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 Aripiprazole in Children and Adolescents With Bipolar I Disorder (NCT00110461), a randomized phase 3 study. The primary outcome is Change in Young Mania Rating Scale (Y-MRS) Total Score at Week 4.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00110461 |
| Phase | Phase 3 |
| Condition | Bipolar Disorder |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 296 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Otsuka Pharmaceutical Development & Commercialization, Inc. |
| Results posted | Yes |
2. Clinical Question
Population
Children and adolescents with bipolar I disorder who were experiencing a manic or mixed episode, with or without psychotic features. The primary efficacy description says the analysis included randomized participants with a baseline assessment and at least one post-baseline assessment; the number contributing to that analysis could therefore differ from the randomized group sizes.
Intervention
Aripiprazole was assigned in two dose groups: 10 mg per day and 30 mg per day. The registry lists tablet interventions for both dose groups.
Comparator
The comparator was placebo. The registered parallel-group design assigned participants among the two aripiprazole groups and the placebo group.
Primary question
The primary endpoint was change from baseline to Week 4 in total score on the Young Mania Rating Scale. The statistical question was whether the observed score changes in each aripiprazole group differed from those in the placebo group. The registry record reports sponsor analyses and also permits unadjusted comparisons reconstructed from the posted group means and standard deviations.
3. Trial Design
The registry describes a phase III, randomized, quadruple-masked, parallel-group trial of aripiprazole in children and adolescents with bipolar I disorder. The trial compared 10 mg per day and 30 mg per day with placebo. The recorded enrollment was 296. The registry lists the study as completed, with the start recorded as 2005-03 and primary completion as 2007-02.
The primary efficacy endpoint was change in Young Mania Rating Scale total score from baseline to Week 4, using last observation carried forward. The primary efficacy population was not necessarily identical to the randomized population: the endpoint description specifies randomized participants with both a baseline and at least one post-baseline assessment. The registry record does not give the exact original enrollment target or the reasoning used to choose it.
The record lists 30 outcome measures and 60 analyses, including secondary assessments at Week 4 and later follow-up. The intervention arms are described as aripiprazole 10 mg/day, aripiprazole 30 mg/day, and placebo. The posted primary endpoint group sizes are 96, 99, and 92, respectively; these are analysis counts, not a substitute for the recorded enrollment.
Masking is recorded as quadruple, but the registry record does not describe which roles were masked or how masking was maintained. Allocation concealment procedures, stratification factors, adherence procedures, and the detailed trial protocol are not reported in the registry record. These omissions limit the ability to assess design implementation beyond the broad randomized, masked, parallel-group description.
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.
Before assignment: Participants were screened over a 28-day period.
30-Week, Double-blind Treatment Phase
| Stage | Aripiprazole 10 mg/Day | Aripiprazole 30 mg/Day | Placebo |
|---|---|---|---|
| STARTED | 98 | 99 | 99 |
| COMPLETED | 34 | 22 | 12 |
| NOT COMPLETED | 64 | 77 | 87 |
Acute Phase
| Stage | Aripiprazole 10 mg/Day | Aripiprazole 30 mg/Day | Placebo |
|---|---|---|---|
| STARTED | 98 | 99 | 99 |
| COMPLETED | 84 | 77 | 76 |
| NOT COMPLETED | 14 | 22 | 23 |
Analysis population for the primary outcome, as defined in the registry: Since the primary efficacy endpoint is change from baseline in Y-MRS total score, only randomized subjects who had both baseline and at least one post-baseline were included in the primary efficacy analysis. Therefore, number of randomized subjects be different number subjects included in 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.
