This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Efficacy of 300 mg Ibuprofen Prolonged-Release Tablets for the Treatment of Pain After Surgical Removal of Impacted Third Molars (NCT03785756), a randomized phase 3 study. The primary outcome is Summed Pain Intensity Difference Over 0 to 12 Hours (SPID12) After Time 0.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03785756 |
| Phase | Phase 3 |
| Condition | Pain |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 280 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Reckitt Benckiser Healthcare (UK) Limited |
| Results posted | Yes |
2. Clinical Question
Population
Participants with postoperative dental pain after surgical removal of impacted third molars. The primary efficacy population was the ITT Population: participants treated with study drug who had at least one pain assessment after Time 0. The registry record reports enrollment of 280 and primary-outcome group counts of 120.0 in each ibuprofen group and 39.0 in the placebo group.
Intervention
The prolonged-release group received 2 × 300 mg ibuprofen PR tablets at Hours 0 and 12. Placebo tablets were scheduled at other dosing times to support the double-dummy design.
Comparator
The immediate-release group received 2 × 200 mg ibuprofen IR tablets at Hours 0, 8, and 16. The placebo group received placebo PR and IR tablets at the scheduled times. These groups allow comparisons with both an active regimen and placebo.
Primary question
How did the mean summed pain intensity difference from Time 0 through 12 hours compare between each ibuprofen group and placebo? SPID12 summarizes pain-intensity change over time; a higher score indicates a better outcome according to the endpoint definition. The registry record also reports a sponsor ANCOVA comparison of the prolonged-release group with placebo.
3. Trial Design
This was a completed, Phase 3, randomized, quadruple-masked, parallel-group study. Its official title describes a double-blind, double-dummy, multiple-dose, active- and placebo-controlled efficacy study; the registry fields separately identify masking as quadruple. The study evaluated ibuprofen prolonged-release tablets for pain after surgical removal of impacted third molars. The brief summary characterizes it as a single-centre study.
The three groups were prolonged-release ibuprofen, immediate-release ibuprofen, and placebo. The prolonged-release regimen used 2 × 300 mg tablets at Hours 0 and 12. The immediate-release regimen used 2 × 200 mg tablets at Hours 0, 8, and 16. Placebo PR and IR tablets were scheduled across dosing times to maintain the double-dummy arrangement. A double-dummy design uses matching placebo preparations so that participants in different treatment groups can follow comparable dosing procedures; this is a general explanation of the design concept.
The registry record reports enrollment of 280. For the primary outcome, the posted group summaries include 120.0 participants in the prolonged-release group, 120.0 in the immediate-release group, and 39.0 in the placebo group. The primary efficacy population was defined as treated participants with at least one post-Time 0 pain assessment. The registry record does not report why the number contributing to these summaries differs from total enrollment, nor does it report further detail about participant flow.
The reported primary endpoint was SPID12, measured from the first dose through 12 hours. The record also lists secondary pain-intensity and pain-relief outcomes at other time windows. The protocol’s intended sample-size justification, allocation ratio rationale, and original statistical plan 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
| Stage | Prolonged Release Group | Immediate Release Group | Placebo Group |
|---|---|---|---|
| STARTED | 120 | 120 | 40 |
| COMPLETED | 111 | 112 | 35 |
| NOT COMPLETED | 9 | 8 | 5 |
Analysis population for the primary outcome, as defined in the registry: The ITT Population included all subjects who were treated with study drug and had at least 1 pain assessment after Time 0; it was the primary population for the efficacy analysis.
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.
