kg ketamine plus 324mg aspirin with a proprietary oral formulation of 0.5mg/kg ketamine alone in adults presenting to an emergency department with acute musculoskeletal pain.

The sole posted primary outcome is mean change in pain score at 60 minutes on the NRS. The outcome summaries include 28 participants per group. The reported mean difference, comparing the OK Group with the AOK Group, is 1.83 units, with a 95% confidence interval from 0.73 to 2.93 and an unadjusted p-value of 0.001. The registry record does not define the sign convention for change.

No secondary outcomes or analyses are posted. The adverse-event record reports zero serious events, zero other events, and zero deaths in each group. The relationship between enrollment and outcome counts, missing-data handling, analysis populations, and the full statistical plan are not reported in the registry record.