Multimodal Analgesia With Acetaminophen vs. Narcotics Alone After Hip Arthroscopy: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Multimodal Analgesia With Acetaminophen vs. Narcotics Alone After Hip Arthroscopy (NCT03510910), a randomized phase 4 study. The primary outcome is Patient Satisfaction.

2. Clinical Question

The key statistical question is how the mean satisfaction score recorded for each group compares, and how much uncertainty surrounds that estimated difference. The recorded means are 8.48 for acetaminophen with reduced Percocet and 8.83 for Percocet only. The unadjusted difference is reported as 0.35 points, defined as the Percocet-only mean minus the mean in the acetaminophen group. The confidence interval spans values on either side of no difference, so the estimate is not precise enough to distinguish a positive difference from no difference using that interval alone.

This outcome addresses satisfaction at the specified postoperative time, not every part of the study’s stated purpose. Although the summary says the study compares pain scores and narcotic consumption, no secondary outcome results are posted. The registry record therefore does not give numerical results for those outcomes. A satisfaction score cannot, by itself, establish how much pain participants experienced or how much narcotic medication they consumed.

3. Trial Design

The registry identifies the study as randomized, phase 4, and completed. Its summary describes a prospective comparison at a single center between acetaminophen with a reduced quantity of Percocet and Percocet only after hip arthroscopy. Masking is listed as none. The registry’s model field says single-group, while the results are organized into two groups and the allocation is listed as randomized. These entries do not align cleanly; the record does not explain the model designation, so it is not possible to resolve that inconsistency from the registry information alone.

The enrollment figure is 100. The posted primary-outcome results report 40 participants in the acetaminophen-with-reduced-Percocet group and 40 in the Percocet-only group. These are the numbers attached to the outcome summaries, not a full accounting of enrollment, randomization, or follow-up. The reason the outcome results include fewer participants than the enrollment figure, and whether the remaining participants were excluded, lacked measurements, or were handled in another way, is not reported in the registry record.

The study start is recorded as 2018-04-10, primary completion as 2019-12-01, and status as completed. The registry summary describes both pain-management options as standard of care and says both groups receive aspirin for DVT prophylaxis and celecoxib for heterotopic ossification prophylaxis. The registry does not provide full medication schedules in the arm descriptions, and detailed procedures for allocation concealment, participant flow, adherence, or follow-up are not reported in the registry record.

The posted results include the primary satisfaction outcome and adverse-event counts. Although the summary names pain and narcotic consumption as study objectives, no secondary outcome results are posted. The registry reports no posted analysis records. The original statistical analysis plan, the sample-size rationale for the trial, and any interim analysis procedures 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

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 Patient Satisfaction, measured over 7 days post-surgery.

The primary endpoint is patient satisfaction 7 days post-surgery. Satisfaction is reported on a Likert-type scale of 1-10, with higher values indicating higher satisfaction. The registry treats the outcome as continuous and reports a mean and standard deviation for each group. The observed mean is 8.48 in the acetaminophen-with-reduced-Percocet group and 8.83 in the Percocet-only group.

Satisfaction is a patient-reported measure. It captures participants’ overall evaluation of their pain-management experience at the stated time, which may be useful alongside measures focused more narrowly on pain intensity or medication use. The study summary names pain and narcotic consumption as objectives, but satisfaction is the registered primary outcome with posted numerical results. No numerical pain-score or narcotic-consumption results are posted, so satisfaction should not be treated as a substitute for those outcomes.

Using a mean makes it possible to describe the average score in each group and estimate a mean difference. That summary does not display the full distribution of individual scores. The registry does not report the number of participants at each response value, a median, or other distributional details. It also does not report a rationale for analyzing this scale as a continuous measure. Those details matter when assessing how fully the group averages represent participants’ varied responses.

7. Results Posted in the Registry

• Percocet Only: mean 8.83 versus 8.48 on control; difference 0.35 (95% CI -0.32 to 1.02), standardized effect d = 0.23; z-test p = 0.308.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is a continuous measure in the registry’s statistical classification, and its summaries are means with standard deviations. A mean describes the average score, while a standard deviation describes how spread out participants’ scores are around that average. These statistics provide a compact account of each group, but they do not show every individual response or the shape of the score distribution.

What does the mean difference represent?

The comparison is expressed as the mean score for Percocet only minus the mean score for acetaminophen with a reduced quantity of Percocet. The group means are 8.83 and 8.48, respectively, and the reported difference is 0.35. A positive difference under this stated ordering means the observed mean is higher in the Percocet-only group. Reversing the subtraction order would reverse the sign, so the direction of comparison is essential to reading the estimate.

