Ibuprofen Sodium Tension Headache Study: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Ibuprofen Sodium Tension Headache Study (NCT01362491), 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 record describes a completed phase 3, randomized, quadruple-masked, parallel-group trial. The stated enrollment was 226. Its brief summary says the study compared the ability of a single dose of a novel ibuprofen formulation to relieve pain with placebo and standard ibuprofen in the treatment of tension-type headache. The listed interventions were ibuprofen sodium, standard ibuprofen, and placebo.

The primary outcome reported for this analysis is narrower than the overall study aim: it compares ibuprofen sodium with placebo on SPRID 0-3. The record also lists a standard-ibuprofen intervention, but the primary endpoint result presented for interpretation does not provide a result for ibuprofen sodium versus standard ibuprofen. Arm descriptions are blank in the record, so further details about the specific treatment assignments and procedures are not reported in the registry record.

Randomization is intended to assign participants to trial groups by chance, helping make groups comparable on average with respect to factors that could affect outcomes. Masking is intended to limit the influence of knowing treatment assignment on participants, investigators, or other parties involved in the study. The registry identifies quadruple masking but does not specify in the record which roles were masked or how masking was maintained. A parallel design means the groups are followed as separate treatment groups rather than participants crossing between treatments; this is a general explanation of the design label.

The primary endpoint analysis identifies an intent-to-treat population of randomized participants who received study medication and provided a baseline assessment. Endpoint group counts were 91 for ibuprofen sodium and 46 for placebo. The analysis population definition and those counts do not establish how participants with missing follow-up outcome data were handled. That handling is not reported in the registry record.

4. Participant Flow and Accounting

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

Overall Study

Reasons for not completing this period:

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 0-3 Hours.

The primary endpoint, SPRID 0-3, is the time-weighted sum of pain relief rating and pain intensity difference over 0-3 hours. It combines participants’ pain relief ratings with changes in pain intensity from baseline. The registry describes pain relief on a scale from 0, no relief, to 4, complete relief. Pain intensity difference is baseline pain severity minus severity at a later time point. The combined PRID score is the sum of the pain intensity difference and pain relief rating at each time point, and SPRID accumulates this combined information over the endpoint’s time window.

The stated SPRID 0-3 range is -3, worst, to 21, best. A higher score therefore represents a more favorable combined pain-relief and pain-intensity profile within this measure’s defined scoring system. Time-weighting is used to incorporate the pattern of measurements over the stated period rather than treating a single assessment as the entire outcome. This is a general description of what a time-weighted endpoint does; the registry record does not provide further detail about the calculation schedule or weighting procedure.

This kind of continuous summary can help compare average outcomes across randomized groups while incorporating both pain relief and change in pain intensity. It does not show the experience of every participant, nor does it independently describe how quickly relief began. The record lists time-to-relief outcomes separately among the secondary outcomes. The primary endpoint’s unit is recorded as units on scale, and its dispersion is reported as standard deviation.

7. Results Posted in the Registry

• Ibuprofen Sodium: mean 9.60 versus 3.50 on control; difference 6.10 (95% CI 4.54 to 7.66), standardized effect d = 1.32; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: it is a numerical score that can take a range of values. The registry says the analysis parameter was a mean and that variability was expressed as a standard deviation. Comparing means is a way to summarize whether the average score differed between groups. It does not imply that every participant had the group’s average result.

What does the mean difference represent?

The sponsor reports an ANOVA least-square mean difference of 6.11 for ibuprofen sodium versus placebo. A least-square mean is a model-based group mean or contrast. ANOVA, or analysis of variance, is a general statistical framework for comparing group averages. The registry reports the method and the least-square mean difference, but does not report the full model specification or covariates used. Those details are not reported in the registry record.

The recalculated estimate is an unadjusted mean difference of 6.1. It is formed from the posted group means, 9.6 and 3.5, without the sponsor’s reported model-based analysis. The unadjusted recalculation gives a useful check of the scale and direction of the comparison, but it is not a replacement for the sponsor’s stated analysis. Because the discrepancy flag is false, the record does not identify a material disagreement requiring the sponsor’s analysis to take precedence on that basis. The analyses nevertheless differ in method, and their estimates and intervals should be named accurately rather than treated as interchangeable.

What does the standard deviation describe?

A standard deviation describes how dispersed individual scores are around a group mean. The reported standard deviations are 4.8 for ibuprofen sodium and 4.2 for placebo. A larger standard deviation indicates more spread in scores on the same measurement scale. It does not indicate uncertainty about the estimated difference by itself. The standard error and confidence interval for a group contrast also depend on the sample sizes and the method used to estimate the contrast.