Population: One subject in the placebo group withdrew from the study before receiving the allocation intervention.
| Characteristic | Unit | Prolonged Release Group | Immediate Release Group | Placebo Group | Total |
|---|---|---|---|---|---|
| Participants analysed | 120 | 120 | 39 | 279 | |
| Age, Continuous | years | 19.6 (SD 2.02) | 19.8 (SD 2.47) | 20.7 (SD 3.13) | 19.8 (SD 2.42) |
| Sex: Female, Male: Female | Participants | 72 | 53 | 24 | 149 |
| Sex: Female, Male: Male | Participants | 48 | 67 | 15 | 130 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 17 | 12 | 8 | 37 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 101 | 105 | 30 | 236 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 2 | 3 | 1 | 6 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 1 | 1 | 0 | 2 |
| Race (NIH/OMB): Asian | Participants | 3 | 2 | 1 | 6 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 5 | 2 | 2 | 9 |
| Race (NIH/OMB): Black or African American | Participants | 2 | 1 | 0 | 3 |
| Race (NIH/OMB): White | Participants | 107 | 108 | 36 | 251 |
| Race (NIH/OMB): More than one race | Participants | 1 | 2 | 0 | 3 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 1 | 4 | 0 | 5 |
| Baseline Pain | units on a scale | 7.5 (SD 1.23) | 7.6 (SD 1.17) | 7.8 (SD 1.12) | 7.6 (SD 1.19) |
| Baseline Pain Category: Moderate | Participants | 63 | 57 | 15 | 135 |
| Baseline Pain Category: Severe | Participants | 57 | 63 | 24 | 144 |
| Height | cm | 168.72 (SD 9.753) | 171.61 (SD 8.517) | 167.85 (SD 6.223) | 169.84 (SD 8.917) |
| Weight | kg | 67.99 (SD 13.931) | 73.17 (SD 13.921) | 69.69 (SD 12.041) | 70.46 (SD 13.847) |
| BMI | kg/m² | 23.82 (SD 4.085) | 24.79 (SD 4.033) | 24.71 (SD 3.947) | 24.36 (SD 4.057) |
| Surgery duration | minutes | 9.2 (SD 4.60) | 9.0 (SD 4.89) | 11.1 (SD 5.81) | 9.4 (SD 4.94) |
6. Primary Endpoint
The registry lists the primary outcome as Summed Pain Intensity Difference Over 0 to 12 Hours (SPID12) After Time 0, measured over 0-12 hours.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | score on a scale*hours |
| Endpoint classification | Continuous Endpoint |
The primary endpoint, Summed Pain Intensity Difference Over 0 to 12 Hours (SPID12), summarizes change in pain intensity over time after the first dose. Pain intensity was assessed with an 11-point numeric rating scale, from 0 to 10, where a higher rating means greater pain. The endpoint uses change from Time 0 and integrates those changes from 15 minutes through 12 hours using the linear trapezoidal rule and actual assessment times.
In general, an area-under-the-curve summary can represent both the size of change and how long that change is observed. SPID12 is expressed as a score on a scale*hours. The registry record defines 0 as no change in pain intensity from Time 0 to 12 hours and gives a theoretical maximum of 120 under a particular pattern of pain-score reduction. A higher SPID12 score indicates a better outcome under this definition.
This type of endpoint is used to summarize repeated pain assessments across a period rather than relying on a single rating. The registry record identifies the mean as the reported summary measure and standard deviation as its dispersion measure. SPID12 was the primary efficacy outcome in the ITT Population, defined as treated participants with at least one pain assessment after Time 0. The registry record does not report further detail about how missing assessments were handled in calculating the endpoint.
7. Results Posted in the Registry
- Prolonged Release Group: mean 51.84 versus 19.11 on control; difference 32.73 (95% CI 24.10 to 41.36), standardized effect d = 1.47; z-test p = <0.001.
- Immediate Release Group: mean 56.33 versus 19.11 on control; difference 37.22 (95% CI 28.79 to 45.65), standardized effect d = 1.83; z-test p = <0.001.
Mean difference: Prolonged Release Group
95% CI: 24.10 to 41.36
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Summed Pain Intensity Difference Over 0 to 24 Hours (SPID24) After Time 0 | Continuous Endpoint | Mean difference | 51.43 (32.28 to 70.58) | 14 per arm |
| Summed Pain Intensity Difference Over 0 to 4 Hours (SPID4) After Time 0 | Continuous Endpoint | Mean difference | 13.44 (10.29 to 16.59) | 8 per arm |
| Summed Pain Intensity Difference Over 0 to 8 Hours (SPID8) After Time 0 | Continuous Endpoint | Mean difference | 22.13 (16.72 to 27.54) | 9 per arm |
Summed Pain Intensity Difference Over 0 to 24 Hours (SPID24) After Time 0
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Prolonged Release Group: mean 115.75 versus 64.32 on control; difference 51.43 (95% CI 32.28 to 70.58), standardized effect d = 1.06; z-test p = <0.001.
