Subcutaneous Ketamine for Postoperative Pain Relief in Rwanda: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Subcutaneous Ketamine for Postoperative Pain Relief in Rwanda (NCT02514122), a randomized phase 2, phase 3 study. The primary outcome is Postoperative Pain as Measured on a 11-point Numerical Rating Scale.

2. Clinical Question

The clinical question is about pain ratings over the early postoperative period, rather than a single rating at one specified moment. The record describes an average of twice daily pain scores and compares the assigned treatment groups. It also lists hallucination as a secondary outcome. The registry record does not give a more detailed description of who was eligible, how participants were selected, or the clinical circumstances of the operations.

The posted arm summaries report a mean score of 3.5 for ketamine and 4.9 for saline. Since lower values on the stated scale correspond to less reported pain, those posted summaries place the ketamine-arm mean lower. The interpretation of that contrast must also account for the different statistical results reported in the registry record: the summary-statistic recalculation and the sponsor's own analysis do not match. The sponsor's analysis takes precedence when interpreting the trial's reported analysis.

3. Trial Design

The registry classifies this as a randomized, parallel-group trial with quadruple masking and phases listed as Phase 2 and Phase 3. The brief description calls it a randomized double blind control trial. These are the descriptions recorded for the trial; further details about how randomization was generated, how assignments were concealed, or which trial roles were masked are not reported in the registry record.

The trial status is completed. The record lists a start date of 2015-06 and a primary completion date of 2015-07. Enrollment was 61. The sponsor is the University of Saskatchewan, and the title situates the study in Rwanda. The registry record does not give additional information about the number or type of participating sites.

The comparison was between subcutaneous ketamine and subcutaneous saline. The ketamine description specifies 1mg/kg after surgery, again the evening after surgery, and every 12 hours thereafter for 5 injections in total. The saline description specifies 0.02cc/kg on the same schedule, also for 5 injections in total. The record lists both interventions as drugs.

The reported primary outcome is average pain measured with an 11-point numerical rating scale. Its timeframe is the average of twice daily ratings from the end of surgery until 60 hours postoperative. Arm summaries include 30 participants assigned to ketamine and 29 assigned to saline. The registry record does not explain why those counts differ from each other or how missing outcome observations, if any, were handled.

The registry lists 2 outcome measures and 2 analyses, and identifies hallucination as a secondary outcome. More complete protocol information, including planned analysis populations and any prespecified interim analyses, is not reported in the registry record. The record also does not report the trial's original sample-size assumptions or justification.

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

Reasons for not completing this 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.

6. Primary Endpoint

The registry lists the primary outcome as Postoperative Pain as Measured on a 11-point Numerical Rating Scale, measured over The average of twice daily pain scores, from end of surgery until 60 hours postoperative..

The primary endpoint is postoperative pain, expressed as the average of twice daily pain scores collected from the end of surgery until 60 hours postoperative. The instrument is an 11-point numerical rating scale: 0 represents no pain and 10 represents worst pain imaginable. The registry describes the endpoint as a mean and identifies standard deviation as the measure of spread in the arm summaries.

Using an average across ratings is one way to represent pain over a period of postoperative recovery, rather than relying only on a rating at a single time. The scale gives participants a common ordered range for expressing their pain intensity. Treating the reported score as a continuous measure permits a comparison of group means, which is the form of the posted arm summaries and the recalculated mean difference.

This endpoint describes reported pain scores; it is not a direct measure of every aspect of postoperative recovery or of treatment safety. The registry record does not provide the precise timing of each rating beyond twice daily, the rules for forming an individual's average, or details about what happened when a rating was unavailable. The sponsor analysis names final values, while the primary outcome description names an average over the stated timeframe. How those descriptions correspond is not explained in the registry record.

7. Results Posted in the Registry

• Saline: mean 4.90 versus 3.50 on control; difference 1.40 (95% CI 0.63 to 2.17), standardized effect d = 0.93; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The outcome is a continuous score, and the registry reports means and standard deviations for the two randomized arms. A mean describes the arithmetic average of the scores in a group. A standard deviation describes how spread out individual scores are around that group mean. Neither quantity alone shows the full distribution of scores, and similar means can coexist with different patterns of individual responses.

