Study Evaluating A Novel Ibuprofen Formulation In Episodic Tension-Type Headache: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Study Evaluating A Novel Ibuprofen Formulation In Episodic Tension-Type Headache (NCT01077973), a randomized phase 3 study. The primary outcome is Time-weighted Sum of Pain Relief Rating and Pain Intensity Difference From 0-3 Hours (SPRID 0-3) for Ibuprofen Sodium Versus Placebo Tablet.

2. Clinical Question

3. Trial Design

The registry describes a Phase 3, randomized, quadruple-masked, parallel-group study. Its title concerns a novel ibuprofen formulation for episodic tension-type headache, and its brief summary states that a single dose was to be compared with placebo and standard ibuprofen. The listed interventions are Novel Ibuprofen, Standard Ibuprofen, and Placebo. The arm descriptions are blank, however, so the record does not specify how each intervention corresponds to every treatment-arm label in the posted results.

The recorded overall enrollment is 200. The study status is completed, with a start date of 2010-03 and a primary completion date of 2010-10. These record-level details describe the study, but they do not establish the number of participants contributing to each outcome. For the primary comparison, the endpoint results list 41 participants for placebo and 79 for ibuprofen sodium. A separate safety group is labeled Ibuprofen (Motrin IB) and has its own at-risk count. These outcome-specific group counts should not be treated as a reconstruction of overall enrollment.

The primary outcome is continuous: a mean SPRID score over 0 to 3 hours, reported in units on a scale. The primary endpoint population is described as randomized participants who received study medication and provided a baseline assessment. The record also lists multiple secondary outcome measures, including pain relief ratings, pain intensity differences, combined scores, and time-to-relief outcomes. It records 15 outcome measures and 84 analyses, but the registry record does not explain how those analyses were organized or whether any multiplicity adjustment was planned.

The original sample-size justification, allocation ratio, planned analysis details beyond what is reported, interim analyses, and missing-data procedures are not reported in the registry record. The observed-outcome sample-size illustrations are separate planning calculations and should not be read as documentation of the original trial design.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Analysis population for the primary outcome, as defined in the registry: Intent-to-treat (ITT) population included all randomized participants who received study medication and provided a baseline assessment.

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 Time-weighted Sum of Pain Relief Rating and Pain Intensity Difference From 0-3 Hours (SPRID 0-3) for Ibuprofen Sodium Versus Placebo Tablet, measured over 0 to 3 hours.

The primary endpoint is the time-weighted sum of pain relief rating and pain intensity difference from 0 to 3 hours, abbreviated SPRID 0-3. It combines two kinds of patient-reported information: change in pain intensity from baseline and a rating of pain relief. The registry describes pain intensity difference as baseline pain severity minus pain severity at a later assessment, and pain relief rating as an assessment on a scale from no relief to complete relief. The combined PRID score is then used in the time-weighted SPRID measure.

The endpoint is reported as a mean in units on a scale, with a range from -3, described as worst, to 21, described as best. A higher score therefore represents a more favorable combined score under the registry's stated scale direction. Weighting the combined observations over the assessment period is intended to reflect both the degree of change and how that change develops across the 0-to-3-hour interval. It is not a direct measure of a single moment or a count of participants who experienced relief.

Using a continuous summary allows the comparison to retain information about the range of observed scores rather than reducing the outcome to a binary category. That can be useful when pain intensity and relief vary across participants. At the same time, a mean difference does not reveal the full distribution of individual scores, the proportion reaching a particular level of relief, or how the endpoint relates to other outcomes. Those details are not established by the primary mean comparison alone.

7. Results Posted in the Registry

• Ibuprofen Sodium: mean 10.80 versus 11.20 on control; difference -0.40 (95% CI -2.30 to 1.50), standardized effect d = -0.08; z-test p = 0.680.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is a continuous score, so the reported group summaries are means and standard deviations. A mean describes the average score in a group, while a standard deviation describes how dispersed participant scores are around that average. The posted means are 11.2 for placebo and 10.8 for ibuprofen sodium; the corresponding standard deviations are 4.9 and 5.3. These quantities describe the observed endpoint groups and do not, by themselves, show how uncertain the mean difference is.