| Characteristic | Unit | Aripiprazole 10 mg/Day | Aripiprazole 30 mg/Day | Placebo | Total |
|---|---|---|---|---|---|
| Participants analysed | 98 | 99 | 99 | 296 | |
| Age Continuous | years | 13.70 (SD 2.17) | 13.31 (SD 2.32) | 13.28 (SD 2.12) | 13.43 (SD 2.21) |
| Sex: Female, Male: Female | Participants | 46 | 48 | 43 | 137 |
| Sex: Female, Male: Male | Participants | 52 | 51 | 56 | 159 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 6 | 10 | 15 | 31 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 92 | 89 | 84 | 265 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Asian | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 2 | 0 | 0 | 2 |
| Race (NIH/OMB): Black or African American | Participants | 24 | 18 | 23 | 65 |
| Race (NIH/OMB): White | Participants | 65 | 68 | 60 | 193 |
| Race (NIH/OMB): More than one race | Participants | 2 | 2 | 2 | 6 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 5 | 11 | 14 | 30 |
| Height | centimeters (cm) | 161.05 (SD 12.45) | 158.37 (SD 12.21) | 158.69 (SD 11.63) | 159.36 (SD 12.12) |
| Weight | kilograms (kg) | 63.76 (SD 20.11) | 60.49 (SD 21.50) | 60.48 (SD 17.31) | 61.57 (SD 19.71) |
| Body Mass Index (BMI) | kg/m^2 | 24.15 (SD 5.37) | 23.66 (SD 6.70) | 23.68 (SD 4.98) | 23.83 (SD 5.72) |
| Young Mania Rating Scale Score (Y-MRS) | points | 29.8 (SD 6.5) | 29.5 (SD 6.3) | 30.7 (SD 6.8) | 30.0 (SD 6.5) |
| Children's Depression Rating Scale - Revised (CDRS-R) Suicidal Ideation Score | points | 1.1 (SD 0.4) | 1.1 (SD 0.5) | 1.2 (SD 0.5) | 1.2 (SD 0.5) |
| Treatment given for previous episodes: Yes | participants | 57 | 50 | 63 | 170 |
| Treatment given for previous episodes: No | participants | 41 | 49 | 36 | 126 |
6. Primary Endpoint
The registry lists the primary outcome as Change in Young Mania Rating Scale (Y-MRS) Total Score at Week 4, measured over Baseline and Week 4.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | points |
| Endpoint classification | Continuous Endpoint |
The primary endpoint measures change in total Young Mania Rating Scale score from baseline to Week 4. The scale has 11 items assessing core symptoms of mania, each with five severity grades. Its stated range runs from 0, described as absent or normal, to 60, described as a worse outcome or more severe symptoms. In that scoring context, a more negative change indicates a larger decrease in the measured score over the assessment period.
A continuous score can retain information about the magnitude of change across participants, rather than reducing outcomes to a simple category such as improved or not improved. Comparing average change between randomized groups can therefore estimate how the groups differed on the scale during the acute assessment period. The registry describes the primary result as a mean change and reports standard deviations for the groups.
The primary endpoint is relevant to the stated trial question because the enrolled population was described as having a manic or mixed episode and the measure assesses core manic symptoms. The endpoint description says assessments were performed at baseline and weekly through the acute phase, with later assessments in the continuation phase as well. The primary time point was Week 4, not the later follow-up assessments.
The analysis used last observation carried forward, according to the registry description. That approach uses a participant’s last observed measurement for a later endpoint when follow-up measurements are unavailable. Its assumptions and handling details are not reported in the registry record, so the posted summary alone cannot establish how missing measurements affected the group estimates.
7. Results Posted in the Registry
- Aripiprazole 10 mg/Day: mean -14.04 versus -8.67 on control; difference -5.37 (95% CI -8.01 to -2.73), standardized effect d = -0.58; z-test p = <0.001.
- Aripiprazole 30 mg/Day: mean -16.16 versus -8.67 on control; difference -7.49 (95% CI -10.09 to -4.89), standardized effect d = -0.82; z-test p = <0.001.
Mean difference: Aripiprazole 10 mg/Day
95% CI: -8.01 to -2.73
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 |
|---|---|---|---|---|
| Change in Young Mania Rating Scale (Y-MRS) Total Score at Week 30 | Continuous Endpoint | Mean difference | -5.22 (-8.17 to -2.27) | 62 per arm |
| Change in Children's Global Assessment Scale (CGAS) Total Score at Week 4 | Continuous Endpoint | Mean difference | 8.76 (5.23 to 12.29) | 32 per arm |
| Change in Clinical Global Impressions Scale-Bipolar Version (CGI-BP) Severity Mania Score at Week 4 | Continuous Endpoint | Mean difference | -0.71 (-1.06 to -0.36) | 46 per arm |
Change in Young Mania Rating Scale (Y-MRS) Total Score at Week 30
- 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:
- Aripiprazole 10 mg/Day: mean -13.91 versus -8.69 on control; difference -5.22 (95% CI -8.17 to -2.27), standardized effect d = -0.50; z-test p = <0.001.