- Immediate Release Group: mean 121.90 versus 64.32 on control; difference 57.58 (95% CI 39.06 to 76.10), standardized effect d = 1.36; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Prolonged Release Group than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Immediate Release Group than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Summed Pain Intensity Difference Over 0 to 4 Hours (SPID4) After Time 0
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Prolonged Release Group: mean 14.68 versus 1.24 on control; difference 13.44 (95% CI 10.29 to 16.59), standardized effect d = 1.43; z-test p = <0.001.
- Immediate Release Group: mean 16.99 versus 1.24 on control; difference 15.75 (95% CI 12.77 to 18.73), standardized effect d = 1.97; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Prolonged Release Group than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Immediate Release Group than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Summed Pain Intensity Difference Over 0 to 8 Hours (SPID8) After Time 0
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Prolonged Release Group: mean 33.13 versus 11.00 on control; difference 22.13 (95% CI 16.72 to 27.54), standardized effect d = 1.40; z-test p = <0.001.
- Immediate Release Group: mean 34.48 versus 11.00 on control; difference 23.48 (95% CI 18.35 to 28.61), standardized effect d = 1.75; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Prolonged Release Group than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Immediate Release Group than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The listed secondary outcomes extend pain-intensity summaries to other observation windows and include total pain-relief and combined relief-and-intensity measures. The posted secondary summaries cover several time windows, including SPID measures, and the broader registry record lists additional outcome measures. Across the posted secondary pain-intensity outcomes, the group means and unadjusted comparisons follow a pattern consistent with the primary result: both ibuprofen groups have higher average summaries than placebo, with reported unadjusted p-values below 0.001 for the displayed SPID comparisons.
These outcomes are related to SPID12 because they use pain-intensity change over time or related pain-relief measures. Their different time windows and definitions provide additional descriptions of the response trajectory, but they are not independent confirmations in the same way as separate trials would be. The primary endpoint remains the prespecified focus represented in the registry record, while secondary measures add context about other periods and related summaries.
Unadjusted secondary results carry less weight when many outcomes or comparisons are examined. In general, multiple testing increases the chance of observing apparently strong results by chance if each test is considered separately. The registry record lists multiple secondary outcomes and reports 23 posted secondary results, but a comprehensive multiplicity adjustment is not reported. Therefore, nominal p-values for secondary comparisons should be interpreted cautiously and alongside the primary result, outcome definitions, and analysis methods.
The registry record does not report all details needed to determine how the secondary outcomes were prioritized, whether any were considered confirmatory, or how missing observations were handled for each measure. The broad consistency of the posted pattern is descriptive; it should not be used to make claims beyond the measured outcomes, time windows, and trial population.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Summed Pain Intensity Difference Over 0 to 24 Hours (SPID24) After Time 0
- Summed Pain Intensity Difference Over 0 to 4 Hours (SPID4) After Time 0
- Summed Pain Intensity Difference Over 0 to 8 Hours (SPID8) After Time 0
- Sum of Total Pain Relief Over 0 to 4 Hours (TOTPAR4) After Time 0
- Sum of Total Pain Relief Over 0 to 8 Hours (TOTPAR8) After Time 0
- Sum of Total Pain Relief Over 0 to 12 Hours (TOTPAR12) After Time 0
- Sum of Total Pain Relief Over 0 to 24 Hours (TOTPAR24) After Time 0
- Summed Pain Relief and Intensity Difference (Sum of TOTPAR and SPID [SPRID]) Over 0 to 4 Hours (SPRID4) After Time 0
9. Statistical Interpretation
For SPID12, the posted mean was 51.84 in the prolonged-release group, 56.33 in the immediate-release group, and 19.11 in the placebo group. The simple unadjusted recalculated mean difference was 32.73 for prolonged-release ibuprofen versus placebo, with a 95% confidence interval from 24.1 to 41.36 and p < 0.001. For immediate-release ibuprofen versus placebo, the recalculated mean difference was 37.22, with a 95% confidence interval from 28.79 to 45.65 and p < 0.001. These are comparisons of posted group summaries, not adjusted estimates.