What does a mean difference express?

A mean difference puts the groups' averages on the original outcome scale. In this trial, the scale ranges from 0 to 10, with lower values representing less pain. The recalculation uses the posted arm means and expresses the contrast as saline minus ketamine: 4.9 minus 3.5 is reported as a mean difference of 1.4 units. This is an unadjusted contrast based on the group summaries; it does not adjust for participant characteristics or other variables.

The recalculation also uses the posted group sizes and standard deviations. Its interval and p-value are based on an unadjusted comparison of means. Such a calculation is useful for checking how the reported arm summaries relate to a simple two-group comparison, but it need not match an analysis using individual participant data, a different outcome definition, or other modeling choices. The registry record does not provide enough detail to identify the reason for the mismatch with the sponsor's analysis.

What does the reported t-test test?

The sponsor's listed method is a two-sided t-test. In general, a t-test compares group means while accounting for variability and sample size under its assumptions. A two-sided test considers departures in either direction, rather than testing only whether one group is higher or lower. The sponsor reports a mean difference of 0.83, a 95% confidence interval from 0.29 to 1.9, and p = 0.009. The record describes the analysis as using final values.

A test result is conditional on the analysis definition and assumptions. The registry record does not report whether the sponsor's comparison was adjusted, which participants were included in that analysis, or how missing values were treated. It also does not explain whether the final values represent the same average endpoint defined in the primary outcome description. Those details matter for reproducing the reported analysis and understanding why it differs from the summary-statistic recalculation.

Why can a confidence interval and p-value be useful together?

A p-value gives a measure of how unusual the observed data, or data more extreme, would be under a null hypothesis and the test's assumptions. It does not describe the probability that the null hypothesis is correct. A confidence interval gives an estimate of the range of effect values that remain reasonably compatible with the data and method. The interval also conveys the uncertainty and direction associated with the estimated contrast. In this trial, both the recalculated and sponsor-reported intervals are above zero, but the estimates and interval endpoints differ.

Statistical evidence and clinical importance are distinct questions. A small p-value alone does not tell readers whether the magnitude is important to patients, and a confidence interval does not define a threshold for clinical importance unless such a threshold is specified. A threshold for meaningful change is not reported in the registry record. The scale's endpoints describe its range, but they do not supply a clinical-importance threshold.

Why does over-dispersion matter in general?

Over-dispersion is a general concern when observed variability is greater than a statistical model assumes. If a model understates variability, estimated uncertainty can be too small, which may make intervals narrower and tests appear more decisive than warranted. This trial's primary outcome is reported as a continuous measure with standard deviations, and the record does not report a model that explicitly addresses over-dispersion. Over-dispersion is more commonly discussed for count or binary outcomes, where a model may assume a particular relationship between the mean and variance; it should not be presumed to be present for these pain scores.

The sample-size planning assumptions use a normal approximation. In general, a normal approximation simplifies planning by using an assumed sampling distribution for the estimated contrast. It is an assumption for the planning illustration, not a description of the actual distribution of participant scores. The registry record does not report whether distributional assumptions were assessed in the sponsor's analysis.

What is the role of the recalculation?

The recalculated estimate is a simple, unadjusted check based on the posted summary statistics. It helps readers compare the numerical arm summaries with a conventional mean-difference calculation. It is not an alternative sponsor result, does not incorporate unavailable participant-level information, and should not be treated as a replacement for the sponsor's analysis. The registry record flags a discrepancy, so the sponsor's own analysis takes precedence in reporting the trial's stated analysis. The reason for the difference is not reported in the registry record.

Finally, statistical methods cannot answer questions that the outcome data do not cover. The registry record does not report an analysis plan with enough detail to establish the planned handling of multiplicity, missing observations, or analysis populations. Such information is needed to assess whether the reported statistical test corresponds to the originally intended analysis and how robust its interpretation is to alternative choices.

10. Confidence Intervals and Precision

The sponsor-reported 95% confidence interval for the mean difference runs from 0.29 to 1.9. The recalculated 95% confidence interval runs from 0.632 to 2.168. A confidence interval expresses uncertainty around an estimate under the method used to construct it. In repeated applications of the same method under its assumptions, intervals constructed this way have the stated coverage property; for an individual trial, the interval is not a probability statement that the true effect lies within the observed endpoints.