- Aripiprazole 30 mg/Day: mean -14.60 versus -8.69 on control; difference -5.91 (95% CI -8.76 to -3.06), standardized effect d = -0.58; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Aripiprazole 10 mg/Day 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 lower for Aripiprazole 30 mg/Day than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Change in Children's Global Assessment Scale (CGAS) Total Score at Week 4
- 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:
- Aripiprazole 10 mg/Day: mean 14.97 versus 6.21 on control; difference 8.76 (95% CI 5.23 to 12.29), standardized effect d = 0.70; z-test p = <0.001.
- Aripiprazole 30 mg/Day: mean 16.96 versus 6.21 on control; difference 10.75 (95% CI 7.52 to 13.98), standardized effect d = 0.93; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Aripiprazole 10 mg/Day 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 Aripiprazole 30 mg/Day than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Change in Clinical Global Impressions Scale-Bipolar Version (CGI-BP) Severity Mania Score at Week 4
- 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:
- Aripiprazole 10 mg/Day: mean -1.60 versus -0.89 on control; difference -0.71 (95% CI -1.06 to -0.36), standardized effect d = -0.59; z-test p = <0.001.
- Aripiprazole 30 mg/Day: mean -2.02 versus -0.89 on control; difference -1.13 (95% CI -1.47 to -0.79), standardized effect d = -0.94; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Aripiprazole 10 mg/Day 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 lower for Aripiprazole 30 mg/Day than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The registry lists multiple secondary measures, including later Young Mania Rating Scale assessments and measures of global functioning, mania severity, depressive symptoms, behavior, and attention-related symptoms. The secondary results cover different constructs and follow-up times, so they provide context beyond the primary Week 4 mania-score endpoint. The posted analyses for the secondary outcomes include group comparisons, but their results should not be treated as interchangeable with the primary result.
For the secondary results with detailed numerical summaries in the registry record, the broad pattern is that the reported mean changes and recalculated contrasts generally point in the same direction as the primary score comparison. The global assessment measure is scored in a different direction from symptom-severity measures, so its numerical signs cannot be read using the same shorthand. The record also includes later follow-up results, which address a different time point from the primary acute-phase assessment.
Secondary findings usually carry less evidential weight when many outcomes, time points, or comparisons are examined. A nominally small p-value does not by itself account for the chance of observing at least one apparently notable result among a large collection of tests. The registry lists 30 outcome measures and 60 analyses, while the posted secondary outcomes are only part of the trial’s overall measurement program. A multiplicity adjustment or prespecified hierarchy is not reported in the registry record.
These analyses can be useful for understanding whether findings extend across related measures and time points, but they are better regarded as supporting context than as independent confirmation. The record does not establish that every secondary endpoint was planned, powered, or interpreted under a specific multiplicity strategy. Avoiding a simple tally of significant results is particularly important when endpoints differ in meaning, scale, timing, and analysis method.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Change in Young Mania Rating Scale (Y-MRS) Total Score at Week 30
- Change in Children's Global Assessment Scale (CGAS) Total Score at Week 4
- Change in Clinical Global Impressions Scale-Bipolar Version (CGI-BP) Severity Mania Score at Week 4
- Change in Children's Depression Rating Scale-Revised (CDRS-R) Total Score at Week 4
- Change in General Behavior Inventory Scale (GBI) Total Parent/Guardian Version Mania Score at Week 4
- Change in Attention Deficit Hyperactivity Disorders Rating Scale (ADHD-RS-IV) Total Score at Week 4
- Change in Children's Global Assessment (CGAS) Total Score at Week 30
- Change in Clinical Global Impressions Scale-Bipolar Version (CGI-BP) Severity Mania Score at Week 30
9. Statistical Interpretation
At Week 4, the posted group mean changes in Young Mania Rating Scale score were -14.04 for aripiprazole 10 mg/day, -16.16 for aripiprazole 30 mg/day, and -8.67 for placebo. The recalculated unadjusted mean difference was -5.37 points for 10 mg/day versus placebo, with an interval from -8.015 to -2.725, and -7.49 points for 30 mg/day versus placebo, with an interval from -10.09 to -4.886. Both unadjusted p-values were reported as <0.001. These are comparisons of posted summary statistics, not adjusted sponsor model estimates.
