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 Study of Aripiprazole in the Treatment of Children and Adolescents With Autistic Disorder (AD). (NCT00332241), a randomized phase 3 study. The primary outcome is Mean Change (Week 8 - Baseline) in the Autistic Behavior Checklist (ABC) Irritability Subscale Score.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00332241 |
| Phase | Phase 3 |
| Condition | Autistic Disorder |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 98 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Otsuka Pharmaceutical Development & Commercialization, Inc. |
| Results posted | Yes |
2. Clinical Question
Population
Children and adolescents diagnosed with autistic disorder. The primary outcome description identifies an efficacy population based on randomized participants, with specified exclusions and a last-observation-carried-forward data set.
Intervention
Flexibly dosed aripiprazole.
Comparator
Placebo.
Primary question
What was the mean change from baseline to Week 8 in the Autistic Behavior Checklist Irritability subscale score in each group, and how did the posted group means compare?
The registry describes a randomized, double-blind, parallel-group comparison intended to examine whether aripiprazole and placebo were associated with different changes in serious behavioral problems. The primary outcome focuses on irritability, one of the Autistic Behavior Checklist domains. It is a continuous score, so the posted group means describe average change rather than the number of participants who crossed a response threshold.
The scale description says that lower scores indicate improvement. The posted mean change was -12.9 units for aripiprazole and -5.0 units for placebo. The unadjusted mean difference, aripiprazole minus placebo, was -7.9 units, with a 95% confidence interval from -11.88 to -3.922 and an unadjusted p value of <0.001. These figures describe the posted summaries and their calculated unadjusted contrast; they do not by themselves establish how the trial's prespecified analysis was conducted. The registry record does not report a detailed statistical analysis plan or a sponsor-reported primary comparison analysis.
3. Trial Design
This was a phase 3, randomized, double-blind, parallel-group study comparing aripiprazole with placebo. The official study description characterizes the trial as multicenter and flexibly dosed. The registry lists 98 participants enrolled. The study start date was 2006-06-01, the primary completion date was 2008-04-01, and the record status is completed.
The two interventions were aripiprazole and placebo. The posted primary outcome has 49 participants in the placebo group and 46 in the aripiprazole group. Its population description states that the efficacy population excluded 2 placebo participants, 1 lost to follow-up and 1 who withdrew consent, and 1 aripiprazole participant who discontinued due to an adverse event on Day 2. The same description says the data set used last observation carried forward. These details apply to the primary outcome description; other outcomes have their own posted group counts.
Randomization assigns participants to treatment groups, while double masking is intended to limit the influence of treatment knowledge on participants and study personnel. A parallel-group design follows separate groups receiving the assigned intervention rather than having participants cross between interventions. These are general descriptions of the design terms, not details about implementation beyond the registry labels.
The registry record does not report the original sample-size justification, the planned allocation ratio, the trial's detailed dosing schedule, or the methods used to maintain masking. It also does not report whether interim analyses were planned or performed. The record labels the study phase and design but does not provide a protocol-level account of all procedures. The reported enrollment and outcome-specific analysis counts should therefore be read as distinct pieces of information, not as a complete description of the trial's conduct.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Overall Study
| Stage | Placebo | Aripiprazole |
|---|---|---|
| STARTED | 51 | 47 |
| COMPLETED | 36 | 39 |
| NOT COMPLETED | 15 | 8 |
Reasons for not completing this period:
| Reason | Placebo | Aripiprazole |
|---|---|---|
| Lack of Efficacy | 6 | 1 |
| Adverse Event | 3 | 5 |
| Withdrawal by Subject | 2 | 1 |
| Lost to Follow-up | 4 | 1 |
Analysis population for the primary outcome, as defined in the registry: Efficacy population=all randomized participants minus 2 patients in the placebo group (1 lost to follow-up, 1 withdrew consent) and 1 participant in the aripiprazole group who discontinued due to AE on Day 2. Data set is LOCF.