What does a mean difference represent?

A mean difference subtracts one group's mean from the other group's mean. For the unadjusted recalculation, the direction is ibuprofen sodium minus placebo, giving -0.4 units. A negative value means the observed mean is lower in the group named first under that subtraction convention. The endpoint scale is oriented so that higher scores are better, but the estimate remains a summary of group averages, not a count of participants who improved or a measure of each participant's response.

The standard error describes the sampling uncertainty of an estimate. It is not a measure of variation between individuals. The recalculation uses the posted group sizes and standard deviations to estimate uncertainty around the unadjusted mean difference. The displayed standard errors for the group means are 0.765 for placebo and 0.596 for ibuprofen sodium. Standard errors are useful for constructing confidence intervals and testing a null hypothesis, but they depend on the statistical model and the quality of the data summaries.

Why distinguish an unadjusted recalculation from ANOVA?

The recalculation uses the posted group means and dispersions to form a simple, unadjusted contrast. The registry-reported analysis is an ANOVA result with a least-square mean difference. Least-square means are model-based estimates and can reflect features of the fitted analysis that are not captured by a direct subtraction of the displayed raw means. The registry reports the sponsor's estimate as -1.12, its 95% confidence interval as -3.23 to 1.00, and p = 0.299. The recalculated estimate is -0.4, with a 95% confidence interval from -2.301 to 1.501 and p = 0.68.

Those contrasts should be kept distinct. The methods differ, and the registry record does not report the model's covariates, coding, or further details needed to reproduce the ANOVA estimate. The posted record does not indicate that the recalculation supersedes the sponsor's analysis. It is best understood as a transparent, unadjusted comparison from the available summary statistics, alongside the analysis recorded by the sponsor.

What does a confidence interval add?

A confidence interval conveys uncertainty about an estimated contrast. Its width reflects the amount of information and variability under the method used. A narrower interval is more precise than a wider interval in the sense that it covers a smaller range of compatible values. A confidence interval is not a guarantee that the true value lies within its particular endpoints, and it does not indicate the probability that a treatment effect is present. Interpretation also depends on whether the analysis assumptions are reasonable.

For both contrasts, the 95% interval includes zero and extends to values on either side. The interval therefore does not rule out a zero mean difference at that confidence level. It also leaves uncertainty about the direction and magnitude of the difference. Statistical uncertainty should not be confused with evidence that the groups are equivalent: an equivalence conclusion requires a prespecified margin and an analysis designed to assess it, neither of which is reported in the registry record.

Why can over-dispersion matter?

In general, over-dispersion means that observed variability is greater than a statistical model expects. When a model underestimates variability, its standard errors can be too small, making confidence intervals too narrow and tests too optimistic. This concept is especially relevant to count or event data, though the primary endpoint is a continuous score summarized by means and standard deviations. The registry's reported primary analysis is ANOVA; the record does not report a diagnostic assessment of the model assumptions or an adjustment for over-dispersion. There is not enough information to say whether over-dispersion was relevant to the sponsor's analysis.

What role do the p-values play?

The unadjusted p-value of 0.68 belongs to the recalculated contrast, while p = 0.299 is reported for the ANOVA result. Each p-value is calculated under its corresponding statistical procedure and null hypothesis. Neither quantifies the probability that the null hypothesis is true, the probability that the observed result occurred by chance in an everyday sense, or the size of a clinically meaningful effect. A p-value is also not a substitute for examining the estimate, interval, endpoint definition, and analysis population together.

Multiplicity is a separate methodological concern because the record lists numerous outcome measures and analyses. When many hypotheses are examined, the chance of at least one apparently unusual finding can increase if no correction or prespecified hierarchy is used. The registry record does not report a multiplicity strategy for the posted analyses. This does not establish that no strategy was used; it means the record does not describe one.

10. Confidence Intervals and Precision

The unadjusted mean difference is -0.4 units, with a 95% confidence interval from -2.301 to 1.501. This interval is wide enough to include zero as well as values on either side of zero. It therefore does not pin down a single direction or a narrowly defined magnitude for the unadjusted difference. The sponsor's ANOVA estimate is -1.12, with a 95% confidence interval from -3.23 to 1.00. That interval also includes zero and spans values in both directions.