Because lower scale scores correspond to less severe symptoms on the scale description, the negative changes indicate that the average score decreased in each group over the assessment period. The negative recalculated differences indicate a greater average decrease in the aripiprazole groups than in the placebo group. They describe the direction and estimated magnitude of the group contrasts; they do not by themselves establish why the difference occurred or how it should be interpreted clinically.
The registry’s own reported Week 4 analyses use a different description of the comparison. For 10 mg/day, the registry reports a mean difference in final values of -5.99, with a 95% interval from -8.49 to -3.5 and p < 0.001. For 30 mg/day, it reports a median difference in final values of -8.26, with a 95% interval from -10.7 to -5.77 and p < 0.001. A mean change contrast reconstructed from arm summaries is not interchangeable with a reported contrast in final values, and a mean contrast is not the same summary as a median contrast. The registry record does not explain the full analysis specifications behind these reported contrasts.
The Week 4 group summaries and recalculated comparisons are consistent in direction, while the sponsor-reported summaries are separate analyses with their own stated estimands. These results concern a single endpoint and time point. They do not, on their own, resolve questions about multiplicity across outcomes, missing-data assumptions, or the practical importance of the score differences. Nor do group averages describe the range of individual responses. Interpretation should remain tied to the endpoint, time point, analysis population, and methods actually recorded.
10. Statistical Methods Explained
What does the mean difference represent?
A mean difference compares the average outcome in one group with the average outcome in another. For the recalculation, the reported group mean changes are contrasted with the placebo mean change. The direction of the estimate depends on the order of subtraction: negative estimates reflect a more negative mean change in the aripiprazole group than in placebo. That sign is not a judgement by itself; it must be read alongside the scale’s scoring direction and the definition of change.
The recalculations use posted summary statistics and are unadjusted. They do not reproduce a participant-level model, correct for baseline covariates, or address missing observations beyond the summary values already posted. A standardized effect-size value is also listed in the calculations, but it is a scale-free expression based on the pooled standard deviation. It does not replace the original point-scale difference, and it should not be treated as a clinical threshold.
What does a confidence interval communicate?
A confidence interval expresses the uncertainty around an estimated contrast under the statistical method used. A narrower interval indicates greater statistical precision than a wider interval, while the interval’s location indicates which effect values are compatible with the data and method. It does not show the probability that a particular fixed effect is true. The intervals for the recalculated contrasts are based on the posted group summaries; the registry also gives 95% intervals for its own analyses.
When an interval for a difference excludes zero, that is consistent with a two-sided test finding evidence against a zero difference under the same model and assumptions. It does not establish clinical importance, eliminate bias, or correct for testing many endpoints. The reported p-values are unadjusted, so they do not account for the collection of comparisons across outcomes or time points.
Why distinguish the registry analysis from the recalculation?
The registry-reported Week 4 results are labelled as comparisons of final values, with a mean difference for the 10 mg/day comparison and a median difference for the 30 mg/day comparison. The recalculations instead compare posted mean changes from baseline. These are not identical quantities. Differences in estimand, summary measure, model, or analysis population can produce different estimates, even when they refer to the same trial and endpoint. The registry record does not fully report the sponsor’s analysis specification, so the posted summaries do not support a complete reconciliation.
The recalculation is therefore descriptive and should be read as a simple unadjusted analysis of the posted summaries. It is not a replacement for the sponsor’s prespecified analysis. In this record, no discrepancy is flagged by the data-processing comparison, but that does not mean the methods or estimands are identical.
