Dose-Ranging Study for Prolonged Postoperative Analgesia in Subject Undergoing Total Knee Arthroplasty: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Dose-Ranging Study for Prolonged Postoperative Analgesia in Subject Undergoing Total Knee Arthroplasty (NCT00485693), a randomized phase 2 study. The primary outcome is Area Under the Curve (AUC) of the Numeric Rating Scale (NRS) With Activity (NRS-A) Pain Intensity Scores Through Postoperative Day 4.

2. Clinical Question

3. Trial Design

This was a phase 2, multicenter, randomized, double-blind, parallel-group, active-control, dose-ranging study. Its stated purpose was to evaluate the safety, efficacy, and comparative systemic bioavailability of a single local-infiltration administration of SKY0402 for prolonged postoperative analgesia in subjects undergoing total knee arthroplasty. The registry status is completed. The study start is recorded as 2007-06, and primary completion as 2009-08.

Participants were assigned to Bupivacaine HCl or one of four SKY0402 dose groups. Bupivacaine HCl is described as Marcaine 0.25% with epinephrine 1:200,000, while the SKY0402 arm descriptions refer to various dosage levels and a single administration. Specific SKY0402 dose amounts are not reported in the registry record. The posted primary-outcome group sizes are 34 for Bupivacaine HCl, 28 for SKY0402 Low Dose, 25 for SKY0402 Low-mid Dose, 26 for SKY0402 High-mid Dose, and 25 for SKY0402 High Dose.

The primary outcome was a continuous measure: the area under the curve of Numeric Rating Scale pain intensity with activity through postoperative day 4, with a timeframe of 0 to 96 hours. The posted arm summaries report means and standard deviations. The registry also lists a secondary safety outcome concerning participants with adverse events or serious adverse events through 30 days. Two outcome measures are posted, but no analyses are listed in the registry record. Details of randomization procedures, allocation concealment, the blinding procedure, dose amounts, and the protocol's planned statistical methods are not reported in the registry record.

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 Area Under the Curve (AUC) of the Numeric Rating Scale (NRS) With Activity (NRS-A) Pain Intensity Scores Through Postoperative Day 4, measured over 0 to 96 hours.

The primary endpoint is the area under the curve (AUC) of Numeric Rating Scale pain intensity with activity (NRS-A) through postoperative day 4. The timeframe is 0 to 96 hours, and the unit is units on a scale*hours. At each assessment, the participant was asked to flex the involved knee to the maximum point possible and rate pain while bending it on a scale from 0, no pain, to 10, worst possible pain.

An AUC combines pain ratings across the stated time interval into a single summary. In general, this can represent both the magnitude of reported pain and how it changes over the observation period, rather than relying on one rating at one moment. The endpoint is therefore intended to characterize the accumulated activity-related pain experience over the early postoperative period. It does not, by itself, show the pattern of ratings at each assessment time, and the registry record does not report the exact assessment schedule or the method used to handle missing ratings when constructing the AUC.

The posted values are group means with standard deviations. A lower mean AUC corresponds to a lower accumulated score on this measure. The trial compares these group summaries for each SKY0402 dose with the Bupivacaine HCl control. The registry record does not provide a threshold for interpreting how large a difference would be clinically important, so the size of an observed mean difference should be read as a statistical contrast rather than as a demonstrated patient-important change.

7. Results Posted in the Registry

• SKY0402 Low Dose: mean 20.70 versus 20.40 on control; difference 0.30 (95% CI -2.09 to 2.69), standardized effect d = 0.06; z-test p = 0.806.
• SKY0402 Low-mid Dose: mean 19.50 versus 20.40 on control; difference -0.90 (95% CI -3.36 to 1.56), standardized effect d = -0.20; z-test p = 0.473.
• SKY0402 High-mid Dose: mean 18.80 versus 20.40 on control; difference -1.60 (95% CI -4.02 to 0.82), standardized effect d = -0.35; z-test p = 0.195.
• SKY0402 High Dose: mean 19.10 versus 20.40 on control; difference -1.30 (95% CI -3.47 to 0.87), standardized effect d = -0.32; z-test p = 0.240.