Confidence intervals are useful because they present a range of estimates compatible with the data under a specified method, rather than reducing the result to a point estimate or p-value. The point estimate is the center of attention, but it has sampling uncertainty. The interval's width provides a way to judge how much precision the data offer under the analysis. A confidence interval is not a range guaranteed to contain the true effect, and it does not assign probabilities to individual values within its bounds.

Both intervals are compatible with no mean difference at the stated confidence level, but that is not proof that the groups are identical. A failure to exclude zero is different from demonstrating equivalence or ruling out differences that might matter. Such conclusions require a defined margin and an appropriate design and analysis; these are not reported in the registry record.

Precision also depends on the analysis population, outcome variability, and methods used to estimate the contrast. The outcome groups have different posted sizes and standard deviations, and the sponsor-reported model-based result is not the same as the unadjusted recalculation. Because the registry record does not report full model details or missing-data handling, the intervals should be read as results of their respective stated approaches rather than as exact answers to every possible analysis question.

11. Planning a Similar Trial: Sample Size

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

The sample-size figures are planning illustrations based on the observed effect, not the trial's original design calculation. For this continuous outcome, the displayed figures are participants per arm, rather than total events. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The planning effect is set at a stated fraction of the observed effect. The original trial's sample-size assumptions are not reported in the registry record.

The 80% power column gives the planned participants per arm under the stated assumptions for a design that would have an 80% probability of detecting the specified effect if that effect were the true one. The 90% power column gives the corresponding per-arm planning figure for a higher probability of detection under the same assumptions. These are design targets, not statements about what the completed trial achieved.

The rows represent planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. The corresponding per-arm figures are 2,621 and 3,508 for 100% of the observed effect; 4,659 and 6,237 for 75%; and 10,481 and 14,032 for 50%, for 80% and 90% power respectively. Smaller effects require more participants to detect under these assumptions, which is why the planning figures rise as the effect fraction gets smaller.

This is not observed power. It is a forward-looking illustration using the observed effect as an input; it does not measure the probability that the completed study found a true effect. The curve should be read in the same planning context: it illustrates how required per-arm sample size changes with the assumed effect, rather than showing an observed trial outcome or validating the trial's original design.

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 = -0.400; pooled standard deviation σ = 5.168.
2. n = 2 × (1.96 + 0.842)² × 5.168² / -0.400² = 2,620.2, rounded up to 2,621 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 <- -0.399999999999999                      # observed difference in means
sigma <- 5.16787665802333                     # 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(1077973)
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 = 2,621 (80% power), 3,508 (90% power)
 75% of observed effect: n per arm = 4,659 (80% power), 6,237 (90% power)
 50% of observed effect: n per arm = 10,481 (80% power), 14,032 (90% power)
power.t.test: 2621.2 
Simulated power at n = 2,621 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. Analyses Reported by the Sponsor

The registry reports the sponsor's primary analysis as an ANOVA least-square mean difference of -1.12, with a 95% confidence interval from -3.23 to 1.00 and p = 0.299. The unadjusted recalculation from the posted group summaries gives a mean difference of -0.4, with a 95% confidence interval from -2.301 to 1.501 and p = 0.68. Both intervals include zero, but the estimates and p-values differ because the results come from different analysis approaches.

The recalculation is a simple unadjusted comparison of the posted means and their variability. It does not reproduce the ANOVA model or its least-square mean contrast. The registry record does not provide sufficient detail about the sponsor's model to explain the difference or to independently reconstruct the reported estimate. The recalculation should therefore be read as a separate descriptive statistical check, not as a replacement for the sponsor's own analysis. The record does not flag a discrepancy between these results.