Why can variation matter?
Standard deviations describe how spread out participant outcomes are around the group mean. The standard error, in contrast, describes the uncertainty of an estimated group mean and is related to both outcome variability and the number of observations. Larger variability generally makes a group contrast less precise when other aspects of the study are held constant. In the recalculated comparisons, the pooled standard deviation is used in the standardized effect calculation; the group-specific standard deviations remain useful for understanding variability within each arm.
These formulas assume the summary statistics are suitable for the stated comparison. General statistical methods may rely on approximate distributional conditions; whether those conditions were checked for this trial is not reported in the registry record. A simple summary-statistic calculation also cannot account for correlations among repeated observations or other features that might be modeled in a participant-level analysis.
What does the missing-data description imply?
The registry says the primary efficacy analysis used last observation carried forward and required a baseline and at least one post-baseline assessment. Last observation carried forward can make the endpoint available for participants without a Week 4 measurement, but it carries assumptions: the last recorded value is used as a stand-in for the later value. Whether this is reasonable depends on the reasons measurements are missing and on how outcomes would have changed afterward. Those reasons and sensitivity analyses are not reported in the registry record.
Thus, statistical significance in a posted comparison describes evidence under a particular analysis and its assumptions. It does not remove uncertainty arising from missing data, incomplete reporting, multiple testing, or differences between analysis populations. The registry record supports a careful reading of the stated estimates, but not a full independent audit of the trial’s statistical plan.
11. Confidence Intervals and Precision
The recalculated Week 4 mean difference for aripiprazole 10 mg/day versus placebo is -5.37 points, with an interval from -8.015 to -2.725. For 30 mg/day versus placebo, the recalculated mean difference is -7.49 points, with an interval from -10.09 to -4.886. The intervals communicate uncertainty around these unadjusted estimates. Both lie on the negative side of zero, consistent with a greater average decrease in the aripiprazole groups under this calculation.
The widths of the intervals matter as much as the point estimates: a point estimate alone can make a result seem more definite than the data warrant. Each interval contains a range of values compatible with the observed summaries and the calculation’s assumptions. It does not mean every value in the range is equally likely, and it does not represent the range of individual participants’ responses.
The registry reports its own 95% intervals for final-value comparisons. Those intervals should be interpreted in relation to their stated analysis, which is not identical to the recalculated comparison of mean changes. The registry record’s reported quantities include both mean and median differences, making direct numerical comparison particularly important to qualify.
Precision is not the same as clinical importance. A statistically distinguishable group contrast may or may not be large enough to matter in a clinical context, and the registry record does not supply a threshold for interpreting a meaningful difference on this scale. The summaries also do not show how effects varied across participants. The intervals quantify sampling uncertainty under their methods, not uncertainty from every potential source, such as missing-data assumptions, outcome selection, or study conduct.
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 | 47 | 63 |
| 75% of the observed effect | 83 | 111 |
| 50% of the observed effect | 187 | 250 |
The sample-size illustrations give participants per arm, not a total across the two comparison groups. They are planning illustrations based on the observed effect in these results, rather than a reconstruction of the trial’s original design. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each illustration sets the effect to detect as a stated fraction of the observed effect.
The 80% power column indicates the number of participants per arm estimated to give an 80% chance of detecting the specified effect under those assumptions, if that effect were the true one. The 90% power column uses a higher target chance of detection and therefore generally calls for more participants per arm. These are planning calculations; they are not observed power.
Rows that plan for a smaller fraction of the observed effect require more participants per arm than rows planning for the full observed effect. This reflects the general principle that a smaller group difference is harder to distinguish from random variation at a given level of precision. The illustrations are conditional on the assumed effect, variability, allocation, and statistical approximation. They do not include an allowance for loss to follow-up or other design considerations unless specified, and the registry record does not report the trial’s original sample-size justification or design assumptions.
The curve should be read as a visual version of the same planning relationship: participant requirements change as the target effect changes. It is not evidence that a future trial will achieve a particular outcome. Since the observed effect is used as the planning reference, the values are especially sensitive to how well the observed effect reflects what might be expected in another study.