The direction of both reported contrasts is consistent with higher average SPID12 scores in the ibuprofen groups than in the placebo group. Because higher SPID12 is defined as a better outcome, the posted means and unadjusted comparisons show greater average pain-intensity improvement over the endpoint window in each ibuprofen group than in placebo. This describes the data; it does not establish that either regimen is appropriate for an individual or answer questions beyond the measured population, treatment schedules, and time window.
The registry record also reports a sponsor ANCOVA analysis comparing the prolonged-release group with placebo. It gives a mean difference of 34.05, a 95% confidence interval from 26.72 to 41.38, and p < 0.001. That adjusted result is not identical to the simple unadjusted recalculation. The analyses use different approaches, so their estimates should not be treated as interchangeable. The registry record labels the reported analysis type as EQUIVALENCE, but does not report an equivalence margin or the details needed to interpret that label as a complete equivalence assessment.
The standard deviations of the primary outcome were 21.46, 18.77, and 24.63 in the prolonged-release, immediate-release, and placebo groups, respectively. These describe variation among participant scores, not uncertainty in the estimated mean difference. The confidence intervals address uncertainty in the contrasts. The registry record gives no clinically important difference threshold for SPID12, so statistical evidence against a zero difference cannot by itself establish the clinical importance of the observed difference.
The results apply to the defined trial population and outcome window. The registry record reports one analysis for the primary outcome and lists multiple secondary outcomes. It does not report a comprehensive multiplicity procedure, detailed missing-data methods, or all analysis decisions. Those omissions limit how much can be concluded from nominal p-values, especially when interpreting outcomes beyond the prespecified primary endpoint.
10. Statistical Methods Explained
For a continuous outcome such as SPID12, a group mean describes the average observed score, while the standard deviation describes how dispersed participant scores are around that mean. In general, neither quantity alone gives the full picture: the mean difference compares group averages, while its confidence interval expresses uncertainty about that contrast. The primary-outcome summaries report means and standard deviations for each group.
What does the unadjusted mean difference represent?
The simple recalculated comparison subtracts the posted placebo mean from the posted mean in the relevant ibuprofen group. For the prolonged-release group, the posted comparison is 32.73; for the immediate-release group, it is 37.22. These are unadjusted contrasts based on the group summaries. They do not account for baseline characteristics or other covariates. The registry record’s sponsor analysis uses ANCOVA for the prolonged-release comparison, so it is an adjusted analysis rather than the same calculation.
In general, ANCOVA estimates a group contrast while accounting for selected covariates. The registry record identifies the method as ANCOVA but does not report the covariates, model specification, or other implementation details. It is therefore possible to describe the reported adjusted estimate and its interval, but not to reconstruct the model from the registry record.
What does a p-value tell the reader?
In general, a p-value measures how incompatible the observed data are with a specified null model, assuming the model and analysis assumptions hold. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The posted unadjusted comparisons report p < 0.001 for each ibuprofen-versus-placebo contrast; the sponsor ANCOVA reports p < 0.001 for prolonged-release versus placebo. These values are evidence against a zero-difference null under their respective analyses. The registry record does not provide enough detail to assess every modeling assumption or any multiplicity adjustment for these comparisons.
Why is the outcome integrated over time?
SPID12 uses pain-intensity changes from Time 0 across repeated post-dose assessments. In general, the trapezoidal rule approximates the area under a curve by connecting neighboring observations with straight lines. Using actual assessment times accounts for spacing between observations in the recorded time scale. The resulting score combines the observed magnitude and duration of pain-intensity change into one summary. The endpoint description states that the calculation begins at 15 minutes and extends through 12 hours.
The scale begins at 0 and ends at 10 for pain intensity; larger pain ratings indicate greater pain. SPID12 is defined in the opposite direction for its summary: higher scores indicate a better outcome. The registry record defines the minimum as 0, meaning no change from Time 0 through 12 hours, and describes a theoretical maximum of 120 for the specified pattern of a reduction to no pain that remains at that level.