Neither estimate should be interpreted in isolation. The direction and size of each point estimate, its interval, the endpoint's scale, and the analysis method all matter. The registry's analysis is the trial's reported result; the recalculation helps readers understand what follows from a direct contrast of the posted summaries. The registry record does not report enough detail to determine whether the model incorporated additional factors or how any such factors affected the estimate.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists multiple outcome measures and analyses. It records 15 outcome measures and 84 analyses, and includes secondary outcomes such as time to relief, pain relief rating, pain intensity difference, and time-weighted combined measures. With multiple statistical tests, the chance of obtaining at least one result that appears unusual can increase when each test is interpreted without regard to the others. In general, multiplicity can be addressed through prespecified outcome hierarchies, adjustments to significance thresholds, or other planned procedures.

The multiplicity strategy for this trial is not reported in the registry record. The record also does not explain whether the primary outcome was tested within a hierarchy, whether any adjustment was applied to secondary outcomes, or how the numerous analyses relate to the study's objectives. It is therefore not possible to determine from the registry information whether the reported p-values account for the full set of analyses. The primary p-values should be read as the values reported for their respective analyses, not as evidence that a multiplicity procedure was or was not used.

The primary endpoint population is defined as randomized participants who received study medication and provided a baseline assessment. This definition is reported, but the registry does not describe how missing post-baseline endpoint measurements were handled, how many participants lacked measurements, or whether imputation or sensitivity analyses were used. It also does not report a detailed participant flow for the primary endpoint. These omissions limit assessment of whether missing outcomes could have influenced the comparison.

The registry identifies the primary analysis method as ANOVA and the reported parameter as a least-square mean difference. Further model details, including covariates and diagnostics, are not reported in the registry record. The record does not report whether interim analyses were planned or conducted, nor does it provide the original sample-size justification. These absences should be treated as limitations in the available record, not as evidence that the trial had no such procedures.

For these reasons, the primary contrast can be interpreted as a posted result with a defined population and named analysis, but not as a fully reproducible account of every decision affecting the estimate. Any broader interpretation across outcomes would require the prespecified analysis plan and fuller information on multiplicity, missing data, and model specification.

15. Safety Results

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

Other (non-serious) adverse events

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

The serious adverse event figures report zero events among 41 participants at risk in the placebo group, zero among 79 at risk in the Ibuprofen Sodium group, and zero among 80 at risk in the Ibuprofen (Motrin IB) group. The registry also reports zero other adverse events in each of those groups. These are the posted counts for the stated categories and at-risk groups.

A zero count in a group means that no event in that category was recorded among the participants counted at risk in that group. It does not establish that an event is impossible, that risk is absent, or that groups have identical safety profiles. Counts from groups of different sizes also do not have equal precision. The registry does not list serious adverse event terms among the top serious terms.

The deaths values are not reported in the registry record. The available adverse-event figures do not give detail about event definitions, timing, follow-up completeness, or the method used to collect events. They should be read as descriptive registry counts, not as a complete assessment of safety or as evidence for a treatment recommendation.

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

The posted primary comparison describes a continuous pain-related score over 0 to 3 hours. The mean was 10.8 for ibuprofen sodium and 11.2 for placebo. The sponsor-reported ANOVA estimate and the unadjusted recalculation both have confidence intervals that include zero. The data therefore leave uncertainty about the mean difference under both reported approaches; they do not establish that the groups are equivalent, nor do they precisely resolve the direction or magnitude of the difference.

The endpoint combines pain relief rating and pain intensity difference across an assessment period. It is a summary measure, not a direct count of participants who experienced meaningful relief. The mean comparison cannot show the full distribution of scores, how individual participants changed, or what proportion met a particular threshold. The registry record does not report a threshold for a clinically important difference on this endpoint.

The result is limited to the posted primary comparison between ibuprofen sodium and placebo in the defined endpoint population. Although the study summary describes a comparison that also includes standard ibuprofen, the primary results do not provide an efficacy contrast for standard ibuprofen. Safety counts are reported for a separately labeled Ibuprofen (Motrin IB) group, but those counts do not supply the missing efficacy comparison.

The study also lists secondary outcomes and many analyses. The primary result cannot stand in for all of those outcomes, and the registry does not report the multiplicity approach or detailed missing-data procedures. The posted evidence is therefore best understood as a specific mean comparison with substantial uncertainty, rather than a complete account of every effect or outcome evaluated in the trial.