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 | Placebo | Aripiprazole | Total |
|---|---|---|---|---|
| Participants analysed | 51 | 47 | 98 | |
| Age, Customized: 6 to 12 years | participants | 46 | 37 | 83 |
| Age, Customized: 13 to 17 years | participants | 5 | 10 | 15 |
| Sex/Gender, Customized: Female | Participants | 7 | 5 | 12 |
| Sex/Gender, Customized: Male | Participants | 44 | 42 | 86 |
| Race, Customized: Asian | participants | 0 | 2 | 2 |
| Race, Customized: Native Hawaiian or Other Pacific Islander | participants | 0 | 1 | 1 |
| Race, Customized: Black or African American | participants | 7 | 11 | 18 |
| Race, Customized: White | participants | 41 | 32 | 73 |
| Race, Customized: Other | participants | 3 | 1 | 4 |
| Ethnicity, Customized: Hispanic/Latino | participants | 8 | 6 | 14 |
| Ethnicity, Customized: Not Hispanic/Latino | participants | 43 | 41 | 84 |
| Weight Group: <40 kilograms | Participants | 32 | 26 | 58 |
| Weight Group: ≥40 kilograms | Participants | 19 | 21 | 40 |
| Body Mass Index | kg/cm2 | 19.96 (SD 5.392) | 21.08 (SD 5.394) | 20.50 (SD 5.395) |
| Height | centimeters | 138.6 (SD 14.7) | 140.9 (SD 18.80) | 139.7 (SD 16.74) |
| Weight | kilograms | 40.6 (SD 18.92) | 43.9 (SD 19.15) | 42.2 (SD 19.01) |
6. Primary Endpoint
The registry lists the primary outcome as Mean Change (Week 8 - Baseline) in the Autistic Behavior Checklist (ABC) Irritability Subscale Score, measured over Week 8.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Error |
| Unit | units on a scale |
| Endpoint classification | Continuous Endpoint |
The primary endpoint was mean change from baseline to Week 8 in the Autistic Behavior Checklist Irritability subscale score. The registry describes the ABC as an informant-based assessment of problem behaviors in children and adolescents with mental retardation. It contains 58 items rated on a 4-point scale, with responses ranging from 0, no problem, to 3, severe problem; the items resolve into 5 domain subscales. The primary endpoint uses the irritability domain rather than an overall score.
A change score expresses how the group average at Week 8 differs from its baseline value. The registry states that a decrease in this score indicates improvement. The endpoint is continuous, meaning that it retains the measured score values rather than reducing them to a binary category such as responder or non-responder. The posted summary is therefore a mean change with a standard error for each group.
Using a named behavioral scale gives the trial a defined outcome for comparing average change between randomized groups. A caregiver or other informant supplies the ratings, so the score reflects reported behavior rather than a direct count of events. General measurement principles apply: a scale score summarizes selected items, and interpretation depends on the content and scoring of that instrument. The registry record does not report a threshold for a clinically meaningful change on this subscale. The score difference should consequently be read as a difference in measured scale change, not translated into an unreported clinical category.
7. Results Posted in the Registry
- Aripiprazole: mean -12.90 versus -5.00 on control; difference -7.90 (95% CI -11.88 to -3.92), standardized effect d = -0.80; z-test p = <0.001.
Mean difference: Aripiprazole
95% CI: -11.88 to -3.92
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 |
|---|---|---|---|---|
| Mean Clinical Global Impressions Improvement Scale (CGI-I) Score | Continuous Endpoint | Mean difference | -1.40 (-1.90 to -0.90) | 13 per arm |
| Mean Change (Week 8 - Baseline) in the Children's Yale-Brown Obsessive Compulsive Scale (CY-BOCS; Compulsion Scale Only) | Continuous Endpoint | Mean difference | -3.00 (-4.41 to -1.59) | 20 per arm |
| Mean Change (Week 8 - Baseline) in CGI-Severity (CGI-S) | Continuous Endpoint | Mean difference | -0.80 (-0.86 to -0.74) | 1 per arm |
Mean Clinical Global Impressions Improvement Scale (CGI-I) Score
- 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 errors.
- Result:
- Aripiprazole: mean 2.20 versus 3.60 on control; difference -1.40 (95% CI -1.90 to -0.90), standardized effect d = -1.13; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Aripiprazole than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Mean Change (Week 8 - Baseline) in the Children's Yale-Brown Obsessive Compulsive Scale (CY-BOCS; Compulsion Scale Only)
- 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 errors.