The posted recalculation uses a pooled standard deviation of 4.609 and reports a standardized difference of 1.324. These are recalculated, unadjusted summaries, not additional sponsor analyses. A standardized difference expresses the group contrast relative to the pooled spread of scores, which can help describe magnitude on a scale less tied to the original measurement units. It does not replace the difference in SPRID units, and it does not establish clinical importance. The registry record gives no threshold for a clinically important SPRID difference.

Why is the confidence interval useful?

A confidence interval describes statistical uncertainty around an estimated effect under the assumptions of the analysis. It gives a range of values compatible with the observed data and method at its stated confidence level. The sponsor’s reported 95% confidence interval is 4.49 to 7.73 for the least-square mean difference. The recalculated 95% interval is 4.536 to 7.664 for the unadjusted difference. These intervals belong to their respective analyses. Neither interval gives the range of individual participant scores, and neither accounts for limitations that may arise from missing data, selective reporting, or unreported design details.

The sponsor’s p-value is <0.001, and the recalculated unadjusted p-value is also <0.001. A p-value measures how incompatible the observed data are with a specified null model, assuming the 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 the difference. The record does not report an adjustment for testing multiple outcomes or analyses.

Why can over-dispersion matter?

Over-dispersion is a general concern when observed variability is greater than a statistical model assumes. If a model understates variability, its standard errors may be too small and its confidence intervals too narrow. The primary endpoint is continuous and the record reports standard deviations, but it does not report an over-dispersion assessment or a model diagnostic. There is no basis in the registry record to say that over-dispersion was present or that it affected this analysis.

The primary analysis population is described as intent-to-treat, including randomized participants who received study medication and provided a baseline assessment. This definition is specific to the posted outcome description. The handling of participants who lacked a follow-up SPRID measurement, any imputation, and any sensitivity analysis are not reported in the registry record. Those missing-data choices can affect the interpretation of a mean comparison, particularly if the availability of outcome data is related to treatment assignment or the outcome.

Finally, an analysis method cannot be fully evaluated from a method label alone. The record identifies ANOVA and least-square mean difference but does not provide the model terms, diagnostic checks, or detailed analysis plan. The interpretation should therefore stay with the reported estimate, interval, p-value, outcome definition, and stated population rather than assume additional methods that are not documented.

10. Confidence Intervals and Precision

The sponsor’s 95% confidence interval for the least-square mean difference is 4.49 to 7.73. Its width reflects uncertainty in the estimated contrast under the sponsor’s analysis. The whole interval is on the positive side of zero, so the reported direction of the mean difference is supported across the interval’s range. The estimate is 6.11. This interval does not mean that 95% of individual participant results fall between its endpoints; it concerns the estimated group contrast.

The unadjusted recalculation gives a mean difference of 6.1 and a 95% confidence interval from 4.536 to 7.664. Its interval is close to, but not the same as, the sponsor’s interval. That is expected to be possible because the calculations are not the same analysis: the sponsor reports an ANOVA least-square mean contrast, while the recalculation is unadjusted and based on posted summary statistics. The sponsor’s p-value is <0.001; the recalculated p-value is <0.001.

The group standard deviations, 4.8 and 4.2, show that individual scores varied around their respective means. The confidence interval for the difference is the more direct description of precision for the between-group contrast. It does not resolve questions about the representativeness of the analysis population, missing outcomes, multiplicity, or clinical importance. Those matters require information not reported in the registry record, such as the missing-data approach, the complete analysis plan, and an established interpretation threshold for SPRID. Thus, the result is statistically precise enough to distinguish the reported mean contrast from zero under the stated analysis, while important aspects of broader evidential precision remain undocumented.

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

The 80% power column gives the illustrated number of participants per arm for a design that would have an 80% probability of detecting the specified effect under the listed assumptions, if that effect and the assumptions were correct. The 90% power column describes the corresponding planning target for a 90% probability. These are planning concepts, not guarantees that a future study will produce a statistically significant result. The displayed scenarios cover planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect.

The figures increase as the effect to be detected becomes smaller: a smaller difference is harder to distinguish from ordinary variation, so more participants are generally needed to achieve the same planned power under otherwise unchanged assumptions. The posted values are 9 and 12 participants per arm for planning at 100% of the observed effect, 16 and 22 for planning at 75% of the observed effect, and 36 and 48 for planning at 50% of the observed effect, for 80% and 90% power respectively. These are not observed power calculations; they are planning illustrations derived from the observed effect.

