Response Variability in Children With Attention Deficit Hyperactivity Disorder (ADHD): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Response Variability in Children With Attention Deficit Hyperactivity Disorder (ADHD) (NCT01238822), a randomized phase 4 study. The primary outcome is Attention Deficit / Hyperactivity Disorder Total Sum Score of All 18 ADHD Symptom Items.

2. Clinical Question

The endpoint is a symptom-rating score, not a direct measurement of response variability. The registry summary describes wider aims concerning response variability and neuropsychological tasks, but the posted primary outcome is the Vanderbilt ADHD Rating Scales total symptom score. Thus, the results should be read as comparisons on that rating-scale measure, rather than as a complete account of the study's broader research questions.

3. Trial Design

The registry identifies this as a Phase 4 randomized, quadruple-masked crossover trial, sponsored by Children's Hospital Medical Center, Cincinnati. The recorded enrollment is 96. The record gives a start date of 2006-06, a primary completion date of 2009-06, and a status of completed.

The four listed conditions are placebo, low dosage, medium dosage, and high dosage. The arm summaries report 96 for each condition. Because the study is described as crossover, those arm counts should not be read as evidence that each condition comprised a separate, independent group of participants. In a crossover design, participants may contribute observations under more than one condition; the exact condition sequence and the relationship between the reported arm counts are not reported in the registry record.

The broad study summary describes recruiting children with ADHD-Combined Type, children with ADHD-Predominantly Inattentive Type, and normal controls, with 45 described for each cohort. The registry enrollment is 96. How those narrative recruitment plans relate to the recorded enrollment and the reported outcome arms is not reported in the registry record. The registry also describes interest in response variability across neuropsychological tasks, subtype differences, medication and environmental manipulations, and naturalistic performance. Those aims provide context, but they do not replace the specific posted primary endpoint.

The record does not report the randomization sequence, treatment-period schedule, washout procedures, masking roles, adherence, or methods for handling period and carryover effects. It also does not report the original sample-size justification or the trial's own detailed statistical analysis plan. These omissions matter when interpreting crossover results, because an analysis ordinarily needs to reflect the within-participant structure rather than treat each condition as unrelated observations.

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 with imputation for missing data.

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 Attention Deficit / Hyperactivity Disorder Total Sum Score of All 18 ADHD Symptom Items, measured over end of first week, end of second week, end of third week, end of fourth week. Total of 4 weeks..

The primary endpoint is the Attention Deficit / Hyperactivity Disorder Total Sum Score of All 18 ADHD Symptom Items. It is described as the sum of the parent and teacher Vanderbilt ADHD Rating Scales symptom items, with a range of 0-54. The registry labels 0 as no ADHD symptoms and 54 as the highest ADHD symptoms. Lower scores therefore correspond to fewer symptoms on this scale, while higher scores correspond to more symptoms. The unit is a score, and the reported summary measure is the mean with standard deviation.

Measurements were scheduled at the end of the first week, the end of the second week, the end of the third week, and the end of the fourth week, for a total of 4 weeks. The posted results report a mean and standard deviation for each condition, but do not give week-specific results. The record therefore does not show how scores changed over time or whether a reported condition mean represents a particular week or a summary across the measurement period.

A symptom-rating endpoint can describe the average level of rated ADHD symptoms under the recorded conditions. It is distinct from the study's broader interest in response variability, which concerns inconsistency in performance across tasks or settings. The endpoint is useful for comparing symptom-rating summaries, but by itself it does not quantify every neuropsychological domain described in the study summary.

The stated analysis population is intent to treat with imputation for missing data. Details of the imputation procedure and the way repeated measurements contributed to the posted means are not reported in the registry record.

7. Results Posted in the Registry

• Low Dosage: mean 25.00 versus 26.54 on control; difference -1.54 (95% CI -5.04 to 1.96), standardized effect d = -0.12; z-test p = 0.389.
• Medium Dosage: mean 18.94 versus 26.54 on control; difference -7.60 (95% CI -10.89 to -4.31), standardized effect d = -0.65; z-test p = <0.001.
• High Dosage: mean 18.46 versus 26.54 on control; difference -8.08 (95% CI -11.43 to -4.73), standardized effect d = -0.68; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The posted endpoint is continuous: each participant's outcome is a score on a scale, and the registry reports means and standard deviations. A mean describes the average score in a condition. A standard deviation describes how spread out scores are around that average; it is not the uncertainty in the mean difference. The reported condition summaries are placebo 26.54 with standard deviation 12.03, low dosage 25.0 with standard deviation 12.73, medium dosage 18.94 with standard deviation 11.18, and high dosage 18.46 with standard deviation 11.68.

What does a mean difference represent?

A mean difference expresses the average score in one condition minus the average score in the comparator condition, as represented by the posted comparisons. A negative estimate means the active-condition mean is lower than the placebo mean. For low dosage, that estimate is -1.54; for medium dosage, it is -7.6; for high dosage, it is -8.08. Since lower scores correspond to fewer symptoms on the scale, the direction of these estimates is interpretable in relation to the scale. A mean difference does not describe every participant's score or guarantee that individual responses follow the group average.