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 = -5.370; pooled standard deviation σ = 9.252.
- n = 2 × (1.96 + 0.842)2 × 9.2522 / -5.3702 = 46.6, rounded up to 47 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 <- -5.37 # observed difference in means
sigma <- 9.25206614529907 # 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(110461)
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 = 47 (80% power), 63 (90% power)
75% of observed effect: n per arm = 83 (80% power), 111 (90% power)
50% of observed effect: n per arm = 187 (80% power), 250 (90% power)
power.t.test: 47.6
Simulated power at n = 47 per arm: 0.794 (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 |
|---|---|---|---|
| t-test, 2 sided | Mean Difference (Final Values) -5.99 | -8.49 to -3.5 | < 0.001 |
| t-test, 2 sided | Median Difference (Final Values) -8.26 | -10.7 to -5.77 | < 0.001 |
The registry’s Week 4 reported analyses give a mean difference in final values of -5.99 for aripiprazole 10 mg/day versus placebo and a median difference in final values of -8.26 for aripiprazole 30 mg/day versus placebo. Each is accompanied by a 95% interval and p < 0.001. The recalculated values, by contrast, are unadjusted differences between the posted group mean changes from baseline. They are not a reproduction of the sponsor’s analysis.
This distinction is important because a contrast in final values is not necessarily the same estimand as a contrast in changes, and a median difference is not interchangeable with a mean difference. The registry record does not provide enough detail to reconstruct every analysis choice or reconcile the estimates completely. The recalculated summaries can help readers understand the direction and scale of a simple comparison, but the sponsor’s reported analysis remains the trial’s own analysis and should be interpreted according to its stated method.
The record does not flag a discrepancy between sponsor and recalculated analyses. This should not be read as proof that their estimands, populations, or assumptions are identical; the descriptions themselves indicate differences in the reported quantities.
15. Multiplicity, Missing Data and Analysis Populations
The registry describes a broad outcome program: 30 outcome measures and 60 analyses, with 29 secondary outcomes posted. Testing multiple outcomes and time points increases the opportunity for apparently strong findings to arise by chance, even when each individual test uses a conventional significance threshold. The Week 4 recalculated p-values are unadjusted. The registry record does not report a multiplicity correction, a testing hierarchy, or a prespecified strategy for controlling the overall error rate.
The primary endpoint has a clearer role than the secondary measures because it is identified as the primary efficacy endpoint. That designation does not by itself resolve multiplicity across dose comparisons or other analyses. Whether the primary comparisons were jointly adjusted, ordered, or interpreted under another plan is not reported in the registry record. The statistical analysis plan is not reported in the registry record.
Missing-data handling is described in the primary endpoint text as last observation carried forward. The primary efficacy population also required both a baseline assessment and at least one post-baseline assessment. The registry explicitly notes that the number of randomized participants could differ from the number included in the efficacy analysis. The exact analysis population counts and the extent and reasons for missingness are not reported in the registry record.
Last observation carried forward can yield an endpoint value for a participant with an incomplete assessment history, but it does so by assuming that the last observed score is an adequate substitute for the later measurement. The record does not report sensitivity analyses testing alternative missing-data assumptions. It also does not provide enough detail to assess whether missingness differed between groups or was related to outcome severity.
These gaps constrain interpretation of both the primary and secondary results. The posted estimates remain informative descriptions of the recorded analyses, but they cannot answer how robust the results are to other analysis populations, missing-data methods, or multiplicity adjustments. Those matters should be distinguished from the numerical uncertainty represented by the reported intervals.