- Result:
- Aripiprazole: mean -3.80 versus -0.80 on control; difference -3.00 (95% CI -4.41 to -1.59), standardized effect d = -0.89; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Aripiprazole than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Mean Change (Week 8 - Baseline) in CGI-Severity (CGI-S)
- 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: mean -1.20 versus -0.40 on control; difference -0.80 (95% CI -0.86 to -0.74), standardized effect d = -5.51; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Aripiprazole than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes cover several related aspects of behavior and overall assessment: a global improvement rating, response status, compulsive behavior, other ABC subscales, severity, safety, and body weight. The posted numeric summaries include a global improvement score, CY-BOCS compulsion score, and CGI-Severity change. These measures are not interchangeable with the primary ABC Irritability subscale; they address different constructs or summarize them in different ways.
Across the posted secondary continuous outcomes, the calculated contrasts are in the direction of lower mean scores or changes in the aripiprazole group, and the posted unadjusted p values are <0.001 for the displayed comparisons. The registry also lists other secondary outcomes for which numeric results are not included in the posted summaries described in this record. The overall pattern can be considered alongside the primary outcome as context, but it should not be treated as a substitute for the primary endpoint or as proof that every secondary measure had a reported result.
Unadjusted secondary comparisons carry less weight because multiple outcomes and comparisons create more opportunities for apparently strong findings to arise by chance. General statistical practice may address this through a prespecified testing sequence or an adjustment for multiplicity, but neither a complete testing strategy nor a multiplicity adjustment is reported in the registry record. The record lists outcome names and some summaries; it does not supply a complete analysis plan or sponsor-reported analyses for the secondary comparisons.
Differences in group counts and dispersion labels also matter when reading the secondary summaries. The outcomes do not all use the same analysis population or the same reported measure of spread. Their calculated intervals and p values should be viewed as descriptive, unadjusted comparisons unless the record documents otherwise. They add dimensions to the account of the trial, but their statistical evidence should be interpreted with the multiplicity and reporting limitations in mind.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Mean Clinical Global Impressions Improvement Scale (CGI-I) Score
- Number of Participants With Response at Week 8
- Mean Change (Week 8 - Baseline) in the Children's Yale-Brown Obsessive Compulsive Scale (CY-BOCS; Compulsion Scale Only)
- Mean Change (Week 8 - Baseline) in the Other ABC Subscale Scores
- Mean Change (Week 8 - Baseline) in CGI-Severity (CGI-S)
- Summary of Safety
- Change From Baseline in Body Weight
9. Statistical Interpretation
At Week 8, the posted mean change in the ABC Irritability subscale was -12.9 units for aripiprazole and -5.0 units for placebo. Since the registry states that a decrease indicates improvement, both group means were decreases, with a larger average decrease in the aripiprazole group. The unadjusted mean difference, calculated as aripiprazole minus placebo, was -7.9 units. Its 95% confidence interval was -11.88 to -3.922, and the unadjusted p value was <0.001.
The confidence interval describes uncertainty around this unadjusted contrast under the calculation used for the posted summaries. Its endpoints are both below zero, so the calculated interval is consistent with a larger mean decrease in the aripiprazole group than in the placebo group. This is an interpretation of the posted estimate and interval, not a statement about individual participants. Group averages do not show how much participants varied, whether every participant changed in the same direction, or what proportion met a response criterion.
The posted comparison is an unadjusted recalculation from the group summaries. The registry record does not include a reported primary analysis result or enough analysis-plan detail to establish whether the trial's original inferential method adjusted for baseline values, other covariates, or other design features. The reported p value is likewise an unadjusted recalculation, not a registry-reported sponsor analysis. No discrepancy is flagged between the available summaries and the recalculation, but that does not turn it into a documented prespecified analysis.
The primary outcome is based on the stated efficacy population and a last-observation-carried-forward data set. This approach uses an earlier recorded value for a participant with a later missing value, according to the method named in the registry. The record identifies some exclusions from the efficacy population, but does not provide a complete account of missingness at each assessment, the reasons for every missing observation, or sensitivity analyses testing alternative assumptions.
The result describes change on one informant-based scale at one stated time point. It does not establish how the observed contrast relates to a threshold for meaningful change, because such a threshold is not reported. Nor does a result on this endpoint alone summarize all secondary outcomes, safety findings, or the balance of benefits and harms. Statistical evidence about a group mean is not a guarantee of a particular outcome for an individual, and the registry record does not establish effects beyond the measured outcomes and follow-up described.