Both intervals are reported as lying above zero, but their endpoints and estimates differ. The recalculated estimate is 1.4 units and the sponsor's estimate is 0.83. This difference between analyses means that precision should not be assessed by looking at one interval in isolation: readers also need to know which analysis generated it and whether its outcome definition and participants match the primary endpoint. That reconciliation is not reported in the registry record.

Interval width reflects sampling uncertainty under the selected method, but it does not capture every source of uncertainty. It does not automatically account for bias, measurement limitations, missing outcomes, or an analysis that differs from the prespecified plan. Those issues are not resolved by the interval's nominal confidence level. The registry record does not report the original analysis plan or enough detail to evaluate all such possibilities.

The posted standard deviations, 1.4 for ketamine and 1.6 for saline, describe variability in the observed arm scores. The interval estimates uncertainty in a group contrast, which is a different quantity. The number of participants contributing to a particular sponsor analysis is not reported separately from the posted arm counts. The discrepancy between the estimates therefore limits how confidently the intervals can be linked to the same estimand.

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 illustrations based on the observed effect, not the trial's original design justification. The planning assumptions listed in the registry record are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect considered in each planning scenario is a stated fraction of the observed effect.

For planning for 100% of the observed effect, the figures are 19 participants per arm for 80% power and 25 participants per arm for 90% power. For planning for 75% of the observed effect, they are 33 participants per arm for 80% power and 43 participants per arm for 90% power. For planning for 50% of the observed effect, they are 73 participants per arm for 80% power and 97 participants per arm for 90% power.

In plain language, the 80% power column gives the estimated participants per arm under the stated assumptions for a design with an 80% chance of detecting the chosen effect if that effect were the true one. The 90% power column gives the corresponding estimate for a design targeting a 90% chance. These are planning concepts, not guarantees about what any particular trial will find. The smaller the effect a study aims to detect, the more participants it generally needs under otherwise similar assumptions; the listed scenarios follow that pattern.

These figures are planning illustrations, not observed power for this completed trial. The registry record does not report the original sample-size assumptions, the target effect used when the trial was designed, or the original design justification. Therefore, the planning figures should not be used to infer whether the trial was adequately designed according to its original plan.

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 = 1.400; pooled standard deviation σ = 1.502.
2. n = 2 × (1.96 + 0.842)² × 1.502² / 1.400² = 18.1, rounded up to 19 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 <- 1.4                      # observed difference in means
sigma <- 1.5015781172171                     # 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(2514122)
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 = 19 (80% power), 25 (90% power)
 75% of observed effect: n per arm = 33 (80% power), 43 (90% power)
 50% of observed effect: n per arm = 73 (80% power), 97 (90% power)
power.t.test: 19.1 
Simulated power at n = 19 per arm: 0.796 (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. Analyses Reported by the Sponsor

The registry reports the sponsor's own analysis as a two-sided t-test of mean difference in final values. It gives an estimate of 0.83, a 95% confidence interval from 0.29 to 1.9, and p = 0.009. The unadjusted recalculation from the posted arm means, standard deviations, and participant counts gives a mean difference of 1.4, a 95% confidence interval from 0.632 to 2.168, and p < 0.001.

These are not identical estimates or inferential results. The recalculation is a simple comparison using summary statistics; the sponsor's result is the trial's reported analysis. Since the registry record flags a discrepancy, the sponsor's own analysis takes precedence. The recalculation remains a check on the relationship between the posted group summaries and an unadjusted mean comparison, rather than a correction to the sponsor's result.

The registry record does not explain the source of the discrepancy. It does not report whether the sponsor analysis used a different analysis population, adjustment, endpoint definition, or method for handling missing observations. The primary outcome is described as an average across twice daily scores, whereas the analysis is described as using final values. The record does not reconcile those descriptions. Without that information, readers should keep the two results distinct and avoid assuming they estimate precisely the same quantity.