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 |
|---|---|---|---|
| Aripiprazole 10 mg/Day | 5 | 98 | 5.1% |
| Aripiprazole 30 mg/Day | 7 | 99 | 7.1% |
| Placebo | 6 | 97 | 6.2% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Aripiprazole 10 mg/Day | 78 of 98 |
| Aripiprazole 30 mg/Day | 84 of 99 |
| Placebo | 64 of 97 |
Most frequent serious adverse event terms
| Event term | Organ system | Aripiprazole 10 mg/Day | Aripiprazole 30 mg/Day | Placebo |
|---|---|---|---|---|
| Bipolar disorder | Psychiatric disorders | 0 of 98 | 5 of 99 | 4 of 97 |
| Bipolar I disorder | Psychiatric disorders | 0 of 98 | 2 of 99 | 1 of 97 |
| Agression | Psychiatric disorders | 2 of 98 | 0 of 99 | 0 of 97 |
| Fatigue | General disorders | 1 of 98 | 0 of 99 | 0 of 97 |
| Accidental overdose | Injury, poisoning and procedural complications | 1 of 98 | 0 of 99 | 0 of 97 |
| Grand mal convulsion | Nervous system disorders | 1 of 98 | 0 of 99 | 0 of 97 |
| Libido increased | Psychiatric disorders | 0 of 98 | 1 of 99 | 0 of 97 |
| Mania | Psychiatric disorders | 0 of 98 | 0 of 99 | 1 of 97 |
| Oppositional defiant disorder | Psychiatric disorders | 1 of 98 | 0 of 99 | 0 of 97 |
| Suicidal ideation | Psychiatric disorders | 1 of 98 | 0 of 99 | 0 of 97 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Aripiprazole 10 mg/Day | Aripiprazole 30 mg/Day | Placebo |
|---|---|---|---|---|
| Headache | Nervous system disorders | 20 of 98 | 23 of 99 | 18 of 97 |
| Somnolence | Nervous system disorders | 24 of 98 | 27 of 99 | 3 of 97 |
| Extrapyramidal disorder | Nervous system disorders | 12 of 98 | 28 of 99 | 3 of 97 |
| Fatigue | General disorders | 18 of 98 | 12 of 99 | 4 of 97 |
| Nausea | Gastrointestinal disorders | 13 of 98 | 14 of 99 | 5 of 97 |
| Vomiting | Gastrointestinal disorders | 13 of 98 | 8 of 99 | 9 of 97 |
| Akathisia | Nervous system disorders | 9 of 98 | 13 of 99 | 2 of 97 |
| Vision blurred | Eye disorders | 10 of 98 | 8 of 99 | 1 of 97 |
| Increased appetite | Metabolism and nutrition disorders | 8 of 98 | 8 of 99 | 3 of 97 |
| Abdominal pain | Gastrointestinal disorders | 9 of 98 | 5 of 99 | 3 of 97 |
Serious events with the highest arm-level rate: bipolar disorder (5.1%), agression (2.0%), bipolar i disorder (2.0%), mania (1.0%), fatigue (1.0%).
The registry reports serious adverse event figures for participants at risk in each group: 5 of 98 in the aripiprazole 10 mg/day group, 7 of 99 in the 30 mg/day group, and 6 of 97 in the placebo group. These are group-level counts as reported, not a basis for inferring why an event occurred or whether it was caused by the assigned intervention. The record also lists other adverse events affecting 78 of 98, 84 of 99, and 64 of 97 participants, respectively.
Serious events and other adverse events are different reporting categories. The listed serious-event terms include percentages, but the registry record does not fully explain the denominator or event-counting conventions associated with each term. The term list should therefore be read as descriptive rather than as a complete comparison of risk. Death counts are not reported in the registry record.
These summaries do not establish equivalence between groups or determine the clinical meaning of individual events. They also do not provide enough information about event timing, duration, severity details, or causal assessment to support a more complete safety interpretation.
17. What the Result Does, and Does Not, Mean
The Week 4 primary endpoint results describe average changes in a mania symptom scale among participants included in the reported analyses. The group summaries show decreases from baseline in all three groups, with larger average decreases in the two aripiprazole groups than in placebo. The unadjusted recalculations quantify those group contrasts and their statistical uncertainty using the posted means and standard deviations.
These results do not establish that every participant experienced a decrease, nor do they show how much individual outcomes varied beyond the group standard deviations. A group mean can conceal substantial differences among participants. The results also do not identify the causes of observed changes, and comparisons in a randomized trial should still be interpreted alongside the analysis population, missing-data handling, and implementation details.
