Opiates Prescribing for Knee Arthroscopies and ACL Reconstruction: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Opiates Prescribing for Knee Arthroscopies and ACL Reconstruction (NCT03876743), a randomized na study. The primary outcome is Numeric Pain Rating Scale (NPRS) Pain Score.

2. Clinical Question

The registry describes a randomized, single-masked, parallel-group study. The two knee arthroscopy groups differ in how an opiate prescription was issued: one group had all prescriptions sent to the pharmacy, while the other received a paper opiate prescription with instructions to fill it only if absolutely needed. The ACL reconstruction groups differ in the number of opiate tablets prescribed, with routine post-operative pain medications included in both descriptions.

The primary endpoint was Numeric Pain Rating Scale pain score at 2 hours post-op. The scale ranges from 0, no pain, to 10, worst imaginable pain; lower values are better. The posted results give separate group means and standard deviations for the two procedure types. They do not report a single combined comparison across all participants, nor do they establish a primary question about later pain, opioid consumption, or medication use. Those outcomes are not reported in the registry record as posted results.

The comparisons therefore address short-term average pain scores for the specified assigned groups. They do not, by themselves, describe every aspect of pain control or prescribing after surgery.

3. Trial Design

The registry identifies this study as randomized, single-masked, and parallel-group, with an enrollment of 201. The status is completed. The recorded start date is 2018-03-26, and the primary completion date is 2020-03-23. The identity of the person or people masked is not reported in the registry record.

The groups are defined separately for knee arthroscopy and ACL reconstruction. For knee arthroscopy, Group 1 had all post-operative prescriptions sent to the pharmacy on the day of surgery. Group 2 had prescriptions sent to the pharmacy except for the opiate prescription, which was provided as a physical paper prescription. Participants in that group were instructed to fill it only if absolutely needed. For ACL reconstruction, Group 1 was prescribed 60 opiate tablets, while Group 2 was prescribed 30; both descriptions include other routine post-operative pain medication regimens.

The registry lists four intervention groups but does not specify a common allocation ratio, the randomization method, or details of sequence generation and concealment. It also does not report a protocol, eligibility criteria, exact participant flow, or reasons for withdrawal in the record summarized. These details should not be inferred from the fact that the study was randomized.

For the primary outcome, the posted group sizes are 48 and 47 for knee arthroscopy, and 43 and 42 for ACL reconstruction. The reported measure is a mean, with standard deviation, for Numeric Pain Rating Scale score at 2 hours post-op. The registry lists 14 outcome measures, but the posted primary-outcome results do not describe every outcome measure. The number of additional posted secondary results is zero. The registry record lists no sponsor analysis results; the numerical comparisons discussed are unadjusted recalculations from the posted group summaries.

The trial’s original sample-size calculation, its rationale, and its analysis plan are not reported in the registry record. Accordingly, planning illustrations based on observed effects should not be treated as evidence about the choices used to design or conduct the trial.

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 Numeric Pain Rating Scale (NPRS) Pain Score, measured over 2 hours post-op.

The primary endpoint is Numeric Pain Rating Scale (NPRS) pain score at 2 hours post-op. The scale is reported as running from 0, meaning no pain, to 10, meaning the worst imaginable pain. A lower score represents less pain on this measure. Results are presented as group means and standard deviations, so the central comparison concerns average pain scores rather than the proportion of participants who reached a particular threshold.

A numerical pain rating scale gives participants a common way to describe pain intensity at a specified time. Using the same scale and assessment time across groups makes it possible to compare group-level scores under the assigned strategies. The timing matters: the result addresses pain at 2 hours after surgery, not pain throughout recovery or at a later follow-up. It also does not directly measure opioid use, prescription filling, unused medication, or other components of analgesia.

The registry reports mean scores of 5.2 and 5.3 for the knee arthroscopy groups, and 5.0 and 5.6 for the ACL reconstruction groups. Standard deviations describe the spread of individual scores around each group mean. These group averages and spreads summarize the recorded endpoint, but they do not reveal every participant’s experience or the distribution of scores. The minimum and maximum scale values define the instrument’s range; they do not identify a clinically meaningful difference or threshold. Such a threshold is not reported in the registry record.