8. Statistical Interpretation

9. Statistical Methods Explained

What does the endpoint mean?

The primary endpoint is a continuous outcome: an AUC of activity-related pain-intensity ratings over 0 to 96 hours. A continuous outcome can take a range of numerical values, rather than belonging only to categories such as present or absent. Each participant's ratings across the observation period contribute to an accumulated score. In general, AUC is useful when the clinical question concerns experience over time, because a single summary can reflect the trajectory across the measurement window. It cannot show exactly when scores were higher or lower; that requires time-specific results, which are not reported in the registry record.

Why report means and standard deviations?

The registry reports the mean and standard deviation for each group. The mean is the arithmetic average of the observed AUC values in that group. The standard deviation describes how dispersed individual observations are around the group mean. It is not the same as the uncertainty around the group mean or around a difference between groups. The posted means are 20.4 for Bupivacaine HCl, 20.7 for Low Dose, 19.5 for Low-mid Dose, 18.8 for High-mid Dose, and 19.1 for High Dose. The corresponding standard deviations are 3.9, 5.4, 5.3, 5.3, and 4.4.

How should a mean difference be read?

Each comparison is expressed as the SKY0402 mean minus the Bupivacaine HCl mean. A positive value means the SKY0402 group had a higher average AUC; a negative value means it had a lower average AUC. Since lower accumulated pain ratings correspond to lower AUC, the sign gives the direction of the observed contrast, but not its clinical importance. The point estimate is only one estimate of the underlying difference. Its confidence interval communicates the range of values reasonably compatible with the data under the calculation's assumptions.

What does a confidence interval convey?

In general, a confidence interval expresses statistical uncertainty around an estimate. A narrower interval indicates greater precision, while a wider interval indicates less precision. It is not a range containing every participant's outcome, and it does not indicate that the true value has a particular probability of lying in the interval. In these comparisons, each interval includes zero. That means the posted data are compatible with no mean difference as well as with differences in either direction over the interval's span. The estimates should therefore be read with their intervals, not as exact effects.

What do the p-values convey?

In general, a p-value describes how unusual data at least as inconsistent with a specified null hypothesis would be if that hypothesis and the statistical model were correct. It does not give the probability that the null hypothesis is true, nor does it measure clinical importance. The unadjusted p-values for the four comparisons are 0.806, 0.473, 0.195, and 0.24. The registry record does not report the trial's planned inferential threshold or whether these comparisons were intended as confirmatory tests. The p-values should thus be understood as unadjusted recalculations, not as evidence of a prespecified decision rule.

Why does the dose-ranging design matter?

In general, a dose-ranging study compares multiple dose levels to explore how measured outcomes vary across them. Looking at the means can suggest whether a pattern is present, but a pattern in point estimates alone is not proof of a dose-response relationship. Variation within groups and uncertainty in the comparisons also matter. Here the group means do not move steadily in one direction across the listed dose levels. The registry record does not report a formal trend test, dose-response model, or the actual dose amounts, so the posted summaries cannot establish a dose-response curve.

How should the recalculations be understood?

The posted mean differences, confidence intervals, and p-values are unadjusted recalculations from the group summaries. They do not incorporate covariate adjustment or other features of a potential sponsor analysis. The discrepancy flag is false, and there is no sponsor analysis posted in the registry record. These recalculations are therefore useful for describing the contrast implied by the displayed means and variability, but they cannot substitute for an analysis plan or a full analysis using participant-level data.

What does variation among participants imply?