What does a confidence interval add?

A confidence interval communicates the range of estimates compatible with the data and the method used to calculate the interval. It gives a view of precision as well as direction. The low dosage interval, -5.044 to 1.964, includes zero; the medium dosage interval, -10.89 to -4.315, and the high dosage interval, -11.43 to -4.726, do not. The interval is not a range containing every participant's score, nor does it represent a guarantee about the true value. Its interpretation depends on the analysis assumptions being suitable for the study design.

How should the p-values be read?

The posted p-values are unadjusted: 0.389 for low dosage, and p < 0.001 for both medium and high dosage. A p-value describes how unusual data at least as incompatible with a specified null model would be, assuming that model and its assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of an effect. The record does not report whether the sponsor used these particular comparisons in a prespecified inferential analysis.

The standard error relates to the variability of an estimate across repeated samples under an analysis model. Standard errors are reported for the placebo and active-condition means in the comparison information, but the registry record does not explain the calculation. For crossover data, measurements from the same participant can be related. A paired analysis can use that relationship; an analysis that treats observations as independent may not. The within-participant correlation and the treatment of repeated observations are not reported in the registry record, so the calculation basis cannot be verified from the posted summaries.

Why does the crossover model matter?

In general, a crossover design lets participants receive more than one condition, so each person may serve as their own comparator. This can improve precision when within-person measurements are suitably related and the analysis accounts for that dependence. It also makes treatment order, period effects, washout, and possible carryover relevant. These are general features of crossover analysis, not confirmation of how this trial was conducted. The registry record does not report the treatment sequence, washout schedule, or analysis of period and carryover effects.

The posted arm summaries show 96 for each condition, but those values do not establish that the condition observations come from independent groups. Nor do the summary values allow reconstruction of a paired treatment effect, because the participant-level pairing and covariance are not reported. Consequently, the comparisons can be described as posted, but their alignment with the crossover design cannot be independently assessed from the registry record.

For a continuous outcome, over-dispersion in a count model is not the relevant issue. More generally, an analysis model should match the outcome type and the dependence structure. Here, the endpoint is a bounded score from 0-54, reported as a mean and standard deviation. The record does not say whether the distribution, bounded scale, repeated measurements, or missingness assumptions were examined in the sponsor's analysis. These absences limit assessment of model suitability.

The specified analysis population is intent to treat with imputation for missing data. In general, intent-to-treat analysis aims to retain participants according to their assigned treatment strategy, while imputation replaces or accounts for missing outcome values using an explicit statistical procedure. Different imputation assumptions can produce different results. The imputation model, amount and pattern of missing data, and sensitivity analyses are not reported in the registry record. The posted summary therefore does not allow a reader to assess how missing observations influenced the estimates.

10. Confidence Intervals and Precision

Precision is reflected in the width of a confidence interval: a narrower interval generally gives a more concentrated range of estimates, while a wider interval leaves more uncertainty. The low dosage mean difference was -1.54, with an interval from -5.044 to 1.964. Since that interval includes zero and values on either side, the comparison does not pin down the direction of the difference with the same clarity as an interval wholly below zero.

The medium dosage estimate was -7.6, with an interval from -10.89 to -4.315. The high dosage estimate was -8.08, with an interval from -11.43 to -4.726. Both intervals are below zero, so their reported estimates indicate lower mean scores in those conditions than under placebo. The interval ranges nevertheless show uncertainty about the size of each difference. They do not establish whether the magnitude is important in practice, because a threshold for a meaningful score change is not reported in the registry record.

Confidence intervals are conditional on the method used to calculate them. This is especially relevant for a crossover trial: if measurements within participants are related, interval estimation should reflect that dependence. The registry record does not describe the covariance structure or the analysis details behind these intervals. It is therefore possible to describe their stated bounds, but not to verify from the record whether they fully reflect the trial design.

The posted intervals also do not show uncertainty in every weekly measurement separately. The endpoint schedule includes four weekly assessments, but the reported comparisons do not specify time-specific estimates. No interval for a change over time or for a treatment-by-time pattern is reported in the registry record.

11. Planning a Similar Trial: Sample Size

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

The sample-size figures are planning illustrations, not observed power. They use the observed effect as a starting point and show the participants per arm needed under the stated assumptions. The assumptions are a two-sided significance level of 0.05, equal allocation between two arms, a normal approximation, and an effect to detect set at the stated fraction of the observed effect. These are planning assumptions for the illustration; the trial's original design assumptions are not reported in the registry record.

For the low dosage comparison, planning for 100% of the observed effect gives 1,016 participants per arm for 80% power and 1,360 participants per arm for 90% power. Planning for 75% gives 1,805 and 2,417 participants per arm, respectively; planning for 50% gives 4,062 and 5,437 participants per arm. For the medium dosage comparison, the corresponding pairs are 37 and 50 at 100%, 66 and 88 at 75%, and 147 and 197 at 50%. For high dosage, they are 34 and 46 at 100%, 61 and 81 at 75%, and 136 and 181 at 50%.