A mean difference retains the original scale: its unit is score points on the satisfaction scale. This can make it easier to relate the estimate to the endpoint itself, although the registry does not state what size of difference participants or clinicians would consider important. The reported confidence interval is an interval estimate for the mean difference. It covers zero and runs from a negative value to 1.023, meaning that the data do not pin down the direction of the difference with high precision.

What do variability and standardization add?

The standard deviations are 1.52 and 1.55. They describe variation among recorded scores in each group and contribute to the uncertainty in the estimated difference. The reported pooled standard deviation is 1.535, combining variability across groups for the standardized comparison. The standardized effect is 0.228; it expresses the difference in relation to pooled variability rather than in satisfaction-score points. Standardized effects can help describe magnitude on a scale that is less tied to the original measurement unit, but they do not replace the original-scale estimate or give a clinical importance threshold.

In general, group means and standard deviations are most informative when a continuous-outcome summary is an appropriate representation of the data. Since the endpoint uses a Likert-type scale, the registry’s choice to classify it as continuous is relevant context. The registry does not report the distribution of individual scores or a justification for this analytic treatment. It is therefore not possible to assess from the posted summaries whether the scores are concentrated at particular response values or whether unusual observations influence the means.

How should the p-value be read?

The unadjusted p-value is 0.308. In general, a p-value measures how compatible data are with a specified null model, assuming that model and the analysis conditions hold. It is not the probability that the null model is true, and it does not measure the probability that the observed result occurred “by chance” in a broad, assumption-free sense. It also does not measure the size or importance of a difference. Here, the p-value is considered with the estimated mean difference and its confidence interval, rather than as a stand-alone verdict.

The comparison is an unadjusted recalculation from posted summary statistics. The registry lists 0 posted analyses, so the exact analysis method used by the investigators is not reported in the registry record. Details such as a prespecified test, adjustments for baseline variables, the handling of missing outcome scores, and the analysis population are also not reported. The recalculation should not be mistaken for a complete account of the trial’s original analysis plan.

Why can over-dispersion matter in general?

In general, over-dispersion means the observed variability is greater than a statistical model assumes. If a method underestimates variability, its standard errors can be too small, producing intervals that are too narrow and tests that appear more decisive than warranted. If variability is modeled appropriately, uncertainty estimates better reflect the observed spread. The registry reports standard deviations for this outcome, but does not state that over-dispersion was assessed or that a model requiring such an assessment was used. There is no basis in the registry record to claim that over-dispersion occurred in this trial.

The main methodological reading is therefore straightforward but bounded: the posted summaries provide group averages, within-group variability, and an unadjusted estimate of their difference. The confidence interval and p-value quantify uncertainty under the recalculation, while important details about the investigators’ original statistical methods are not reported in the registry record.

10. Confidence Intervals and Precision

Precision concerns how narrowly the data estimate the group difference. The mean difference is 0.35 points, with a confidence interval extending from a negative value to 1.023. Because zero lies within that interval, the estimate is compatible with no mean difference as well as with a range of differences in either direction. The interval is not a declaration that every value inside it is equally likely, and it is not a range containing a fixed proportion of individual participants’ scores.

In general, a confidence interval reflects both the estimated effect and its uncertainty under the statistical method used. A narrower interval indicates a more precise estimate; a wider interval leaves more possible values consistent with the data. The posted interval makes clear that the observed difference of 0.35 is not estimated with enough precision to settle its direction. The p-value of 0.308 conveys related information about the unadjusted comparison but does not replace the interval’s description of plausible effect sizes.

The reported standard errors are 0.240 for the acetaminophen group mean and 0.245 for the Percocet-only group mean. The group sizes attached to the primary outcome are 40 in each group. These summaries help describe the uncertainty in the individual group means; the interval for the between-group difference is the more direct measure for the comparative question.

Precision is not the same as clinical importance. The registry does not specify a minimum important difference in satisfaction, so the interval cannot be classified as excluding or including a clinically meaningful threshold based on the record. The interval also does not account for unreported concerns such as missing outcomes or the choice of analysis population. Those reporting gaps limit how completely its nominal precision can be evaluated.

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 display is a planning illustration based on the observed effect, not a report of the trial’s original sample-size rationale. For this continuous outcome, its figures are participants per arm, not total events. The calculation assumes a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. It uses the stated fraction of the observed effect as the effect to detect. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the number of participants per arm the planning calculation estimates would be needed to have an 80% chance of detecting the chosen effect under those assumptions, if that effect is the true one and the model assumptions hold. The 90% power column gives the corresponding planning count for a 90% chance. These are planning probabilities, not guarantees for a future study and not properties that can be assigned to the observed result.