These statistics do not provide medical advice and do not establish whether a treatment should be used. They describe what the registry reports for this endpoint and how precisely the difference is estimated under the stated methods. Broader conclusions would require the full analysis context, complete outcome reporting, and consideration of clinical meaning in addition to statistical uncertainty.

17. Why This Trial Matters Statistically

This trial illustrates why a clinical result should be read through both its estimate and its uncertainty. The point estimates alone are not enough: the posted mean difference is -0.4 in the unadjusted recalculation, while the sponsor's model-based estimate is -1.12. Their confidence intervals include zero and cover a range of values in both directions. A reader who looks only at a p-value or at the direction of a point estimate could miss that uncertainty.

It also demonstrates the distinction between a direct recalculation from summary statistics and a trial's own reported analysis. The recalculation is useful as a transparent comparison of posted means, but it does not reproduce the sponsor's ANOVA least-square mean result. Without fuller model details, the differences cannot be attributed to any particular analytic choice. Keeping the estimates separate is more informative than treating one as a correction of the other.

The endpoint itself combines pain intensity and relief ratings over time. This can retain more information than a single binary outcome, but its mean difference is not self-interpreting. The scale direction, construction, uncertainty, and clinical meaning all matter. The registry does not report a threshold for a meaningful difference, limiting interpretation of the numerical contrast beyond its statistical description.

Finally, the record lists many outcomes and analyses, yet does not report the multiplicity approach or missing-data procedures. Those details are central to judging how a primary result fits into the full body of analyses. The trial is therefore a useful example of reading an estimate in context: distinguish the endpoint, population, analysis, and precision, and avoid extending one comparison beyond what it can answer.

18. Limitations

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

The registry record leaves several trial-specific questions unanswered. The arm descriptions are blank, so the correspondence between the named interventions and all treatment-arm labels cannot be reconstructed from the record. The primary result compares ibuprofen sodium with placebo, but the reported primary contrast does not include an efficacy estimate for standard ibuprofen. The additional safety group labeled Ibuprofen (Motrin IB) should not be mistaken for an efficacy result.

The primary endpoint is described in detail, but the registry does not report a clinically meaningful difference threshold for SPRID 0-3. Without such a threshold, the clinical importance of the estimated mean differences cannot be judged from these statistics alone. The two analyses also differ in method: one is a sponsor-reported ANOVA least-square mean contrast, and the other is an unadjusted recalculation. Model details are not available to explain or reproduce the sponsor's estimate.

The registry does not report how missing post-baseline endpoint data were handled, the number of missing endpoint values, or sensitivity analyses for missingness. It does not describe the multiplicity strategy despite listing many analyses. Nor does it report the original sample-size justification or interim analysis plans. These gaps limit assessment of the analysis context and the robustness of the result.

Finally, the registry's adverse-event counts are descriptive and provide no detail about collection procedures, event timing, or follow-up completeness. Deaths are not reported in the registry record. These limitations concern the information available in the record; they do not establish that additional trial documents or analyses do not exist.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Study Evaluating A Novel Ibuprofen Formulation In Episodic Tension-Type Headache — NCT01077973.
• Registry record last updated 2012-08-20; status last verified 2012-07.
• Results first posted 2012-08-20.
• 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.

22. Record Summary

The registry describes a completed Phase 3, randomized, quadruple-masked, parallel-group study of a novel ibuprofen formulation for episodic tension-type headache. The recorded enrollment is 200, and the study dates are 2010-03 to 2010-10. Its primary outcome is the mean time-weighted sum of pain relief rating and pain intensity difference from 0 to 3 hours.

The primary endpoint results list means of 11.2 for placebo and 10.8 for ibuprofen sodium. The sponsor-reported ANOVA least-square mean difference is -1.12, with a 95% confidence interval from -3.23 to 1.00 and p = 0.299. The unadjusted recalculation gives -0.4, with a 95% confidence interval from -2.301 to 1.501 and p = 0.68. Both intervals include zero.

The record also lists numerous secondary outcomes and analyses. Multiplicity handling, detailed missing-data procedures, the original sample-size justification, and further model details are not reported in the registry record. Posted adverse-event counts are zero for serious and other adverse events in the listed groups; deaths are not reported in the registry record.