Dose Response of Ketorolac in Knee Arthroscopy: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Dose Response of Ketorolac in Knee Arthroscopy (NCT02181426), a randomized na study. The primary outcome is PACU Opiate Consumption.

2. Clinical Question

The clinical question is about the amount of opioid consumed during the PACU stay, rather than pain scores, recovery after discharge, or later opioid use. The recorded endpoint is total consumption expressed in intravenous morphine equivalents (IV MME), with the timeframe described as less than 1 day during the postoperative PACU stay. The trial therefore compares group averages for this specific period and measure.

The record identifies one primary outcome measure. It does not report secondary posted outcomes. The available comparisons are each against the 0 mg group; they do not establish how the active-dose groups compare directly with one another. This distinction matters when interpreting a dose-response question: the reported estimates describe separate differences from the comparator, not a formal test of a trend across all doses. Whether a dose-trend analysis was prespecified or conducted is not reported in the registry record.

3. Trial Design

The registry describes a randomized, double-masked, parallel-group study of ketorolac dose in outpatients undergoing knee arthroscopy. Four groups are listed: 0 mg, 7.5 mg, 15 mg, and 30 mg of ketorolac. The record gives enrollment as 112, and the primary-outcome description says 28 participants were randomized to each group. The study status is completed. Its start is listed as 2012-03 and its primary completion date as 2016-12-15. The sponsor is Medical University of South Carolina, and the phase is listed as NA.

Randomized allocation means the study assigned participants to groups rather than simply comparing groups chosen by patients or clinicians. Double masking indicates that the record classifies the study as masked at two levels, but it does not identify which participants, clinicians, outcome assessors, or other personnel were masked. The method used to generate the allocation sequence, concealment procedures, and masking details are not reported in the registry record.

A parallel-group design assigns participants to a group and compares outcomes across groups. Here, the primary outcome is a continuous measure summarized as a mean with standard error. The posted comparison estimates and confidence intervals are unadjusted mean differences against the 0 mg group. The record does not describe the trial’s original sample-size justification, prespecified statistical analysis plan, or any interim analyses. Those details should not be inferred from the enrollment or from the calculations used to illustrate planning for future studies.

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 study enrolled 112 patient with 28 patients randomized to each group.

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 PACU Opiate Consumption, measured over Less than 1 day (PACU stay in the postoperative period).

The primary endpoint is total opioid consumption during the postoperative stay in the post-anesthesia care unit (PACU), expressed in intravenous morphine equivalents (IV MME). The registry describes the timeframe as less than 1 day, corresponding to the PACU stay. Reporting consumption in morphine equivalents places opioid use from different sources on a common scale, so that total use can be represented with one continuous outcome.

This endpoint is used to quantify opioid administration during the defined recovery period. A mean summarizes the average consumption in each randomized group. The posted group means are 7.7 for 0 mg, 6.3 for 7.5 mg, 6.5 for 15 mg, and 5.0 for 30 mg. The unit is IV MME (mg). The registry also reports a standard error of 0.86 for each group. A standard error describes the precision of an estimated mean; it is not the spread of individual participants’ values.

The endpoint is limited to opioid consumption during the PACU stay. It does not by itself describe pain intensity, side effects, opioid use after discharge, or longer-term recovery. Those outcomes are not among the posted primary results, and secondary posted outcomes are not reported in the registry record.

7. Results Posted in the Registry

• 7.5 mg of Ketorolac: mean 6.30 versus 7.70 on control; difference -1.40 (95% CI -3.78 to 0.98), standardized effect d = -0.31; z-test p = 0.250.
• 15 mg Ketorolac: mean 6.50 versus 7.70 on control; difference -1.20 (95% CI -3.58 to 1.18), standardized effect d = -0.26; z-test p = 0.324.
• 30 mg Ketorolac: mean 5.00 versus 7.70 on control; difference -2.70 (95% CI -5.08 to -0.32), standardized effect d = -0.59; z-test p = 0.026.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous, and the registry identifies the summary measure as a mean. In general, a mean is the arithmetic average of observed values in a group. It gives a concise description of the group’s central level of opioid consumption, but it does not show how individual values are distributed. A mean can be influenced by unusually high or low values, so information about the distribution and variability can be useful when assessing a continuous outcome.

What does the standard error describe?