What is the role of uncertainty intervals?
In general, a confidence interval gives a range of values compatible with the data and the analysis procedure at a stated confidence level. It should be considered alongside the point estimate: a narrow interval indicates greater precision than a wide interval, but the interval does not resolve questions about bias, clinical importance, or whether the model is appropriate. For the recalculated comparisons, the posted 95% intervals are 24.1 to 41.36 for prolonged-release ibuprofen and 28.79 to 45.65 for immediate-release ibuprofen. The sponsor ANCOVA interval is 26.72 to 41.38. These intervals are associated with distinct analyses and should be read separately.
The recalculated comparisons use standard deviations and group sizes from the posted summaries. This is a simple, unadjusted analysis. The registry record does not report a recalculated comparison for every secondary outcome as a sponsor analysis, and it does not provide full details of the sponsor’s statistical plan. Statistical methods not described in the registry record should not be inferred from the summary results.
Why can variation matter?
In general, larger variability makes a group mean less precise when other features, including sample size, are held constant. The primary-outcome standard deviations are 21.46 for prolonged release, 18.77 for immediate release, and 24.63 for placebo. These figures convey participant-to-participant variation in SPID12. They are distinct from the confidence intervals for mean differences, which also depend on the group sizes and the analysis used.
The posted recalculations use a pooled standard deviation as part of their standardized effect summaries, but those summaries do not replace the mean difference in the endpoint’s original units. The registry record’s original design assumptions and sample-size justification are not reported. Planning illustrations based on observed effects, described separately in the record, are not evidence about the trial’s original power or its design rationale.
11. Confidence Intervals and Precision
The unadjusted recalculated mean difference for prolonged-release ibuprofen versus placebo is 32.73, with a 95% confidence interval from 24.1 to 41.36. For immediate-release ibuprofen versus placebo, the estimate is 37.22, with a 95% confidence interval from 28.79 to 45.65. Both intervals lie above zero, in the direction of higher SPID12 scores in the ibuprofen groups. The intervals describe uncertainty under these unadjusted comparisons; they do not show the range of individual participant outcomes.
The sponsor’s ANCOVA estimate for prolonged release versus placebo is 34.05, with a 95% confidence interval from 26.72 to 41.38. Because that estimate comes from an adjusted analysis, its interval should not be collapsed with or substituted for the unadjusted interval. The registry record does not report the covariates or full model details, so the reason for the difference between estimates cannot be assessed from the registry record alone.
In general, a confidence interval is most informative when read with the point estimate, the analysis method, and the outcome’s scale. It communicates statistical precision, not whether a difference matters to patients. The record does not give a threshold for a clinically important SPID12 difference. It also does not report a prespecified equivalence margin, despite labeling the sponsor analysis type as EQUIVALENCE. The interval therefore cannot be used by itself to establish equivalence.
The group standard deviations show noticeable variation in observed SPID12 scores, while the confidence intervals quantify uncertainty in estimated average differences. These are different aspects of the data. Precision also does not eliminate concerns about the population analyzed, missing assessments, outcome selection, or multiplicity. Further information on those matters is not reported in the registry record.
12. 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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 8 | 10 |
| 75% of the observed effect | 13 | 18 |
| 50% of the observed effect | 30 | 39 |
The sample-size illustrations are planning calculations based on observed effects, not the trial’s original design assumptions. For continuous outcomes, the reported entries are participants per arm. The record’s general planning 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 set as the stated fraction of the observed effect. Time-to-event illustrations, if present, would report total events; the outcomes in this trial are continuous, so the figures refer to participants per arm.
The 80% power column gives the illustrative number of participants per arm under the stated assumptions for a planned analysis to have an 80% chance of detecting the specified effect, if that effect and the assumptions are correct. The 90% power column gives the corresponding illustration for a 90% chance. These are planning concepts, not promises about a future result. For instance, the primary comparison entries vary according to whether planning uses 100%, 75%, or 50% of the observed effect.