For planning at 100% of the observed effect, the illustration gives 302 participants per arm for 80% power and 405 participants per arm for 90% power. At 75% of the observed effect, it gives 537 and 719 participants per arm, respectively. At 50% of the observed effect, it gives 1,208 and 1,617 participants per arm. Smaller effects require more participants under these assumptions because they are harder to distinguish from random variation.

The curve is a visual representation of how the planning sample size changes as the target effect changes; it should be read as part of the same assumed planning exercise, not as a record of actual enrollment. This is not observed power. It does not show the probability that the completed trial detected its true effect, and it cannot turn the observed p-value into a retrospective probability of success.

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 = 0.350; pooled standard deviation σ = 1.535.
2. n = 2 × (1.96 + 0.842)² × 1.535² / 0.350² = 302.0, rounded up to 302 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 <- 0.35                      # observed difference in means
sigma <- 1.53507328815272                     # 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(3510910)
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 = 302 (80% power), 405 (90% power)
 75% of observed effect: n per arm = 537 (80% power), 719 (90% power)
 50% of observed effect: n per arm = 1,208 (80% power), 1,617 (90% power)
power.t.test: 302.9 
Simulated power at n = 302 per arm: 0.801 (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 5 outcome measures, but no secondary outcome results are posted. The study summary names pain scores and narcotic consumption among the objectives, yet the available numerical outcome result is for patient satisfaction. The registry record therefore does not allow comparison of results across all stated objectives or assessment of whether the posted primary result was consistent with secondary outcomes.

When a study evaluates multiple outcomes or makes multiple statistical comparisons, multiplicity can increase the chance of at least one result appearing notable under chance variation. In general, a prespecified approach can address how multiple comparisons are interpreted or adjusted. The registry does not report whether multiplicity was considered, whether any adjustment was planned, or which analyses were designated as primary beyond identifying patient satisfaction as the primary outcome. The absence of this information does not establish that no plan existed; it means the plan is not reported in the registry record.

The registry lists 0 posted analysis records. The statistical analysis plan, the exact inferential test used by the investigators, covariate adjustment, and definitions of analysis populations are not reported in the registry record. It is not stated whether the analysis followed an intention-to-treat approach or another population definition. The comparison available for interpretation is an unadjusted recalculation from the posted group summaries.

Missing-data handling is also not reported. The primary outcome summaries include 40 participants per group, while total enrollment is 100. The record does not explain the difference between those figures or describe whether any outcome measurements were missing, whether participants were excluded from the endpoint analysis, or how incomplete data were handled. Without participant flow and missing-data details, the influence of missing outcomes on the estimate cannot be assessed.

Interim analyses, stopping rules, and the protocol’s original analysis assumptions are not reported in the registry record. These gaps matter because they can affect how results are interpreted, but they should not be filled in by assumption. The posted data support a descriptive and unadjusted comparison of the recorded satisfaction summaries, not a reconstruction of undocumented trial procedures.

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 registry reports serious adverse events for 40 participants at risk in each group, with 0 affected in the acetaminophen-with-reduced-Percocet group and 0 affected in the Percocet-only group. It also reports other adverse events for 40 participants at risk in each group, with 0 affected in each. Deaths are recorded as 0 in both groups. No serious adverse-event terms are listed.

These figures describe what the registry reports for the participants counted at risk. A zero count means no events of the listed category were recorded in those groups in this registry entry; it does not establish that no such events could occur or that the approaches have identical safety profiles. Event counts are especially limited as a basis for comparisons when the number of participants observed is modest, and the registry does not provide event-specific detail or a follow-up period for these safety summaries.

The record does not report how adverse events were defined, how actively they were sought, their severity apart from the serious-event classification, or whether events led to treatment changes. The absence of listed serious-event terms should be read as absence of terms in the posted record, not as proof that every possible harm was assessed and ruled out. These counts describe registry reporting and should not be interpreted as medical advice.

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

The posted result answers a narrow question: what were the average satisfaction scores 7 days post-surgery in the two groups with recorded primary outcomes, and how uncertain is their unadjusted difference? The mean was 8.48 for acetaminophen with a reduced quantity of Percocet and 8.83 for Percocet only. The difference was 0.35 points in the direction of a higher observed mean in the Percocet-only group. The interval extends across zero, and the unadjusted p-value is 0.308, so the result does not precisely establish the direction or size of a group difference.

This does not demonstrate that the groups are equivalent. Equivalence requires a prespecified margin defining differences small enough to count as practically equivalent, together with an analysis designed to assess that question. No equivalence or noninferiority margin is reported in the registry record. A result that does not provide strong evidence of a difference is not the same as proof that there is no meaningful difference.