A statistically distinguishable difference is not automatically a clinically important difference. The registry record does not state a threshold for meaningful change on the Young Mania Rating Scale, so the numerical contrasts cannot be classified as clinically important on the basis of this record alone. Nor do the Week 4 findings establish whether differences persisted at later times or applied to outcomes beyond those measured.
The sponsor-reported analyses use final-value comparisons and include different summary measures, while the recalculations compare posted mean changes. Their estimates should not be treated as identical analyses. Secondary outcomes and safety summaries add context but do not replace the primary endpoint or settle questions about multiplicity and missing data. Overall, the posted results support a description of observed group differences under the stated analyses, not a broad conclusion extending beyond this trial, population, endpoint, and follow-up.
18. Why This Trial Matters Statistically
This trial illustrates why the estimand matters when interpreting clinical trial results. A contrast in mean change, a contrast in final values, and a median contrast can all be legitimate summaries, but they answer different statistical questions. Treating them as interchangeable can make modest numerical differences seem like contradictions or conceal meaningful differences in analysis.
The primary endpoint also demonstrates the importance of reading a score’s direction before interpreting the sign of an estimate. Negative change on a scale where higher scores mean more severe symptoms has a different meaning from positive change on a global functioning scale. Statistical interpretation requires both the arithmetic definition and the outcome’s measurement direction.
Trial records often contain many outcomes and analyses. The number of posted tests makes multiplicity a relevant concern, particularly when individual p-values are unadjusted and the analysis plan is not reported. A statistically significant result should therefore be understood in the context of the full outcome program, not isolated from it.
Finally, the registry highlights distinctions among enrollment, randomized groups, and efficacy analysis populations. A primary endpoint requiring baseline and follow-up data can have a different analysis count from the randomized group. Clear reporting of missingness, populations, and analysis choices is essential for evaluating precision and reproducibility. These are general lessons in biostatistical interpretation drawn from the reporting features of this particular record.
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 gives a concise design description but does not report the detailed protocol, the original sample-size justification, or the statistical analysis plan. It does not explain the masking procedures, allocation concealment, or whether randomization was stratified. These omissions limit assessment of the design and its implementation.
The primary endpoint description identifies last observation carried forward and an efficacy population requiring baseline and post-baseline measurements. It does not report exact primary analysis population counts, missing-data patterns, reasons for missingness, or sensitivity analyses. Consequently, the robustness of the endpoint estimates to alternative assumptions cannot be evaluated from the record.
There is also a distinction between the registry’s reported analyses and the summary-statistic recalculations. The registry labels the Week 4 comparisons as final-value differences, and the reported measure differs between dose comparisons. The recalculations use mean changes. The full sponsor model specification is not reported in the registry record, limiting direct reconciliation.
The record includes many outcomes and analyses, but does not report a multiplicity strategy. The secondary results therefore need cautious interpretation, particularly where individual p-values are unadjusted. The safety summaries are also limited: event counts and selected terms are reported, but details needed to compare event timing, seriousness definitions, causality, and exposure are not fully described. These limitations do not erase the posted estimates; they define the boundaries of what can be concluded from the registry record.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Aripiprazole in Children and Adolescents With Bipolar I Disorder — NCT00110461.
- Registry record last updated 2012-05-21; status last verified 2012-04.
- Results first posted 2012-05-21.
- 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.
Continue through the Clinical Biostats statistical pathway
Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
23. Record Summary
The registry describes a completed, randomized, quadruple-masked, parallel-group phase III trial in children and adolescents with bipolar I disorder. The groups received aripiprazole 10 mg/day, aripiprazole 30 mg/day, or placebo. Recorded enrollment was 296.
The primary endpoint was change from baseline to Week 4 in Young Mania Rating Scale total score, analyzed using last observation carried forward. The posted group mean changes were -14.04, -16.16, and -8.67, respectively. Unadjusted recalculations showed negative mean differences versus placebo for both dose groups, with p-values reported as <0.001.
The registry’s own analyses are described as comparisons of final values and are not identical to the recalculated change-score comparisons. The record lists multiple secondary outcomes and adverse event summaries, while important details about multiplicity, missingness, and the original statistical plan are not reported in the registry record.