Smaller effects are harder to distinguish from random variation, so the planning illustrations require more participants per arm as the assumed effect becomes smaller. The registry record’s original sample-size justification and design assumptions are not reported. These illustrations are not observed power: they use the effect estimated from the trial and describe hypothetical planning scenarios rather than the probability that this completed trial detected an effect.
Read each entry in relation to the outcome and comparison it describes. The illustrations do not account for every potential design feature, such as covariate adjustment, multiplicity, missing data, or deviations from the assumptions, unless those are explicitly included in the stated planning method. They should not be used to replace the trial’s observed group summaries, confidence intervals, or sponsor analysis.
13. 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 z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = 32.730; pooled standard deviation σ = 22.267.
- n = 2 × (1.96 + 0.842)2 × 22.2672 / 32.7302 = 7.3, rounded up to 8 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 <- 32.73 # observed difference in means
sigma <- 22.2665012497352 # 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(3785756)
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 = 8 (80% power), 10 (90% power)
75% of observed effect: n per arm = 13 (80% power), 18 (90% power)
50% of observed effect: n per arm = 30 (80% power), 39 (90% power)
power.t.test: 8.3
Simulated power at n = 8 per arm: 0.778 (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.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| ANCOVA | Mean Difference (Final Values) 34.05 | 26.72 to 41.38 | < 0.001 |
The registry record reports a sponsor ANCOVA analysis for prolonged-release ibuprofen versus placebo. The reported mean difference is 34.05, with a 95% confidence interval from 26.72 to 41.38 and p < 0.001. The analysis is labeled EQUIVALENCE in the registry record. No equivalence margin or detailed model specification is reported, so the label alone does not establish how an equivalence conclusion was defined.
The simple unadjusted recalculation from the posted group means gives a mean difference of 32.73, with a 95% confidence interval from 24.1 to 41.36 and p < 0.001. The recalculation uses the posted summary statistics and does not adjust for covariates. It is a transparent comparison of group summaries, not a replacement for the sponsor’s reported analysis.
These estimates are not identical because they arise from different analysis approaches. The sponsor’s ANCOVA is the analysis reported by the registry record; the recalculated contrast is useful as a separate, unadjusted reference. The registry record does not provide enough information about the ANCOVA model to explain the difference further. No sponsor ANCOVA result for the immediate-release group is reported in the posted primary analysis details.
15. Multiplicity, Missing Data and Analysis Populations
The registry record identifies SPID12 as the primary outcome and lists multiple secondary outcomes, including pain-intensity, pain-relief, and combined measures. It reports one analysis for the primary endpoint and 23 posted secondary results. When many outcomes or comparisons are tested, the chance of at least one apparently unusual result can increase. In general, multiplicity procedures are used to control this issue, but a plan for adjustment across primary and secondary tests is not reported in the registry record.
The reported p-values should therefore be interpreted in the context of the endpoint hierarchy. The primary comparisons are central to the trial question. Unadjusted secondary p-values are exploratory evidence unless the analysis plan establishes otherwise; that status and any prespecified hierarchy are not reported in the registry record. The record also does not report interim analyses or stopping rules, so none should be assumed.
The primary efficacy population includes participants treated with study drug who had at least one pain assessment after Time 0. This defines who could contribute to the efficacy analysis, but does not by itself describe how missing assessments were handled once participants entered that population. The registry record does not report the extent or reasons for missing pain measurements, imputation procedures, sensitivity analyses, or details of participant disposition by reason. Those omissions make it difficult to evaluate the potential influence of missing data.
The primary-outcome group counts are 120.0, 120.0, and 39.0, while total enrollment is 280. The registry record does not explain the difference between total enrollment and the counts in the primary summaries. It also does not report whether every randomized participant was analyzed according to assigned group or give a complete accounting of exclusions. This limits assessment of how closely the analysis population reflects randomization.