The registry reports a standard error of 0.86 for each group mean. In general, the standard error describes how precisely a sample mean estimates a population mean, given the observed variability and sample size. It is not the standard deviation of individual participants’ consumption. A standard deviation describes spread among individual observations; a standard error describes uncertainty in an estimated mean. The registry does not provide group standard deviations in the outcome summary.

The distinction matters because the posted outcome summaries and comparisons concern average consumption, not individual-level variation. The comparison calculations report a pooled standard deviation of 4.551. In general, a pooled standard deviation combines variability estimates across groups for a comparison. The registry record does not describe a separate sponsor analysis or provide participant-level data with which to examine the distribution, influential observations, or assumptions behind that pooled estimate.

How should a mean difference be read?

A mean difference subtracts the comparator group mean from the other group mean. The posted contrasts are -1.4 for 7.5 mg, -1.2 for 15 mg, and -2.7 for 30 mg, each relative to 0 mg. A negative value indicates that the estimated mean in the ketorolac group is lower on the measured outcome. The unit remains IV MME (mg). These are unadjusted comparisons; they do not account for covariates or other factors in a model.

For general interpretation, a confidence interval represents a range of values compatible with the data and the statistical procedure used. Its width indicates precision: narrower intervals indicate more precise estimates, while wider intervals indicate greater uncertainty. If an interval for a mean difference includes zero, the data are compatible with no difference under that procedure, as well as with some differences on either side of zero. An interval entirely below zero is consistent with a lower mean in the comparison group. These statements describe statistical compatibility, not the probability that a particular effect is true.

What do the p-values add?

The reported p-values are unadjusted: 0.25 for 7.5 mg, 0.324 for 15 mg, and 0.026 for 30 mg. In general, a p-value describes how unusual results at least as incompatible with a specified null hypothesis would be if that null hypothesis and the test assumptions held. It is not the probability that the null hypothesis is true, and it does not quantify the clinical importance of a difference. The p-values accompany the estimated differences and confidence intervals; they should not replace consideration of the estimates’ size and precision.

There are three comparisons against the same 0 mg group. When multiple hypotheses are tested, the chance of at least one apparently unusual result can increase if each test is considered on its own. Statistical approaches can address multiplicity, but the registry record does not report a correction or identify a prespecified strategy for interpreting these comparisons together. Thus the 30 mg p-value should be read as unadjusted, and not as evidence that a multiplicity-controlled analysis reached the same conclusion.

What is not documented about the analysis?

The registry identifies the outcome as a mean and gives standard errors, differences, confidence intervals, and unadjusted p-values. It does not report the statistical test used to obtain the comparisons, whether model assumptions were checked, how missing outcome values were handled, or which participants were included in the analysis. It also does not report whether any covariate adjustment, transformation, or sensitivity analysis was performed. These omissions do not establish that such analyses were absent; they mean that they are not reported in the registry record.

In general, random assignment supports comparison of groups as assigned, but the interpretation also depends on how outcomes were collected and how participants with missing data were handled. An analysis population might include all randomized participants or a defined subset; the record does not specify one. The posted summaries therefore support description of the reported groups and unadjusted contrasts, but they do not permit independent assessment of the analysis population or the robustness of results to alternative methods.

10. Confidence Intervals and Precision

The comparisons are reported with confidence intervals around the mean differences. In general, a confidence interval conveys the precision of an estimate by showing a range of values that are compatible with the data under the method used. A wider interval signals greater uncertainty about the size and direction of the difference. It is not a guarantee that the true value lies within the interval, nor is it a range of individual participants’ outcomes.

For 7.5 mg versus 0 mg, the estimated difference is -1.4 and the interval crosses zero. For 15 mg versus 0 mg, the estimated difference is -1.2 and its interval also crosses zero. These intervals do not rule out no mean difference, and they also allow values on either side of zero. The corresponding unadjusted p-values are 0.25 and 0.324. The evidence for the size and direction of those differences is therefore imprecise.

For 30 mg versus 0 mg, the estimated difference is -2.7 and the interval is entirely below zero. Its unadjusted p-value is 0.026. The interval still represents uncertainty about the size of the difference, and its interpretation should account for the fact that three comparisons are reported without a documented multiplicity adjustment. The record does not provide a multiplicity-adjusted interval.