The secondary outcomes address related but distinct measures, including global ratings, compulsive behavior, severity, response, and safety. Their posted summaries can add context, but their unadjusted calculated comparisons should not be treated as an independent confirmation of the primary finding. The number of analyses and the absence of a reported multiplicity procedure matter when interpreting a collection of outcome comparisons. The record lists secondary measures, but does not report a complete statistical analysis plan or sponsor analyses for the posted secondary comparisons.
10. Statistical Methods Explained
For a continuous endpoint, the mean is the arithmetic average of the measured values or changes in a group. A mean change score summarizes the average difference between baseline and follow-up for the participants included in the analysis. In this trial, negative changes on the primary ABC Irritability subscale are described by the registry as indicating improvement. That direction is important: the sign of a contrast has meaning only when connected to the scale's scoring convention and the order in which groups are subtracted.
The primary group summaries report means and standard errors. A standard error describes the estimated uncertainty in a sample mean; it is not the same quantity as the spread of individual participant scores. In general, the standard error depends on both variability in the observations and the amount of information contributing to the mean. It indicates how precisely a group mean is estimated under the statistical calculation, but does not describe the full range of participant experiences.
The posted mean difference is the aripiprazole mean minus the placebo mean. A negative value therefore indicates a lower mean change for aripiprazole in the stated subtraction. Because lower ABC Irritability scores and decreases in score are described as improvement, the direction of this contrast is read together with that scoring description. This is a simple unadjusted comparison reconstructed from the posted group summaries; it should not be mistaken for a model-adjusted result or a sponsor-reported analysis.
What does a confidence interval express?
A confidence interval gives a range of estimates compatible with the observed data under the calculation and its assumptions. It conveys uncertainty about the estimated group contrast. A narrower interval indicates greater precision than a wider interval for the same type of estimate, while an interval spanning a broad range leaves more uncertainty about the size of the contrast. A confidence interval is not a range containing every participant's response, and it does not assign a probability to the true effect after the data have been observed.
The posted primary interval is attached to the recalculated unadjusted mean difference. Its limits are -11.88 and -3.922. The interval does not include zero, and the posted unadjusted p value is <0.001. These are related descriptions of evidence against a zero mean difference under the unadjusted calculation. Neither figure reports the clinical importance of a difference, and neither resolves limitations of the outcome definition, missing data, or the undocumented original analysis plan.
Why distinguish standard error from standard deviation?
Standard deviation describes variability among observations, whereas standard error describes uncertainty in an estimated mean. Several outcomes in the registry list standard error as the dispersion measure; the CGI-S outcome lists standard deviation. Those labels are not interchangeable. For the primary outcome, the arm-level values of 1.43 and 1.44 are standard errors, not estimates of the typical participant's score variation. The posted comparison also includes a pooled standard deviation of 9.893 for its standardized-effect calculation, but the record does not describe a sponsor analysis using that quantity.
Over-dispersion is a general concern when data vary more than a chosen statistical model expects. In such settings, standard errors can be too small if the model does not account for the extra variation, potentially making intervals too narrow and tests too optimistic. The registry record does not report a model-based analysis or evidence that over-dispersion was assessed for this continuous primary outcome. This general concept should not be read as evidence that over-dispersion occurred in this trial.
What does an unadjusted p value mean?
A p value describes how unusual data at least as discrepant as those observed would be under a specified null model, if that model and its assumptions were appropriate. The posted p value for the primary comparison is <0.001 and is an unadjusted recalculation from the posted summaries. It is not the probability that the null hypothesis is true, nor does it indicate the chance that the observed result arose by bias. It also does not measure the size or importance of the difference.
Randomization supports a comparison between groups by allocating participants through chance, but the validity of an analysis also depends on how outcomes, missing observations, and the analysis population are handled. The registry describes the primary efficacy population and last-observation-carried-forward data set, but does not report the full protocol analysis plan. Details such as adjustment for baseline scores, handling of all missing outcomes, or prespecified testing order are not reported in the registry record.
What can a standardized effect add?
A standardized mean difference expresses a mean contrast relative to a measure of variability, allowing results on different scales to be compared in a common unit. The posted primary comparison lists d as -0.798. This is a calculated standardized effect, not a trial-reported clinical threshold. Standardization does not remove uncertainty or solve differences in measurement, and it can be sensitive to the variability estimate used. The raw-unit contrast remains directly tied to the ABC Irritability subscale and is more immediately connected to the scale description.