In general, variability within groups affects how precisely a group mean and a difference between means can be estimated. Greater spread in outcomes can make estimates less precise when group sizes are limited. The standard deviations reported for these groups range from 3.9 to 5.4, and the posted group sizes range from 25 to 34. Those figures contextualize why the estimated differences have uncertainty; they do not reveal whether the groups were balanced on baseline characteristics, whether all randomized participants contributed an endpoint, or how missing observations were handled. Those details are not reported in the registry record.

10. Confidence Intervals and Precision

The estimated mean differences are accompanied by 95% confidence intervals. For Low Dose, the interval is -2.091 to 2.691 around a difference of 0.3. For Low-mid Dose, it is -3.357 to 1.557 around -0.9. For High-mid Dose, it is -4.023 to 0.823 around -1.6. For High Dose, it is -3.466 to 0.866 around -1.3. Each interval includes zero, and each also spans values on both sides of zero.

In general, the interval indicates the precision of an estimated difference under the calculation's statistical assumptions. These intervals are wide enough that the point estimates should not be treated as exact. For example, the High-mid Dose point estimate is negative, but its interval includes both a negative range and a positive value. The same general caution applies to the other comparisons. The data do not pin down the direction of the mean difference with high precision.

Intervals are not ranges for individual participants' pain scores. They also do not account for every possible source of uncertainty: the registry record does not report the analysis population, handling of missing outcome data, or any adjustment for multiple comparisons. The reported intervals are attached to unadjusted recalculations, and no sponsor analysis is posted. Thus, the precision statements concern these calculated contrasts and should not be extended to unreported analyses or outcomes.

The sample sizes and standard deviations provide context for the intervals, but do not change their interpretation. A point estimate may be numerically above or below zero while remaining uncertain. The posted results are most informative when the means, differences, intervals, and the limitations of the registry's analysis details are considered together.

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 sample-size figures are planning illustrations based on the observed effect for each comparison, not the trial's original design assumptions. They give participants per arm, not a total number across arms. In general, the 80% power column describes the planned number of participants per arm for a design targeting an 80% chance of detecting the specified effect under the stated assumptions. The 90% power column describes the corresponding planning target for a 90% chance. These are design concepts, not probabilities that the posted trial result is correct.

The listed 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. For each comparison, the display gives planning figures for 100%, 75%, and 50% of the observed effect. The smaller the effect targeted for detection, the more participants per arm the illustration requires. The figures are not observed power.

The scale of these planning estimates depends on the observed contrast used as the starting point. For Low Dose, the figures range from 3,748 participants per arm for 80% power and 5,018 for 90% power when planning for 100% of the observed effect, to 14,992 and 20,070 when planning for 50% of it. For High-mid Dose, the corresponding figures are 128 and 171 at 100%, and 510 and 682 at 50%. These examples illustrate why planning numbers differ across comparisons: the observed effects differ in size. They are not evidence about how many participants the original trial intended to enroll, and the original design assumptions are not reported in the registry record.

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 = 0.300; pooled standard deviation σ = 4.635.
2. n = 2 × (1.96 + 0.842)² × 4.635² / 0.300² = 3,747.8, rounded up to 3,748 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 <- 0.300000000000001                      # observed difference in means
sigma <- 4.63546114210873                     # 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(485693)
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 = 3,748 (80% power), 5,018 (90% power)
 75% of observed effect: n per arm = 6,663 (80% power), 8,920 (90% power)
 50% of observed effect: n per arm = 14,992 (80% power), 20,070 (90% power)
power.t.test: 3748.8 
Simulated power at n = 3,748 per arm: 0.802 (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 trial has several active comparisons against the same Bupivacaine HCl control: four SKY0402 dose groups are included in the primary-outcome results. When multiple comparisons are considered, the chance of at least one apparently unusual result can increase if each is assessed separately without adjustment. In general, multiplicity procedures can control or otherwise address this issue, but they may also change the interpretation of estimates, intervals, and p-values. The registry record does not report whether the trial's original analysis plan specified a multiplicity adjustment, a testing hierarchy, or a primary dose comparison.