Nor does the result establish how the groups differed in pain or narcotic consumption. Those outcomes appear in the study summary, but no secondary outcome results are posted. Satisfaction is a distinct patient-reported endpoint, and its mean cannot stand in for unreported pain scores or medication-use measures. The record also does not state what difference in satisfaction would be important to participants.

The available information has further limits: the primary endpoint records include 40 participants per group while enrollment is 100, and the reason for that difference is not reported. Missing-data methods, analysis populations, detailed analysis procedures, and the original sample-size justification are not reported in the registry record. The posted adverse-event counts are zero for serious and other events in both groups, but they do not establish that risks are absent.

Overall, the registry supports a description of close observed satisfaction means with appreciable uncertainty. It does not support claims about all outcomes named in the study summary, equivalence, or the absence of risk.

16. Why This Trial Matters Statistically

This trial is statistically interesting because a randomized comparison is described, while the registry’s model field is labeled single-group and the results themselves contain two arms. That mismatch makes careful attention to the actual posted outcome structure important. The group summaries permit a direct comparison of satisfaction, but they do not resolve the inconsistent design metadata or provide a complete account of participant flow.

The difference between an observed estimate and its precision is also central. The mean difference is 0.35 points, but the confidence interval spans zero and reaches 1.023 at its upper end. Focusing only on the direction of the point estimate would overstate what these data establish. Considering the interval and the p-value together makes the uncertainty visible without treating a nonsignificant result as proof of equivalence.

The distinction between the registered primary endpoint and the study summary’s broader objectives matters as well. Patient satisfaction has a posted result, but the stated interests in pain and narcotic use do not have posted secondary results. This limits the conclusions that can be drawn from the registry entry and illustrates why readers should match each claim to the outcome actually reported.

Finally, planning illustrations based on the observed effect can communicate how demanding a future study might be under stated assumptions, but they are not the original trial’s design rationale and are not retrospective evidence of power. The registry’s missing analysis and missing-data details also show why numerical results should be read alongside documentation of methods and participant flow. The statistical value of this record lies in showing an estimate and its uncertainty, while making clear which questions remain unanswered by the posted data.

17. Limitations

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

The primary outcome summaries include 40 participants in each group, whereas the registry reports enrollment of 100. The registry does not explain the difference. Without participant flow, it is not possible to determine how many participants were randomized, received the assigned approach, completed follow-up, or contributed to this outcome, beyond the counts attached to the reported summaries.

The entry identifies the allocation as randomized and masking as none, but the model is listed as single-group despite results for two groups. The record does not explain this inconsistency. It also does not report allocation concealment, adherence, crossovers, or other trial-conduct details. These omissions restrict assessment of how the comparison was implemented.

The primary outcome is satisfaction on a Likert-type scale treated as continuous. The registry does not report the distribution of individual responses, a justification for this treatment, or a threshold for a meaningful difference. As a result, the means and standard deviations do not describe all features of the response patterns or establish the practical importance of the estimated difference.

The available comparison is an unadjusted recalculation from summary statistics, and the registry lists no posted analysis records. The original analysis plan, missing-data procedures, analysis population, multiplicity approach, and original sample-size justification are not reported in the registry record. The posted primary endpoint is satisfaction; despite the study summary’s stated interest in pain and narcotic use, no secondary results are posted. Adverse-event reporting gives counts but not detailed definitions, event-specific follow-up, or ascertainment procedures.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Multimodal Analgesia With Acetaminophen vs. Narcotics Alone After Hip Arthroscopy — NCT03510910.
• Registry record last updated 2021-01-07; status last verified 2020-12.
• Results first posted 2021-01-07.
• 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, randomized, unmasked, phase 4 study of analgesia after hip arthroscopy, with 100 participants enrolled. It compares acetaminophen with a reduced quantity of Percocet against Percocet only. The record’s model field is single-group, although the posted outcome results are presented for two groups; that inconsistency is not explained.

The primary endpoint is satisfaction 7 days post-surgery on a Likert-type scale of 1-10. The recorded means are 8.48 and 8.83, and the unadjusted mean difference is 0.35, with a confidence interval that includes zero and an unadjusted p-value of 0.308. The endpoint summaries include 40 participants per group. No secondary outcome results are posted, and serious and other adverse-event counts are 0 in each group.

The registry does not report the original sample-size justification, detailed analysis plan, missing-data procedures, or analysis populations. The reported sample-size figures are planning illustrations based on the observed effect, not the trial’s original design assumptions.