Every method description should be matched to what the record actually documents. The randomized, double-blind, parallel-group labels are reported design features. The primary means, standard errors, unadjusted contrast, confidence interval, and p value characterize the posted summaries and their recalculation. The original sample-size rationale, detailed prespecified analysis, interim analyses, and multiplicity strategy are not reported in the registry record. Those gaps limit claims about whether the posted calculations reproduce the trial's planned analysis.
11. Confidence Intervals and Precision
The primary mean difference is -7.9 units, with a 95% confidence interval from -11.88 to -3.922. The interval conveys uncertainty around the estimated unadjusted contrast, rather than uncertainty about the mean within either group or the range of individual changes. Its limits are both negative, consistent with a more negative mean change in the aripiprazole group under the stated subtraction. The interval's width also makes clear that the data do not identify a single exact contrast.
Confidence intervals are most useful when considered alongside the scale and analysis. Here the scale description says that decreases indicate improvement, but the registry record does not report a threshold that would distinguish a clinically meaningful difference from a smaller one. Thus, the interval informs statistical precision in ABC Irritability units; it does not by itself establish practical importance.
The arm means are accompanied by standard errors of 1.43 for placebo and 1.44 for aripiprazole. These quantify uncertainty in the estimated means, not the distribution of individual participant responses. The outcome-specific group sizes are 49 and 46. The record does not provide participant-level data, so the posted summaries cannot show the shape of the distributions or how individual changes overlap between groups.
The interval and p value are unadjusted recalculations from the posted summaries, not a documented sponsor-reported analysis. The registry record does not report whether the original analysis used covariate adjustment or a different method. Precision should therefore be understood as conditional on the calculation used, the stated efficacy population, and the last-observation-carried-forward data set. The record also does not report sensitivity analyses that would show how estimates change under alternative missing-data assumptions.
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 | 25 | 33 |
| 75% of the observed effect | 44 | 59 |
| 50% of the observed effect | 99 | 132 |
The sample-size display gives planning illustrations in participants per arm for this continuous outcome; it does not give total events. The calculations use the observed effect as a starting point and show planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For each effect assumption, the display gives participants per arm for 80% power and participants per arm for 90% power.
The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. These are assumptions for the planning illustration, not confirmed assumptions from the trial's original design. The trial's original sample-size justification and design assumptions are not reported in the registry record.
Power is the chance that a study would meet its chosen statistical criterion if the assumed effect were the true effect and the other planning assumptions held. In plain terms, the 80% column gives the illustrative number of participants per arm for an 80% chance of detecting the assumed effect under those conditions; the 90% column does the same for a 90% chance. Greater target power generally calls for more participants under otherwise matching assumptions. The figures are planning illustrations based on the observed effect, not observed power.
The displayed values for 100% of the observed effect are 25 participants per arm for 80% power and 33 for 90% power. For 75% of the observed effect, they are 44 and 59 participants per arm. For 50% of the observed effect, they are 99 and 132 participants per arm. The pattern illustrates a general planning principle: smaller effects are harder to distinguish from random variation and require more participants to detect at a given power target. It does not mean that those effects were established in a future study or that the original trial was designed to detect each one.
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 = -7.900; pooled standard deviation σ = 9.893.
- n = 2 × (1.96 + 0.842)2 × 9.8932 / -7.9002 = 24.6, rounded up to 25 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 <- -7.9 # observed difference in means
sigma <- 9.89295219971301 # 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(332241)
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 = 25 (80% power), 33 (90% power)
75% of observed effect: n per arm = 44 (80% power), 59 (90% power)
50% of observed effect: n per arm = 99 (80% power), 132 (90% power)
power.t.test: 25.6
Simulated power at n = 25 per arm: 0.790 (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. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when a study evaluates more than one outcome, time point, subgroup, or statistical contrast. In general, making many tests increases the chance that at least one result will appear statistically notable even when the underlying effects are absent. Prespecified priorities, sequential testing, or other adjustment methods can help define how a family of results should be interpreted. The registry lists 8 outcome measures and 7 posted secondary outcomes, but a count of measures does not reveal how many tests were planned or how they were ordered.
The registry record does not report a multiplicity adjustment, a hierarchy for testing outcomes, or a complete statistical analysis plan. The posted p values for the comparisons are unadjusted recalculations. They should not be read as if they necessarily account for the full set of outcomes assessed. This is particularly relevant to the secondary comparisons, which are best treated as contextual evidence rather than independent confirmation of the primary result.