The comparisons posted with the group summaries are unadjusted recalculations. Their p-values should not be read as multiplicity-adjusted. No sponsor analyses are listed in the registry record, and no analysis population is identified for the primary outcome. It is not reported in the registry record whether the primary analysis followed an intention-to-treat, modified intention-to-treat, per-protocol, or another population definition.

The registry record does not report the amount or pattern of missing primary-outcome data, the approach to missing observations, or whether the AUC could be calculated when some ratings were absent. It also does not report details of any covariate adjustment, model diagnostics, interim analyses, or a prespecified inferential threshold for the primary endpoint. These omissions limit the ability to determine whether the recalculated comparisons reproduce the study's planned analysis.

The registry lists one secondary safety outcome concerning participants with adverse events or serious adverse events through 30 days. It does not provide a corresponding inferential analysis in the posted results. In general, secondary outcomes can contribute additional information, but their interpretation depends on how they were defined and analyzed. Such details, including any adjustment across outcomes, are not reported in the registry record. The absence of these details is a limit on interpretability, not evidence that a particular procedure was or was not used.

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 serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: pulmonary embolism (2.9%), bronchitis (2.9%), haematoma infection (2.9%), hypoxia (1.0%), respiratory depression (1.0%).

The registry reports serious adverse events for the Bupivacaine HCl and combined SKY0402 groups. In the Bupivacaine HCl group, 3 of 34 participants at risk were reported with a serious adverse event; in the SKY0402 group, 5 of 104 at risk were reported with a serious adverse event. Other adverse events were reported for 29 of 34 at risk in the Bupivacaine HCl group and 83 of 104 at risk in the SKY0402 group. The registry records 1 death in each group.

These are counts of participants reported as affected, not event rates calculated for comparison. They should not be treated as evidence of a causal relationship to study treatment: the registry record does not provide event attribution, timing, severity details for the other adverse events, or an adjusted safety comparison. The SKY0402 safety figures are combined across dose levels in the adverse-event record, so they do not provide dose-specific safety summaries.

The registry also lists pulmonary embolism, bronchitis, and haematoma infection at 2.9% each, and hypoxia, respiratory depression, and haematemesis at 1.0% each among the top serious-event terms. The record does not identify group-specific percentages for these terms in the posted listing. The secondary safety outcome is described as covering events through 30 days; additional information about ascertainment and event classification is not reported in the registry record.

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

The primary-outcome results describe mean activity-related pain AUC values over 0 to 96 hours for Bupivacaine HCl and four SKY0402 dose groups. The SKY0402 group means were 20.7, 19.5, 18.8, and 19.1, compared with 20.4 in the control group. The corresponding unadjusted mean differences range from 0.3 to -1.6. This is a description of the posted continuous outcome, not a complete account of each participant's experience or of pain at individual times.

The confidence intervals for all four unadjusted comparisons include zero. As a result, the posted estimates remain compatible with no mean difference and with values in either direction. The p-values are also unadjusted, and the registry record does not report whether a multiplicity procedure or another primary inferential strategy was planned. The results do not establish that one group had a reliably different mean AUC from the control group, nor do they establish equivalence. Demonstrating equivalence would require an appropriate prespecified margin and analysis, neither of which is reported in the registry record.

The sequence of group means does not show a steady change across the four dose levels. The High-mid Dose group has the lowest posted mean, but the registry record does not report a formal dose-response analysis or the actual dose amounts. A difference in the point estimates alone cannot establish that increasing dose caused a change in the endpoint.

The safety counts describe reported adverse events in the registry's categories and groups. They do not by themselves establish whether an event was caused by treatment, and the SKY0402 safety results are not separated by dose. The record does not report enough detail to make a comprehensive comparative safety assessment from these counts alone.

In general, trial interpretation depends on the design, outcome definition, uncertainty, analysis methods, and completeness of reporting. Here, randomized, double-blind, parallel-group, active-control design features are stated, but details of the original analysis plan, analysis population, missing-data handling, and multiplicity approach are not reported in the registry record. The posted results therefore support a careful account of observed averages and their imprecision, not a broad claim about treatment benefit, lack of benefit, or comparative safety.