Because the endpoint is a short-term, continuous score, differences between means are one way to describe the groups. A mean difference should be read together with its confidence interval and the scale’s direction, rather than as a complete account of pain control.

7. Results Posted in the Registry

• Group 2-Knee Arthroscopy: mean 5.30 versus 5.20 on control; difference 0.10 (95% CI -0.71 to 0.91), standardized effect d = 0.05; z-test p = 0.809.
• Group 1-ACL Reconstruction: mean 5.00 versus 5.20 on control; difference -0.20 (95% CI -1.15 to 0.75), standardized effect d = -0.09; z-test p = 0.681.
• Group 2-ACL Reconstruction: mean 5.60 versus 5.20 on control; difference 0.40 (95% CI -0.44 to 1.24), standardized effect d = 0.20; z-test p = 0.349.

8. Statistical Interpretation

9. Statistical Methods Explained

The posted primary outcome is continuous: each participant’s pain rating is represented by a numerical score, and the group results are expressed as means and standard deviations. A mean summarizes the group’s average score. A standard deviation describes how dispersed scores are around that average; it is not the same as the uncertainty in the mean. The registry reports means, standard deviations, and group sizes for each of the four groups.

What does a mean difference describe?

A mean difference is the first group’s average minus the reference group’s average according to the contrast being described. Its sign indicates direction, but only in relation to the specified group order. Because lower NPRS scores are better, a negative difference indicates a lower average score in the compared group, while a positive difference indicates a higher average score. A difference of zero would mean identical group means for that contrast. The reported comparisons are unadjusted recalculations from the posted summaries.

There are three reported contrasts. Group 2-Knee Arthroscopy is compared with Group 1-Knee Arthroscopy. Group 1-ACL Reconstruction and Group 2-ACL Reconstruction are each compared with Group 1-Knee Arthroscopy. This means the second ACL contrast is not a direct comparison of the two ACL groups. A direct ACL strategy comparison can be described by comparing the two ACL groups, but the registry’s reported recalculation uses the knee arthroscopy reference for both displayed ACL contrasts. Contrasts across different procedures should not be treated as if procedure type were held constant.

What does a confidence interval add?

A confidence interval gives a range of values that are compatible with the observed data under the calculation’s assumptions. It communicates uncertainty around an estimated mean difference, rather than only giving a single point estimate. A wide interval indicates that the data are compatible with a broad range of possible differences. When an interval crosses zero, it includes no mean difference as well as values in either direction. That is not evidence that the groups are identical; it means the data do not pin down the direction and size of the contrast precisely.

The intervals discussed for this study are 95% confidence intervals. In general, a confidence interval is not a guarantee that the true value lies within the particular interval, nor does it represent the range of individual participants’ pain scores. It concerns uncertainty about the estimated group contrast. The group standard deviations, by contrast, describe variation among participant scores.

How should the p values be read?

A p value describes how unusual a result at least as extreme as the observed one would be under a specified null model and statistical procedure. It is not the probability that the null hypothesis is true, and it does not quantify the probability that a treatment strategy works or fails. The reported p values are unadjusted and come from the recalculated comparisons. Since the analysis plan and multiplicity approach are not reported in the registry record, the p values should not be assumed to reflect a prespecified confirmatory testing strategy.

The commonly used practice of comparing a p value with a significance threshold is only one part of interpretation. The estimate and its confidence interval are important because they show the direction and range of plausible contrasts. A p value alone cannot establish equivalence, clinical importance, or absence of an effect. No equivalence margin or clinically important difference is reported in the registry record.

Why can over-dispersion matter?

General statistical explanation: for a continuous outcome, individual observations may vary substantially around the group mean. If the spread of scores is large relative to the contrast and the number of observations, the estimate can be imprecise. The standard deviations and group sizes help describe this information. The posted score distributions themselves are not reported, so features such as skewness, clustering, or unusually influential observations cannot be assessed from the group summaries alone. Over-dispersion is especially discussed for count outcomes, but the broader point applies: variability not represented adequately by a model can make uncertainty estimates unreliable.