14. Multiplicity, Missing Data and Analysis Populations

The registry record lists 2 outcome measures and 2 analyses. The primary outcome is average postoperative pain, and hallucination is listed as a secondary outcome. However, a complete statistical analysis plan describing how multiple outcomes or analyses were handled is not reported in the registry record. It is therefore not possible to determine whether the reported p-values were adjusted for multiple testing, whether a hierarchy among outcomes was specified, or whether all planned analyses are represented in the posted results.

Multiplicity is a general statistical concern when several hypotheses are tested. Considering more outcomes or analyses can increase the chance of at least one apparently notable result, depending on how the tests are related and how the analysis is conducted. Adjustment or prespecified interpretation rules can address that issue, but whether either was used in this trial is not reported in the registry record. The listed p-values should consequently be read as results for their reported analyses, not as evidence that any multiplicity issue was resolved.

The handling of missing data is also not reported in the registry record. The arm summaries include 30 participants for ketamine and 29 for saline, but the record does not state how many participants were randomized to each arm, whether each participant contributed all scheduled pain ratings, or how an individual's average was formed when a rating was unavailable. The primary outcome is described as an average of twice daily pain scores, while the sponsor analysis is described as using final values; the relationship between these descriptions is not clarified.

The analysis population is not specified. The record does not say whether the sponsor analysis followed an intention-to-treat approach, included only participants with outcome data, or used another population definition. It also does not explain how protocol deviations were handled. These are important for assessing whether the comparison preserves the randomized groups and for reproducing the reported estimate.

Interim analyses and stopping rules are not reported in the registry record. Nor is a detailed statistical analysis plan available in the registry record described for this trial. These omissions do not establish that such methods were or were not used; they mean that their status cannot be determined from the registry record.

15. 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 non-serious adverse event terms

The serious adverse-event figures report 0 serious adverse events among 30 participants at risk in the ketamine group and 0 among 29 participants at risk in the saline group. The record also reports 0 deaths in each group. No serious adverse-event terms are listed. These counts describe what is posted for the listed groups; they are not a guarantee that no serious event could occur in other participants or settings.

The adverse-event record separately gives other adverse events: 11 affected participants in the ketamine group and 0 in the saline group, with 30 listed as at risk in each group for that category. These are not serious adverse-event counts and should not be combined with the serious-event figures. The registry record does not provide detailed event descriptions in the registry record, nor does it describe severity, timing, relatedness, or how these events were collected.

The number of participants at risk is the denominator for interpreting the listed counts. Small groups and limited follow-up can leave uncertainty about uncommon events. The trial's primary outcome timeframe extends until 60 hours postoperative, but the adverse-event collection timeframe is not reported in the registry record. The posted safety counts therefore provide a limited account of observed events, not a complete assessment of risks.

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

The registry's posted arm summaries show mean pain scores of 3.5 for ketamine and 4.9 for saline, on a scale where lower scores indicate less pain. The sponsor-reported analysis gives a mean difference of 0.83, with a 95% confidence interval from 0.29 to 1.9 and p = 0.009. These findings describe the trial's recorded comparison of postoperative pain scores. They do not establish effects beyond the measured endpoint or timeframe.

The recalculation from the arm summaries yields a different mean difference, confidence interval, and p-value. Because the registry record flags a discrepancy, the sponsor analysis takes precedence as the trial's reported analysis. The recalculation is useful for understanding what a simple unadjusted comparison of the posted summaries produces, but the registry record does not explain why it differs from the sponsor result. The mismatch limits a straightforward reading of a single effect estimate as an unambiguous summary of the analysis.

The result does not by itself establish clinical importance. A statistical difference and a difference that patients consider meaningful are not the same question. A threshold for clinically meaningful change is not reported in the registry record. The record also does not include detailed information on eligibility, analysis populations, missing observations, or a full statistical plan, all of which affect how broadly and precisely the result can be interpreted.

The posted serious adverse-event counts are zero in both listed groups, and the death counts are also zero. The record separately lists other adverse events, with 11 affected participants in the ketamine group and 0 in the saline group. These figures are limited by the available event descriptions, follow-up information, and group sizes. They should not be read as a complete account of safety.

Overall, the record documents a randomized comparison and reports a difference in average postoperative pain scores, alongside a discrepancy between the sponsor analysis and a summary-statistic recalculation. The data do not settle questions about unreported outcomes, longer-term effects, generalizability, clinical importance, or the detailed nature of adverse events.