The planning exercise uses the observed contrast, which may overstate the effect expected in a new study. Smaller-effect scenarios help show how planning changes if the true effect is less pronounced. The figures do not include allowances for loss to follow-up, departures from the assumed allocation, or other design features unless specified in the listed assumptions. Such adjustments 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 = 6.100; pooled standard deviation σ = 4.609.
2. n = 2 × (1.96 + 0.842)² × 4.609² / 6.100² = 9.0, rounded up to 9 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 <- 6.1                      # observed difference in means
sigma <- 4.60868744872116                     # 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(1362491)
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 = 9 (80% power), 12 (90% power)
 75% of observed effect: n per arm = 16 (80% power), 22 (90% power)
 50% of observed effect: n per arm = 36 (80% power), 48 (90% power)
power.t.test: 10 
Simulated power at n = 9 per arm: 0.749 (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 sponsor’s posted primary analysis is an ANOVA least-square mean difference of 6.11, with a 95% confidence interval from 4.49 to 7.73 and p < 0.001. The posted group means are 9.6 for ibuprofen sodium and 3.5 for placebo. The unadjusted recalculation from those summaries estimates a mean difference of 6.1, with a 95% confidence interval from 4.536 to 7.664 and p < 0.001.

The estimates are close, but the calculations should not be described as identical. The sponsor’s least-square mean contrast comes from the reported ANOVA, while the recalculation is an unadjusted comparison using posted summary statistics. The registry does not give the complete sponsor model specification, so the reason for every small difference cannot be established from the record. The discrepancy flag is false. There is no recorded discrepancy that calls for the sponsor’s analysis to take precedence over the recalculation; nevertheless, the sponsor’s own analysis remains the trial’s reported primary analysis, and the recalculation is best treated as a separate statistical check.

Both results point in the same direction and both reported p-values are <0.001. The sponsor result is the relevant reference for what the trial’s posted primary analysis concluded statistically. The recalculation helps readers understand the magnitude from group summaries but does not reproduce the full model-based analysis.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 15 outcome measures, 81 analyses, and 13 posted secondary outcomes. The secondary outcomes include time to onset of meaningful relief, time to confirmed first perceptible relief, pain relief rating, pain intensity difference, combined pain relief and intensity measures, and time-weighted summaries. The primary endpoint is one component of a broader set of recorded outcomes.

When many outcomes or analyses are examined, the chance of at least one apparently unusual finding can rise if results are interpreted without accounting for the number of tests. Statistical approaches to multiplicity can adjust significance thresholds, control error rates, or designate a limited set of primary analyses in advance. The registry record does not report whether a multiplicity adjustment was used, how the secondary outcomes were prioritized, or whether the analysis sequence was prespecified. The listed number of analyses alone does not establish that the primary result is invalid; it does mean the primary result should be interpreted with the wider outcome set in mind.

The primary population is described as intent-to-treat participants who were randomized, received study medication, and provided a baseline assessment. The record does not say how missing post-baseline endpoint measurements were handled, whether any values were imputed, or whether sensitivity analyses tested alternative missing-data assumptions. It also does not provide a flow of participants with available primary endpoint data or reasons for missing outcome measurements. These details are not reported in the registry record.

The record identifies a randomized trial and a primary endpoint, but does not report the full statistical analysis plan, the model terms, or the methods used to address missing data and multiplicity. It is therefore not possible to assess from the registry record whether the posted result was robust to those choices. The estimate and interval can be read as the reported primary comparison, while claims about analysis-plan compliance, missing-data robustness, or adjustment across outcomes remain unsupported by the record.

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 registry reports serious adverse events for ibuprofen sodium, standard ibuprofen (Motrin IB), and placebo. The serious adverse event figures are zero for each listed group: 0 among 91 at risk for ibuprofen sodium, 0 among 89 at risk for standard ibuprofen, and 0 among 46 at risk for placebo. The separate count of other adverse events is also zero in each group at risk: 0 among 91, 0 among 89, and 0 among 46, respectively.

These are registry-reported counts for the groups and at-risk populations identified in the safety record. A zero count means no event in that category was recorded for that group in this listing; it does not prove that an event is impossible or that no safety risk exists. The death entries are null, so deaths are not reported in the registry record. The serious adverse event terms list is empty.

The safety listing should not be confused with the primary efficacy endpoint groups. The safety record includes 89 at risk in the standard-ibuprofen group, while the primary endpoint comparison is ibuprofen sodium versus placebo. The registry does not provide additional detail about adverse-event definitions, collection procedures, duration of safety follow-up, or event adjudication. The figures therefore describe the posted record, not a comprehensive assessment of safety.

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

The primary result shows a higher mean SPRID 0-3 score for ibuprofen sodium than for placebo in the posted endpoint analysis. The sponsor reports a least-square mean difference of 6.11, with a 95% confidence interval from 4.49 to 7.73 and p < 0.001. Because higher SPRID scores indicate a more favorable combined pain relief and pain-intensity result, the direction of the group-average difference favors ibuprofen sodium on this measure over 0-3 hours.

This finding is specific to the primary endpoint, the stated time window, the compared groups, and the analyzed population. It does not describe every participant’s experience. Group means can differ even when individual outcomes vary substantially, as reflected in the reported standard deviations of 4.8 and 4.2. The endpoint also combines pain-relief ratings and changes in pain intensity, so it should not be read as a direct estimate of either component alone.