16. Why This Trial Matters Statistically

This trial is statistically informative because it reports a continuous primary outcome across several randomized dose groups and an active control. The mean AUC captures accumulated activity-related pain ratings during the early postoperative period, while the standard deviations give a sense of within-group variability. Considering group means alone would conceal how uncertain the contrasts are; the confidence intervals show that the estimated differences are not precise enough to isolate a direction for any one comparison.

The dose-ranging structure also illustrates an important distinction between descriptive patterns and formal evidence. The group means vary across dose levels, but they do not move consistently in one direction. A dose-response claim requires more than ranking the means, particularly when each comparison has uncertainty and the original trend analysis is not reported in the registry record. The actual SKY0402 dose amounts are also not reported, limiting interpretation of the dose sequence.

There are four comparisons with the same control group, making multiplicity relevant to any inferential interpretation. The posted p-values are unadjusted recalculations, and the registry does not specify the original multiplicity strategy or complete analysis plan. This makes it important to distinguish the numerical comparisons from confirmatory conclusions based on a prespecified testing procedure.

The planning illustrations further show how the observed effect size influences the number of participants per arm needed in a future design under stated assumptions. Their figures are not observed power and are not a record of the original design rationale. Overall, the trial highlights why estimates, uncertainty, design structure, and reporting completeness all matter when interpreting clinical study results.

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 does not report the actual SKY0402 dose amounts, so the four dose labels cannot be translated into a quantitative dose scale. This limits interpretation of any apparent ordering among the group means. The means are also presented as summaries over the whole 0 to 96 hour interval; time-specific outcome results and the assessment schedule are not reported, so the time course cannot be evaluated from these summaries.

The primary-outcome comparisons are unadjusted recalculations based on posted summary statistics. The record lists no analyses and does not report the trial's original statistical plan, analysis population, missing-data approach, or multiplicity strategy. It also does not report a clinically important difference for the AUC measure. These omissions limit assessment of whether the estimates correspond to the intended primary analysis and how large a difference would matter to patients.

The adverse-event results combine SKY0402 dose groups, and the listed serious-event terms are not accompanied by group-specific percentages. Event attribution, detailed timing, and a comparative safety analysis are not reported in the registry record. The posted safety counts therefore do not allow a dose-specific evaluation or a causal interpretation.

The registry identifies the trial as multicenter and double-blind, but further operational details, including center-level results and the procedures used to maintain blinding, are not reported. Baseline characteristics and information about participants who did not contribute to the primary endpoint are also not reported in the registry record. These limitations do not negate the posted summaries, but they narrow the conclusions that can be drawn from them.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Dose-Ranging Study for Prolonged Postoperative Analgesia in Subject Undergoing Total Knee Arthroplasty — NCT00485693.
• Registry record last updated 2022-06-28; status last verified 2022-06.
• Results first posted 2013-08-06.
• 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

NCT00485693 is a completed phase 2, multicenter, randomized, double-blind, parallel-group, active-control dose-ranging study in subjects undergoing total knee arthroplasty. Enrollment was 138. The study compared a single local-infiltration administration of SKY0402 at four dose levels with Bupivacaine HCl, identified as Marcaine 0.25% with epinephrine 1:200,000.

The primary outcome was the mean AUC of activity-related Numeric Rating Scale pain intensity through postoperative day 4, over 0 to 96 hours. Posted group means ranged from 18.8 to 20.7 for the SKY0402 groups and were 20.4 for Bupivacaine HCl. All four unadjusted recalculated confidence intervals include zero. The registry also reports adverse-event counts through 30 days, but the SKY0402 safety results are combined across dose levels. The original analysis plan, missing-data methods, analysis population, and multiplicity approach are not reported in the registry record.