Further details about the allocation process, analysis covariates, model diagnostics, and protocol deviations are not reported in the registry record. These missing details do not negate the posted estimates, but they constrain independent evaluation of the full analysis strategy.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Prolonged Release Group | 0 | 120 | 0.0% |
| Immediate Release Group | 0 | 120 | 0.0% |
| Placebo Group | 0 | 39 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Prolonged Release Group | 0 of 120 |
| Immediate Release Group | 0 of 120 |
| Placebo Group | 0 of 39 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Prolonged Release Group | 11 of 120 |
| Immediate Release Group | 15 of 120 |
| Placebo Group | 12 of 39 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Prolonged Release Group | Immediate Release Group | Placebo Group |
|---|---|---|---|---|
| Nausea | Gastrointestinal disorders | 1 of 120 | 2 of 120 | 6 of 39 |
| Vomiting | Gastrointestinal disorders | 0 of 120 | 2 of 120 | 3 of 39 |
| Alveolar osteitis | Infections and infestations | 1 of 120 | 1 of 120 | 1 of 39 |
| Headache | Nervous system disorders | 0 of 120 | 2 of 120 | 1 of 39 |
| Aphthous ulcer | Gastrointestinal disorders | 1 of 120 | 1 of 120 | 0 of 39 |
| Swelling face | General disorders | 0 of 120 | 1 of 120 | 1 of 39 |
| Upper respiratory tract infection | Infections and infestations | 1 of 120 | 1 of 120 | 0 of 39 |
| Presyncope | Nervous system disorders | 0 of 120 | 1 of 120 | 1 of 39 |
| Tremor | Nervous system disorders | 0 of 120 | 1 of 120 | 1 of 39 |
| Nasal congestion | Respiratory, thoracic and mediastinal disorders | 1 of 120 | 1 of 120 | 0 of 39 |
The registry record reports zero serious adverse events in each group: the prolonged-release group had 0 among 120 at risk, the immediate-release group had 0 among 120 at risk, and the placebo group had 0 among 39 at risk. It also reports zero deaths in all three groups. These are the serious-event and death counts recorded for the groups; they are not evidence that no other adverse events occurred.
Other adverse events were recorded for 11 participants in the prolonged-release group, 15 in the immediate-release group, and 12 in the placebo group, with the corresponding at-risk counts of 120, 120, and 39. The registry record lists no serious adverse-event terms. It does not provide event-level descriptions, severity, timing, attribution, or detail on how events were collected in the information. A group count alone cannot establish that an event was caused by a study treatment.
In general, safety counts should be read with the size of each group, duration of observation, event definitions, and completeness of reporting in mind. The registry record does not report further context needed to assess rare events or make comparisons beyond these posted counts. These figures describe the recorded trial data and do not provide individual medical guidance.
17. What the Result Does, and Does Not, Mean
The posted primary results show higher mean SPID12 scores in both ibuprofen groups than in the placebo group. The unadjusted recalculated mean differences are 32.73 for prolonged-release ibuprofen versus placebo and 37.22 for immediate-release ibuprofen versus placebo; both have confidence intervals above zero and p < 0.001. The endpoint definition assigns higher SPID12 scores to better outcomes, so the observed group summaries indicate greater average improvement in pain intensity over the first 12 hours in the ibuprofen groups than in placebo.
This is a statement about average scores in a specific trial population after surgical removal of impacted third molars, using the reported dosing schedules and endpoint. It does not mean every participant had the same experience, and the group means do not describe the full distribution of individual responses. The standard deviations indicate variation in participant scores.
Statistical evidence of a difference is not the same as evidence that the difference is clinically important. The registry record does not report a threshold for a clinically important SPID12 difference. It also does not resolve whether the reported estimates generalize to other populations, settings, dosing schedules, or observation periods. The study’s brief summary describes a single-centre design, and the registry record does not report further information to assess broader applicability.
The sponsor ANCOVA gives an adjusted prolonged-release versus placebo estimate of 34.05 with a 95% confidence interval from 26.72 to 41.38. This is a separate analysis from the unadjusted recalculation. The registry record labels the sponsor analysis as EQUIVALENCE but does not report a margin or sufficient detail to assess an equivalence claim fully.
The registry record reports no serious adverse events or deaths in the listed groups and records other adverse events in each group. These data are not enough to characterize every possible safety outcome. Overall, the result describes posted efficacy and safety summaries; it does not determine individual treatment decisions or establish conclusions beyond the trial’s measured outcomes.