Each group has 28 participants in the primary-outcome description, and the reported standard error for each mean is 0.86. These details provide context for the uncertainty, but they do not remove it. The registry does not report a prespecified precision target or the original sample-size rationale, so it is not possible to judge the estimates against a documented target precision.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm for 80% power and participants per arm for 90% power. They are not total participants across all groups and are not counts of events. The planning illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses the observed effect as a reference and considers detecting 100%, 75%, or 50% of that effect. The trial’s own original design assumptions are not reported in the registry record.

For the 7.5 mg comparison, planning for 100% of the observed effect gives 166 participants per arm for 80% power and 223 for 90% power; planning for 75% gives 295 and 395, and planning for 50% gives 664 and 889. For 15 mg, the corresponding figures are 226 and 303 for 100%, 402 and 538 for 75%, and 904 and 1,209 for 50%. For 30 mg, they are 45 and 60 for 100%, 80 and 107 for 75%, and 179 and 239 for 50%.

In plain terms, 80% power means that, under the stated planning assumptions and if the target effect is the true effect, the design would have an 80% chance of detecting it using the planned test criterion. The 90% column describes the analogous chance at 90% power. Smaller target effects require more participants because they are harder to distinguish from random variation. The curve represents this same relationship between target effect size and required participants. These figures 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 = -1.400; pooled standard deviation σ = 4.551.
2. n = 2 × (1.96 + 0.842)² × 4.551² / -1.400² = 165.9, rounded up to 166 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 <- 4.5506922550311                     # 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(2181426)
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 = 166 (80% power), 223 (90% power)
 75% of observed effect: n per arm = 295 (80% power), 395 (90% power)
 50% of observed effect: n per arm = 664 (80% power), 889 (90% power)
power.t.test: 166.8 
Simulated power at n = 166 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 registry lists one primary outcome measure and three posted comparisons, each contrasting an active ketorolac dose with 0 mg. Their p-values are unadjusted. When several comparisons are interpreted together, multiplicity can make an apparently unusual result more likely to occur by chance across the family of tests. Methods such as adjusting the significance threshold or using a hierarchical testing plan can address this issue, but the registry record does not report whether any method was prespecified or used. The 30 mg comparison should therefore be understood as an unadjusted result, not as a documented multiplicity-controlled finding.

The registry reports no secondary posted outcomes and lists zero analyses. This does not establish what analyses were conducted outside the registry entry; it means that additional analysis details are not reported in the registry record. The record also does not describe a dose-trend test, direct comparisons between active doses, or an analysis plan for the primary outcome.

Missing outcome data and the analysis population are also not described. The registry does not say whether every randomized participant contributed an endpoint value, how missing values were handled, or whether participants were analyzed according to their assigned group. It does not identify an intention-to-treat, per-protocol, or other analysis population. These details matter because missingness and exclusions can affect the comparability created by randomization.

The record gives group summaries, standard errors, unadjusted differences, confidence intervals, and p-values, but does not describe covariate adjustment, model diagnostics, sensitivity analyses, or the exact statistical test. These methods are not reported in the registry record. The absence of these details limits assessment of analytic choices; it does not show that any particular method was or was not used.

14. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

The registry lists 28 participants at risk for serious adverse events in each dose group and records 0 participants affected in every group. It also lists 28 at risk for other adverse events in each group and records 0 affected in every group. No serious adverse-event terms are listed. These are the posted counts for the recorded categories and groups.

Deaths are marked as not reported in the registry record; they should not be interpreted as zero. Zero recorded events in these group summaries does not establish that no events occurred outside the registry’s reporting scope, nor does it show how events were collected or classified. The record does not provide further details about adverse-event definitions, surveillance, or the time period used for safety ascertainment. The counts should therefore be read as registry-reported results, not as a complete account of all possible safety outcomes.

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

The posted results show lower mean PACU opioid consumption in each ketorolac group than in the 0 mg group. The estimated differences are -1.4 for 7.5 mg, -1.2 for 15 mg, and -2.7 for 30 mg, measured in IV MME (mg). The intervals for the 7.5 mg and 15 mg comparisons cross zero, while the interval for 30 mg is below zero. The unadjusted p-values are 0.25, 0.324, and 0.026, respectively.

This pattern describes the reported group averages; it does not by itself establish a dose-response relationship. Each comparison is against 0 mg, and there is no reported formal trend test or direct comparison among the active doses. The 30 mg result is an unadjusted comparison among three contrasts, and the registry record does not report a multiplicity adjustment. Its statistical interpretation should retain that qualification.