The registry does not report a model, adjustment variables, diagnostic checks, or details of the calculation used for its own analysis. The numerical contrasts are therefore described as unadjusted recalculations, not as adjusted estimates or as results from a documented sponsor model. No assumption about covariate balance, missing-data handling, or analysis population should be inferred beyond what the registry record states.

What do the planning illustrations mean?

The planning illustrations use observed differences as inputs to show how sample-size requirements change under stated assumptions. They are not trial results and they do not describe the sample size originally chosen by the investigators. They are also not observed power. Their role is to illustrate that planning for a smaller effect requires a larger sample under the same assumptions. Details of the trial’s own design calculation are not reported in the registry record.

10. Confidence Intervals and Precision

The confidence intervals show how uncertain the estimated mean differences are. For the knee arthroscopy comparison, the recalculated mean difference is 0.1, with a 95% confidence interval from -0.709 to 0.909. For Group 1-ACL Reconstruction compared with the knee arthroscopy reference, the estimate is -0.2, with an interval from -1.154 to 0.754. For Group 2-ACL Reconstruction compared with that same reference, the estimate is 0.4, with an interval from -0.438 to 1.238.

Each interval includes zero, so none of these estimates precisely establishes a difference in one direction. Each also spans values on both sides of zero, leaving uncertainty about whether the compared group’s average pain score was lower or higher. The ACL intervals include a broader range of possible differences than the point estimates alone might suggest. This does not mean all possible differences are equally likely; it means the posted summary data do not identify a narrow range with high precision.

Precision is affected by the amount of information in the data, including the number of participants and variability in scores. The posted group sizes range from 42 to 48 for these endpoint results, and the reported standard deviations range from 1.8 to 2.7. The intervals should be interpreted as uncertainty about mean contrasts, not as ranges containing most individual pain scores.

No clinically important difference threshold is reported in the registry record. Consequently, it is not possible to determine from these intervals whether the data exclude differences that would be considered important under a defined criterion. The intervals also apply only to the contrasts and endpoint stated; they do not express precision for later pain, medication use, or other outcomes not reported in the registry record.

11. Planning a Similar Trial: Sample Size

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

The sample-size illustrations are planning calculations based on the observed effect, not the trial’s original design assumptions. The registry record does not report the original sample-size justification or calculation. The illustrations use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The entries are participants per arm, not total participants or total events.

The 80% power column gives the number of participants per arm that the illustration estimates would be needed for an 80% chance of detecting the selected effect under those planning assumptions, if the assumptions hold. The 90% power column gives the corresponding number per arm for a 90% chance. These are planning targets, not observed trial characteristics or findings. The event-count convention used for time-to-event calculations does not apply to this continuous pain outcome; the displayed figures concern participants per arm.

Rows planning for 100% of the observed effect use the full observed effect as the target; rows planning for 75% or 50% use smaller targets. Smaller effects need more participants to distinguish them from random variation under otherwise unchanged assumptions. This relationship is visible in the increasing requirements as the target effect gets smaller. The calculations are illustrations from the observed estimates and should not be read as validation of the study design. This is not observed power.

The table and curve are best read as sensitivity illustrations: changing the effect size changes the planning requirement. They do not establish that the observed effect is the true effect, and the estimates used as planning inputs are themselves uncertain. In particular, when an observed estimate is small or imprecise, planning directly from it can yield very large or unstable targets. The original design rationale, any allowance for attrition, and the trial’s own planned power 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 = 0.100; pooled standard deviation σ = 2.008.
2. n = 2 × (1.96 + 0.842)² × 2.008² / 0.100² = 6,328.4, rounded up to 6,329 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 <- 0.0999999999999996                      # observed difference in means
sigma <- 2.00783411901042                     # 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(3876743)
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 = 6,329 (80% power), 8,472 (90% power)
 75% of observed effect: n per arm = 11,251 (80% power), 15,062 (90% power)
 50% of observed effect: n per arm = 25,314 (80% power), 33,888 (90% power)
power.t.test: 6329.4 
Simulated power at n = 6,329 per arm: 0.800 (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 14 outcome measures, while zero additional secondary results are posted. It reports one primary endpoint for the results: mean NPRS pain score at 2 hours post-op. The record does not describe which other outcomes were measured, their results, or whether they were prespecified as primary or secondary in a protocol. The statistical analysis plan and any hierarchy of endpoints are not reported in the registry record.