17. Why This Trial Matters Statistically

This trial is statistically instructive because it places a randomized comparison alongside both arm-level summary statistics and a sponsor-reported analysis. Readers can see how a simple unadjusted mean comparison relates to the group means, yet the resulting estimate and interval do not match the sponsor's reported result. The discrepancy makes clear why numerical consistency checks should be distinguished from the analysis selected and reported by the trial sponsor.

The record also illustrates the importance of keeping outcome definitions aligned. The primary endpoint is described as an average of twice daily pain scores over the postoperative period, while the sponsor's analysis is described as using final values. These descriptions may or may not refer to the same calculated outcome; the registry record does not say. Precise definitions of what was measured and analyzed are central to making statistical results reproducible and interpretable.

The sample-size illustrations also show how planning depends on the effect a study aims to detect. The listed participant counts increase as the planning effect becomes smaller, under the stated assumptions. These are not observed power calculations and do not reveal the original design rationale, which is not reported in the registry record. That distinction prevents a post hoc planning exercise from being mistaken for evidence about the trial's original design quality.

Finally, the limited details about missing data, analysis populations, multiplicity, and adverse-event ascertainment demonstrate that statistical results depend on more than estimates and p-values. A registry record can report a clear numerical result while leaving important methodological context unreported. Recognizing those boundaries is part of responsible statistical interpretation.

18. Limitations

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

Several trial-specific limitations in interpreting the results arise from what the registry record does not report. Detailed eligibility criteria and participant characteristics are not reported, so the enrolled population cannot be characterized beyond the study context and arm counts. The record also does not describe the surgical procedures or provide details about study sites. This limits assessment of how well the findings may apply to other patient groups or settings.

The primary endpoint is described as an average of twice daily pain ratings through 60 hours postoperative, whereas the sponsor analysis is described as a comparison of final values. The registry record does not explain whether these refer to the same endpoint or how participant-level averages were calculated. The timing of individual ratings and the handling of unavailable ratings are also not reported. These omissions make the exact estimand and data handling difficult to reconstruct.

The sponsor result and the unadjusted summary-statistic recalculation differ, and the registry record does not provide a reason. The sponsor analysis takes precedence, but the difference remains a limitation in interpreting the posted results. Details about adjustment, analysis population, missing-data methods, and protocol deviations are not reported. The record does not provide enough information to reproduce the sponsor estimate.

The registry record does not report the original sample-size justification or assumptions, a full statistical analysis plan, interim analyses, stopping rules, or multiplicity procedures. It lists hallucination as a secondary outcome but detailed results for that outcome are not reported among the registry entries available for this analysis. Adverse-event information is also limited: the record gives counts but not detailed event descriptions, relatedness, severity, or the event-collection timeframe.

These limitations do not demonstrate that a method was omitted or that an unreported event did not occur. They identify areas where the registry record does not supply enough information for independent assessment. The findings should therefore be understood as a report of the posted trial results, with these uncertainties kept in view.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Subcutaneous Ketamine for Postoperative Pain Relief in Rwanda — NCT02514122.
• Registry record last updated 2018-11-09; status last verified 2018-11.
• Results first posted 2018-11-09.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT02514122 is a completed randomized parallel-group trial titled “Subcutaneous Ketamine for Postoperative Pain Relief in Rwanda.” The record lists Phase 2 and Phase 3, quadruple masking, enrollment of 61, a start date of 2015-06, and a primary completion date of 2015-07. The sponsor is the University of Saskatchewan.

The trial compared subcutaneous ketamine with subcutaneous saline. The primary outcome was average postoperative pain on an 11-point numerical rating scale, from the end of surgery until 60 hours postoperative. Posted mean scores were 3.5 for ketamine and 4.9 for saline. The sponsor analysis reported a mean difference of 0.83, a 95% confidence interval from 0.29 to 1.9, and p = 0.009. The unadjusted recalculation differs; the sponsor's analysis takes precedence.

Hallucination is listed as a secondary outcome. The serious adverse-event and death counts are zero in both listed groups; other adverse events were also reported. The registry record does not report several details needed to fully reconstruct the analysis, including the original design assumptions, missing-data methods, and analysis population.