18. Why This Trial Matters Statistically
This trial is statistically informative because it includes both an active comparator and placebo, with a randomized parallel-group structure. The placebo comparison provides context for change over time that may occur apart from the active regimens, while the active-comparator group offers another treatment reference. The double-dummy dosing schedule is a design feature intended to maintain comparable treatment procedures across groups; this is a general explanation of the design rationale, not a claim about unreported implementation details.
The primary outcome condenses repeated pain ratings into a time-integrated summary. That approach captures change over the first 12 hours rather than selecting a single assessment time. It also makes the definition and calculation important to interpretation: SPID12 uses change from Time 0, actual assessment times, and the linear trapezoidal rule, and higher values are defined as better outcomes.
The record makes it possible to compare a sponsor-reported adjusted estimate with a simple unadjusted recalculation from posted summaries. Their distinct estimates illustrate why analysis method matters: an adjusted model and a direct comparison of group means need not return the same value. The registry record does not report enough ANCOVA detail to explain the difference, which demonstrates the importance of transparent model reporting.
Finally, the trial highlights limits of registry summaries. The primary outcome is described clearly, but the original sample-size rationale, multiplicity strategy, missing-data procedures, and detailed participant flow are not reported. These features affect how securely estimates can be interpreted, particularly across numerous secondary outcomes. The posted results are useful for understanding the observed pattern while leaving important methodological questions open.
19. 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 describes the study as single centre, which may limit how readily results can be generalized to settings and populations not represented in the trial. It reports enrollment of 280, but does not explain why the primary-outcome summaries include 120.0 participants in each ibuprofen group and 39.0 in the placebo group. Further participant-flow information and reasons for any exclusions are not reported in the registry record.
The primary efficacy population required treatment and at least one pain assessment after Time 0. The record does not describe missing assessments, missing-data handling, imputation, or sensitivity analyses. Without that information, the potential influence of incomplete outcome data cannot be assessed fully.
The registry record does not report the original sample-size justification or the assumptions used to design the trial. Planning illustrations based on observed effects are not a substitute for those original design details. The record also does not report a complete multiplicity strategy despite multiple secondary outcomes and posted analyses. This is relevant when interpreting secondary p-values as confirmatory evidence.
Although the sponsor’s primary comparison is identified as ANCOVA, the covariates and model specification are not reported. The analysis type is labeled EQUIVALENCE, but an equivalence margin is not reported. The record therefore does not supply the information needed to assess the equivalence framing in full. The simple unadjusted recalculation is not a replacement for that sponsor analysis.
The registry summary does not report a clinically important threshold for SPID12, so statistical differences cannot be translated directly into clinical importance. Safety reporting includes serious-event and other-event counts, but detailed event descriptions, timing, severity, and attribution are not reported. These limitations concern interpretation of the registry record and do not change the values it posts.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Efficacy of 300 mg Ibuprofen Prolonged-Release Tablets for the Treatment of Pain After Surgical Removal of Impacted Third Molars — NCT03785756.
- Registry record last updated 2024-06-03; status last verified 2024-05.
- Results first posted 2024-06-03.
- 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.
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23. Record Summary
The registry record describes a completed Phase 3 randomized, quadruple-masked, parallel-group study of prolonged-release ibuprofen, immediate-release ibuprofen, and placebo for pain after surgical removal of impacted third molars. Enrollment was 280. The primary endpoint was SPID12, a time-integrated summary of pain-intensity change from the first dose through 12 hours, with higher scores indicating a better outcome.
The posted primary means were 51.84 for prolonged release, 56.33 for immediate release, and 19.11 for placebo. Unadjusted recalculated comparisons with placebo were 32.73 and 37.22, respectively, with both p-values < 0.001. The sponsor ANCOVA comparison for prolonged release versus placebo reported a mean difference of 34.05 and a 95% confidence interval from 26.72 to 41.38.
The registry record reports no serious adverse events or deaths in the listed groups. Original sample-size assumptions, multiplicity procedures, missing-data methods, and detailed sponsor model specifications are not reported in the registry record.