Multiplicity arises when several outcomes, comparisons, time points, or subgroup analyses are tested. Repeated testing can increase the chance of at least one apparently notable result even when no true differences exist. Whether and how to adjust for this depends on the study’s objectives and analysis plan. No multiplicity adjustment is reported for these recalculated comparisons. The p values are unadjusted, and the registry does not state whether the investigators used another approach to account for multiple comparisons.

Missing-data methods and analysis populations are also not reported in the registry record. The posted group sizes for the primary endpoint are 48 and 47 for knee arthroscopy and 43 and 42 for ACL reconstruction, but these counts alone do not identify whether every randomized participant contributed an outcome, how missing values were handled, or whether the displayed results follow an intention-to-treat or per-protocol approach. Participant flow and reasons for any missing endpoint values are not described in the posted results.

The fact that the study is randomized does not determine how missing outcomes should be analyzed, nor does it establish that all randomized participants were included in each calculation. Without the protocol, analysis plan, and participant-level accounting, it is not possible to assess whether exclusions or missingness could have affected the estimates.

These limitations do not invalidate the posted group summaries, but they constrain what can be inferred from them. The findings should be read as the reported endpoint summaries and unadjusted recalculations, not as a complete account of all planned outcome analyses or of how every participant was handled.

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, other adverse events, and deaths by group. For the knee arthroscopy groups, 48 and 47 participants were listed as at risk; for the ACL reconstruction groups, the at-risk counts were 43 and 42. The registry reports zero serious adverse events and zero other adverse events in each of the four groups, and zero deaths in each group.

These figures describe the events recorded in the registry for the listed groups. A count of zero means no events of that category were reported for the group; it does not demonstrate that the risk is absent. The counts do not provide detailed event definitions, observation periods, severity breakdowns beyond the serious-versus-other categories, or information about how events were collected. Those details are not reported in the registry record.

The safety counts should be kept separate from the pain-score comparisons. They do not quantify pain, opioid use, or unused prescriptions, and they do not establish a difference in safety between strategies. With no events recorded in these categories, the posted counts offer limited information about comparative event rates. They also should not be interpreted as evidence about adverse events that were not recorded or not reported.

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

The posted results describe average pain scores at 2 hours post-op for four groups defined by procedure and prescribing strategy. The knee arthroscopy groups had mean scores of 5.2 and 5.3. The ACL reconstruction groups had mean scores of 5.0 and 5.6. The recalculated unadjusted comparisons have confidence intervals that include zero, leaving uncertainty about the direction and size of the mean differences.

These results do not establish that the groups have identical pain scores. They also do not establish that one strategy causes lower or higher pain, or that any strategy is clinically equivalent to another. There is no reported equivalence margin or clinically important difference threshold. The estimates concern group averages on one scale at one post-operative time point; individuals may have experienced different levels of pain.

The trial’s stated motivation concerned whether opiates are required for adequate analgesia and the possibility of excess prescribed medication. The posted primary results do not report opioid consumption, prescription filling, remaining tablets, diversion, misuse, or later pain. Therefore, these pain-score findings alone cannot answer whether participants needed or used the prescribed opiates, nor can they quantify the potential for unused medication. Those outcomes are not reported in the registry record.

The two procedure-specific comparisons also address different prescribing questions. For knee arthroscopy, the contrast concerns providing an opiate prescription on paper with instructions to fill it only if needed versus having all prescriptions sent to the pharmacy. For ACL reconstruction, the contrast concerns prescribing 60 versus 30 opiate tablets. The comparisons should not be conflated, and comparisons across procedure types should not be taken as direct evidence about one prescribing strategy.