The results do not establish equivalence for the comparisons whose intervals cross zero. An interval that includes zero can reflect uncertainty, and it does not show that the groups are the same. Likewise, a lower mean in the 30 mg group does not determine the clinical importance of the difference. The registry record does not report a threshold for a clinically important change in PACU opioid consumption.

The endpoint is limited to total opioid consumption during the PACU stay. The results do not answer questions about pain, opioid use after discharge, longer-term recovery, or outcomes not posted in the registry. Safety interpretation is also limited to the recorded event counts; deaths are not reported in the registry record, and further ascertainment details are absent. These results describe the available registry findings and their precision, rather than providing medical advice or a general conclusion about treatment.

16. Why This Trial Matters Statistically

This trial is statistically instructive because it reports a continuous endpoint, group means and standard errors, and separate comparisons against a shared comparator. Readers can distinguish the observed averages from the estimated mean differences and see that the uncertainty differs in interpretation across comparisons. The results illustrate why an estimate, its confidence interval, and its p-value should be considered together rather than treating a single test result as a complete account.

The comparisons also raise a common issue in multi-group studies: several contrasts may be reported, while the record does not describe a plan for multiplicity. A result that looks notable in one unadjusted comparison needs to be interpreted in the context of the other comparisons and the analysis plan. Here, the 30 mg contrast has an interval below zero and an unadjusted p-value of 0.026, whereas the other two intervals cross zero. The registry does not report a joint test or a dose-trend analysis.

The planning illustrations offer another statistical lesson. Sample-size requirements depend on the effect a future study aims to detect: planning for a smaller fraction of the observed effect requires more participants per arm. These figures are planning scenarios based on stated assumptions, not evidence that the original trial had a particular power target or that its design was justified by those calculations.

Finally, registry results are easier to evaluate when analysis populations, missing-data handling, outcome distributions, and safety ascertainment are documented. Those details are not reported in the registry record. Their absence limits the conclusions that can be drawn from summary statistics alone, even when the reported estimates are straightforward to describe.

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 registry record leaves several trial-specific details unreported. It does not describe the method used to generate or conceal random allocation, who was masked, or how masking was maintained. Although the study is labeled double-masked, the roles covered by that label are not specified. The original sample-size justification and any interim analyses are also not reported in the registry record.

The primary outcome is summarized by group means and standard errors, but the registry does not provide group standard deviations, participant-level data, or descriptions of the outcome distribution. The comparison results include a pooled standard deviation, but the record does not explain its derivation or report checks of statistical assumptions. The exact test and any covariate adjustment are not reported in the registry record.

There are three unadjusted comparisons against the same control group, and no multiplicity approach is described. The record does not report a formal dose-trend analysis or direct comparisons between active doses. Missing data and the analysis population are also not described, so it is not possible to assess from the registry entry whether every randomized participant contributed to the primary outcome or how any missing values were handled.

The outcome is restricted to PACU opioid consumption during a period described as less than 1 day. Secondary outcomes are not posted. Adverse-event summaries report zero affected for the listed serious and other event categories, but details of collection and follow-up are not given; deaths are not reported in the registry record. These limitations constrain interpretation to the outcomes and analyses that are recorded.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Dose Response of Ketorolac in Knee Arthroscopy — NCT02181426.
• Registry record last updated 2018-09-21; status last verified 2018-08.
• Results first posted 2018-06-08.
• 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 completed study, titled Dose Response of Ketorolac in Knee Arthroscopy, is registered as NCT02181426. It is described as randomized, double-masked, and parallel-group, with four ketorolac dose groups: 0 mg, 7.5 mg, 15 mg, and 30 mg. Enrollment is listed as 112, with 28 participants per group in the primary-outcome description. The sponsor is Medical University of South Carolina.

The primary outcome is total opioid consumption during the postoperative PACU stay, measured in IV MME (mg). Mean consumption was 7.7 in the 0 mg group, 6.3 in the 7.5 mg group, 6.5 in the 15 mg group, and 5.0 in the 30 mg group. The comparison against 0 mg for 30 mg has an interval below zero and an unadjusted p-value of 0.026; the other two comparison intervals cross zero.

The registry does not report secondary posted outcomes, multiplicity handling, missing-data methods, or analysis-population details. Safety summaries list zero affected for serious and other adverse events in each group; deaths are not reported in the registry record.