The result does not establish the comparison with standard ibuprofen. Although standard ibuprofen is listed as an intervention, a primary endpoint result for that comparison is not reported in the registry record. Nor does the result determine effects on the various secondary outcomes, longer-term outcomes, or outcomes that were not recorded. The registry’s secondary outcome list includes separate measures of time to relief, pain ratings, and time-weighted summaries, but their results are not included in the registry record for this analysis.

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 meaningful SPRID difference, so clinical importance cannot be established from the effect estimate and p-value alone. The result also does not support medical advice or conclusions about which treatment an individual should use.

Finally, interpretation is limited by unreported details about missing endpoint data, multiplicity, the sponsor’s full model specification, and the original sample-size rationale. Those gaps do not erase the reported comparison, but they limit how fully it can be independently evaluated. The appropriate conclusion is confined to the registry’s stated analysis and endpoint rather than extended to broader claims.

17. Why This Trial Matters Statistically

This trial illustrates why the endpoint definition matters as much as the treatment labels. SPRID 0-3 is not a single pain rating: it combines pain relief ratings and pain intensity differences over a specified time window. Interpreting the result requires knowing which direction is favorable, what the scale covers, and what period it represents. The registry provides that scale context, allowing the positive mean contrast to be understood as a higher combined score for ibuprofen sodium than for placebo.

It also illustrates the distinction between a sponsor’s model-based result and a summary-statistic recalculation. The sponsor reports an ANOVA least-square mean difference, whereas the recalculation is an unadjusted difference from posted means and standard deviations. Their close values offer a useful cross-check, but method labels matter: the two estimates and confidence intervals should remain attached to the analyses that produced them.

The planning illustration shows how sample-size requirements depend on the effect a study aims to detect. Planning around a smaller effect requires more participants per arm under the stated assumptions. This is distinct from retrospective power, and it cannot recover the trial’s original planning rationale, which is not reported in the registry record.

Finally, the registry identifies a broad set of outcomes and analyses, while leaving multiplicity handling and missing-data methods undocumented. Statistical interpretation therefore involves more than reading a small p-value: it also requires attention to the endpoint, analysis population, interval, and limits of the record. The trial offers a concrete example of how a statistically clear primary contrast can coexist with uncertainty about analysis details and broader interpretation.

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 does not provide detailed arm descriptions, so the exact treatment procedures beyond the intervention names and the brief study summary are not reported. Although it identifies quadruple masking, it does not specify which parties were masked or how masking was implemented. The record also does not provide the full protocol or statistical analysis plan.

The primary analysis is described as an ANOVA of least-square means, but model terms, covariate adjustments, diagnostic checks, and the complete estimation procedure are not reported. The unadjusted recalculation cannot reproduce those details. The primary outcome is defined with its range and components, but further detail on the timing and weighting of measurements is not reported in the registry record.

The record does not explain how missing primary outcome measurements were handled, whether imputation or sensitivity analyses were used, or how many otherwise eligible participants lacked an endpoint score. It also does not report the original sample-size justification or the trial’s design assumptions. The planning figures associated with the observed effect are illustrative and do not fill that gap.

Multiplicity methods are not reported, despite 15 outcome measures and 81 analyses being listed. The registry also does not provide enough information to evaluate the ordering or prespecification of all analyses. A result for the primary endpoint comparison with standard ibuprofen is not reported. Safety details beyond the listed adverse-event counts, including definitions and follow-up procedures, are not reported in the registry record. These limitations constrain independent assessment and broader conclusions without changing the numerical result that the registry reports for the primary comparison.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Ibuprofen Sodium Tension Headache Study — NCT01362491.
• Registry record last updated 2014-07-30; status last verified 2014-07.
• Results first posted 2014-07-30.
• 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

NCT01362491 is a completed phase 3 randomized, quadruple-masked, parallel-group trial sponsored by Pfizer. The registry lists an enrollment of 226 and interventions of ibuprofen sodium, standard ibuprofen, and placebo. Its stated aim was to compare a single dose of a novel ibuprofen formulation with placebo and standard ibuprofen for tension-type headache.

The primary endpoint was SPRID 0-3, a time-weighted combined measure of pain relief rating and pain intensity difference over 0-3 hours. The posted sponsor analysis comparing ibuprofen sodium with placebo reports a least-square mean difference of 6.11, a 95% confidence interval from 4.49 to 7.73, and p < 0.001. The unadjusted recalculation is 6.1, with a 95% confidence interval from 4.536 to 7.664.

The record lists 15 outcome measures and 81 analyses. It reports zero serious adverse events in each listed safety group; deaths are not reported in the registry record. Details on multiplicity, missing-data handling, and the full analysis plan are not reported in the registry record.