In short, the posted data provide descriptive and uncertain comparisons of short-term mean pain scores. They do not, on their own, establish a treatment effect, equivalence, or the adequacy of analgesia, and they do not resolve the broader prescribing questions motivating the study.

16. Why This Trial Matters Statistically

This trial is statistically informative as an example of separating the question of pain from the question of prescribing. A pain score at a specified time is not a direct measure of how much medication was taken or whether a prescription was filled. The endpoint and the broader motivation therefore concern related but distinct outcomes. Keeping them separate helps prevent a short-term score comparison from being used to answer questions the posted endpoint does not measure.

The study also illustrates why comparison definitions matter. The two knee arthroscopy groups differ in how an opiate prescription was issued, while the ACL groups differ in the number of tablets prescribed. A contrast across these procedures cannot be interpreted as a clean test of one common prescribing change. The registry’s recalculated ACL contrasts use the knee arthroscopy reference, so readers should distinguish those from the direct comparison between the two ACL groups.

Precision is central to interpreting the results. Small point estimates alone can look reassuring or meaningful depending on the direction, but their confidence intervals show that a range of underlying differences remains compatible with the data. The intervals include zero, and no clinically important difference is specified in the registry record. Neither the point estimates nor the p values justify a claim of equivalence.

Finally, the planning illustrations demonstrate the dependence of sample-size requirements on the effect one aims to detect. Requirements grow when the target effect is smaller, but these illustrations use observed effects and do not recover the trial’s original design rationale. The record’s limited reporting of the analysis plan, additional outcomes, and missing-data handling further defines the boundary of interpretation. These considerations are broadly relevant whenever randomized group summaries are used to discuss clinical outcomes.

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 posted primary outcome is measured at 2 hours post-op, so it does not describe pain over the full recovery period. Later pain scores and follow-up results are not reported in the registry record. The registry also does not report opioid consumption, whether prescriptions were filled, remaining tablets, or other measures that would directly characterize medication use. This limits the ability to connect the pain endpoint to the prescribing question that motivated the study.

Group sizes for the posted primary outcome range from 42 to 48. The registry does not describe participant flow, missing endpoint values, withdrawals, or analysis populations. It is therefore not possible to determine from the posted record whether all randomized participants contributed to the reported endpoint summaries or how missing observations were handled.

The record identifies the study as single-masked but does not specify who was masked or how masking was maintained. Details about randomization sequence generation, allocation concealment, eligibility criteria, and adherence to assigned strategies are not reported in the registry record. No protocol or statistical analysis plan is posted in the summarized record, and the trial’s original sample-size calculation is not reported.

The comparisons are unadjusted recalculations from group-level summaries, and the registry lists zero posted analyses. The participant-level data and distributions are not available in the registry record described, so the calculations cannot assess score distributions, influential observations, baseline balance, or adjusted estimates. The record also does not report a clinically important difference threshold, making it difficult to judge whether a possible difference would matter clinically.

Finally, the zero adverse-event counts should be interpreted within the reporting available: details of event definitions and collection periods are not reported. These limitations are specific to what the registry record makes available and constrain the strength and scope of conclusions from the posted results.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Opiates Prescribing for Knee Arthroscopies and ACL Reconstruction — NCT03876743.
• Registry record last updated 2020-10-14; status last verified 2020-09.
• Results first posted 2020-09-16.
• 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, single-masked, parallel-group study of post-operative opiate prescribing strategies for knee arthroscopy and ACL reconstruction. Enrollment was 201. The primary endpoint was mean Numeric Pain Rating Scale pain score 2 hours after surgery, with lower scores indicating less pain.

Mean scores were 5.2 and 5.3 in the knee arthroscopy groups and 5.0 and 5.6 in the ACL reconstruction groups. The unadjusted recalculated mean-difference confidence intervals include zero for all three reported contrasts. The record lists zero serious adverse events, zero other adverse events, and zero deaths in each group.

The registry does not report the trial’s original sample-size justification, statistical analysis plan, missing-data methods, or posted secondary outcome results. The findings therefore describe the posted short-term pain summaries and should not be extended to medication use, later pain, equivalence, or outcomes not reported in the registry record.