For the primary endpoint, the registry identifies an efficacy population and states that the data set used last observation carried forward. It names exclusions: 2 participants in the placebo group, one lost to follow-up and one who withdrew consent, and 1 participant in the aripiprazole group who discontinued due to an adverse event on Day 2. The record does not describe the full pattern of missing observations at each visit or whether other approaches to missing data were considered.
Last observation carried forward is a general method in which a prior measurement is used in place of a later missing measurement. Its use can make an analysis depend on an assumption about what would have happened after the last recorded observation. The method may not capture continued change, and its performance depends on why data are missing and how outcomes evolve. These are general methodological concerns, not evidence that a particular bias occurred in this trial. The registry does not report sensitivity analyses comparing alternative missing-data assumptions.
The record also does not report a complete description of analysis populations across all outcomes, an interim-analysis plan, or whether any interim analyses occurred. Nor does it state the original sample-size justification. Those omissions limit the ability to assess how the posted comparisons align with the prespecified design and how missingness, multiplicity, and analysis choices were addressed in the trial's own statistical procedures.
15. 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 | 0 | 47 | 0.0% |
| Placebo | 0 | 50 | 0.0% |
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 | 38 of 47 |
| Placebo | 29 of 50 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Aripiprazole | Placebo |
|---|---|---|---|
| INCREASED APPETITE | Metabolism and nutrition disorders | 7 of 47 | 5 of 50 |
| FATIGUE | General disorders | 10 of 47 | 2 of 50 |
| HEADACHE | Nervous system disorders | 3 of 47 | 8 of 50 |
| SOMNOLENCE | Nervous system disorders | 8 of 47 | 2 of 50 |
| VOMITING | Gastrointestinal disorders | 7 of 47 | 2 of 50 |
| DIARRHOEA | Gastrointestinal disorders | 4 of 47 | 5 of 50 |
| INSOMNIA | Psychiatric disorders | 3 of 47 | 4 of 50 |
| ENURESIS | Renal and urinary disorders | 3 of 47 | 4 of 50 |
| SEDATION | Nervous system disorders | 5 of 47 | 1 of 50 |
| UPPER RESPIRATORY TRACT INFECTION | Infections and infestations | 1 of 47 | 5 of 50 |
The registry lists serious adverse event counts with 47 participants at risk in the aripiprazole group and 50 in the placebo group. The serious adverse event count affecting participants is 0 in each group. These figures indicate that no participants are listed as affected by a serious adverse event in either reported group for these entries. The at-risk counts differ from the group counts for the primary efficacy outcome, reflecting outcome-specific populations rather than a single denominator for every analysis.
These counts do not describe non-serious adverse events. The registry lists other adverse events affecting 38 participants in the aripiprazole group and 29 in the placebo group. Those are separate entries and should not be combined with the serious-event figures. The record does not provide serious adverse event terms in the listed data, and deaths are not reported in the registry record.
A count of zero serious events in these entries is not proof that an intervention has no serious risks. Safety interpretation depends on what events were collected, the duration and completeness of follow-up, and the size and characteristics of the groups. The registry summary does not provide enough detail to characterize every safety outcome or assess rare events. These figures describe the posted counts; they are not medical advice or a complete safety assessment.
16. What the Result Does, and Does Not, Mean
The posted primary outcome shows a larger mean decrease in ABC Irritability score in the aripiprazole group than in the placebo group at Week 8. The registry's scale description says that a decrease indicates improvement. The unadjusted contrast is -7.9 units, with a 95% confidence interval from -11.88 to -3.922 and an unadjusted p value of <0.001. These statistics describe the difference between group averages under the posted summary and recalculation.
They do not show that every participant experienced a decrease, or that any particular participant would have the same outcome. A mean does not disclose the full distribution of responses. The endpoint is an informant-based scale score, not a direct measure of every aspect of behavior or daily life. The registry record does not report a threshold for a clinically meaningful change, so the statistical contrast cannot be translated into a clinical category from these registry entries alone.
The comparison also does not establish findings beyond the recorded outcome and time point. The registry lists other secondary outcomes, but the available secondary summaries do not replace the primary endpoint, and the multiplicity strategy is not reported. The record does not provide follow-up results beyond the stated Week 8 timeframe for the primary endpoint, or enough information to infer durability.
Interpretation is further bounded by the efficacy population and last-observation-carried-forward data set described for the primary outcome. The registry does not report the original statistical analysis plan, detailed missing-data sensitivity analyses, or a sponsor-reported primary comparison. The unadjusted recalculation therefore offers a transparent reading of the posted group summaries, but it is not a complete reconstruction of every planned analysis.
Finally, a trial comparison is evidence about groups studied under the trial's design, not a prediction for an individual. The posted result does not establish an overall benefit-harm judgment, and the serious adverse event counts alone do not provide a comprehensive safety profile. The registry record is most informative when its numerical findings are read alongside these limits on measurement, analysis, and scope.
17. Why This Trial Matters Statistically
This trial offers an example of how a randomized, double-blind, placebo-controlled design can be used to compare group changes on a continuous behavioral scale. Its primary result is not only a p value: it includes arm means, standard errors, a mean difference, and a confidence interval. Reading those elements together distinguishes the estimated direction and magnitude of a group contrast from the precision with which it was estimated.
The outcome also illustrates the importance of understanding scale direction. The primary endpoint is a change score, and the registry states that decreases on the ABC Irritability subscale indicate improvement. Without that scoring context, the negative means and negative mean difference could be misread. Measurement details matter as much as arithmetic when interpreting clinical results.
The record highlights a further statistical distinction between a posted summary and a trial's formal analysis. An unadjusted recalculation from group means is interpretable, but the original statistical plan is not reported. The efficacy population and last-observation-carried-forward approach are described, while details of the broader missing-data strategy, multiplicity handling, and sample-size rationale are not. Those gaps show why transparent reporting of analysis methods is important for judging how closely a displayed comparison reflects prespecified procedures.
Finally, the listed secondary outcomes make clear that clinical trials often measure several related constructs. A pattern across outcomes can provide context, but without a reported multiplicity plan, unadjusted secondary results require restraint. This is a useful statistical case in reading estimates, uncertainty, outcome definitions, and reporting limitations together rather than treating a single threshold as the whole 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 report the original sample-size justification or the assumptions used to plan enrollment. Consequently, the sample-size illustrations based on the observed effect should not be confused with the trial's design rationale. The record also does not report whether interim analyses were planned or performed, or provide a detailed protocol-level statistical analysis plan.
The primary comparison presented in the posted summaries is an unadjusted recalculation. A sponsor-reported primary inferential analysis is not listed, and the record does not specify whether a prespecified model adjusted for baseline scores or other factors. The p value and confidence interval should therefore be understood as properties of the recalculation, not as evidence that every feature of the original analysis has been reproduced.
The primary efficacy population uses last observation carried forward, but the record does not describe all missing observations or report sensitivity analyses under alternative assumptions. The listed exclusions are not a complete account of every possible source of missingness. The outcome-specific group counts also vary across the posted summaries, so a count from one outcome should not automatically be applied to another.
The outcome is an informant-based rating scale, and the registry does not report a threshold for clinically meaningful change. The result therefore quantifies change in scale units without defining a clinical interpretation threshold. The secondary outcomes span distinct measures, and no multiplicity procedure is reported; unadjusted comparisons across several outcomes warrant caution.
Safety entries are also limited: serious adverse event counts are listed, but the registry does not provide serious-event terms in the posted data, and deaths are not reported in the registry record. The information is not a complete account of all safety outcomes. These limitations concern reporting and interpretation; they do not establish that the trial's conduct or results were biased.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: Study of Aripiprazole in the Treatment of Children and Adolescents With Autistic Disorder (AD). — NCT00332241.
- Registry record last updated 2026-05-13; status last verified 2026-04.
- Results first posted 2009-07-23.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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22. Record Summary
The registry describes a completed phase 3, randomized, double-blind, parallel-group study of flexibly dosed aripiprazole versus placebo in children and adolescents with autistic disorder. Enrollment was 98. The study start date was 2006-06-01, and the primary completion date was 2008-04-01.
The primary outcome was mean change from baseline to Week 8 in the ABC Irritability subscale. The posted group means were -5.0 for placebo and -12.9 for aripiprazole. The unadjusted recalculated mean difference was -7.9, with a 95% confidence interval from -11.88 to -3.922 and an unadjusted p value of <0.001. The scale description says that a decrease indicates improvement.
The record describes the primary efficacy population and a last-observation-carried-forward data set, but does not report a complete statistical analysis plan, original sample-size rationale, or multiplicity strategy. The posted comparisons should be interpreted in that context.