The 80% power column represents the number of participants per arm that the planning calculation estimates would give an 80% chance of detecting the specified effect under its assumptions; the 90% column uses a higher target chance. Smaller target effects require more participants, as reflected by the larger figures for 75% and 50% of the observed effects. These illustrations do not account for unreported features of the crossover design or establish the power achieved in the completed trial.

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 = -1.540; pooled standard deviation σ = 12.385.
2. n = 2 × (1.96 + 0.842)² × 12.385² / -1.540² = 1,015.3, rounded up to 1,016 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 <- -1.54                      # observed difference in means
sigma <- 12.3849465077569                     # 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(1238822)
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 = 1,016 (80% power), 1,360 (90% power)
 75% of observed effect: n per arm = 1,805 (80% power), 2,417 (90% power)
 50% of observed effect: n per arm = 4,062 (80% power), 5,437 (90% power)
power.t.test: 1016.2 
Simulated power at n = 1,016 per arm: 0.796 (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. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary outcome measure and no posted secondary outcome measures. It also lists no posted analyses. The absence of posted secondary outcomes does not establish that the study collected no other measurements: the study summary describes broader interests in response variability, ADHD subtypes, medication, environmental manipulations, and naturalistic performance. Results for those interests are not reported in the registry record.

Three active-versus-placebo comparisons are presented for the primary score. Their p-values are unadjusted. When several statistical comparisons are considered, the chance of at least one apparently notable result can increase; multiplicity procedures are methods that can control or otherwise address this issue. The registry record does not report whether any correction, hierarchical testing strategy, or prespecified prioritization among dosage comparisons was used. The posted p-values should therefore be read as unadjusted comparisons, not as results known to have controlled multiplicity.

The outcome population is described as intent to treat with imputation for missing data. The record does not identify the number of missing measurements, the imputation approach, or whether sensitivity analyses were performed. It also does not explain the handling of participants who may have incomplete crossover periods or missing condition-specific observations. These details matter because missingness can affect which observations contribute to a comparison and how uncertainty is estimated.

The record does not describe the randomization procedure, analysis set construction, treatment sequence, period effects, or carryover assessment. Nor does it report a complete statistical analysis plan or the sponsor's detailed inferential model. As a result, it is not possible to determine whether analysis choices were specified before outcome review, or how the reported comparisons relate to any prespecified primary analysis. These omissions do not negate the posted summaries, but they limit assessment of selection, missing-data, and multiplicity risks.

14. 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 1% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: hallucination (1.0%).

The serious adverse event figures report 96 at risk in each condition. Serious adverse events affected 0 participants in placebo, 0 in low dosage, 1 in medium dosage, and 0 in high dosage. The record lists Hallucination at 1.0% among the top serious adverse event terms. That term corresponds to the serious event information reported for the medium dosage condition; the registry record does not provide further clinical details or timing.

These are counts of participants affected as recorded in the registry, not a comparison adjusted for the crossover structure or exposure time. The record does not explain whether adverse event risk periods overlap across conditions, how repeated events were counted, or how the serious adverse event categories were defined. Death counts are not reported in the registry record; the fields contain no posted values, which should not be interpreted as zero deaths.

Other adverse events are reported separately: 13 affected in placebo, 12 in low dosage, 16 in medium dosage, and 37 in high dosage, with 96 at risk in each condition. These other-event counts are not the serious adverse event counts. The registry record does not provide event-specific detail for all other adverse events in the information summarized by these figures.

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

The posted primary outcome summaries show lower average ADHD symptom scores in the medium and high dosage conditions than in the placebo condition, and a smaller estimated difference for low dosage. The mean differences and confidence intervals describe the size and uncertainty of those comparisons on the 0-54 rating-scale measure. They are statistical summaries, not a complete description of how each child responded.

These results do not establish that any condition caused a particular outcome. The registry identifies a randomized crossover design, but important design and analysis details—including condition sequence, washout, period effects, carryover, and the handling of within-participant dependence—are not reported in the registry record. The comparisons cannot be independently checked against those features using the posted summaries alone.

The results also do not show whether a score difference is meaningful to families or clinicians. No threshold for a meaningful change is reported. The rating-scale score captures the designated symptom items; it does not directly measure response variability, all neuropsychological functioning, or everyday performance. Those broader themes appear in the study summary, but the registry record does not post secondary results for them.

The low dosage interval includes zero, whereas the medium and high dosage intervals are wholly below zero. This distinction is about the uncertainty in the reported mean differences, not proof of equivalence for low dosage or proof of clinical importance for the other comparisons. The p-values are unadjusted, and the record does not report multiplicity handling. Thus, the estimates are best understood as posted comparisons with their stated uncertainty, subject to limitations in reporting and analysis detail.

The registry record describes intent-to-treat analysis with imputation, but does not provide the imputation method or missing-data information. It also does not report an original sample-size justification. Readers should keep those limitations in mind when assessing how robustly the posted summaries represent the enrolled study population.

16. Why This Trial Matters Statistically

This trial is statistically notable because the registry identifies a crossover design while reporting condition means and pairwise comparisons. Crossover studies can use within-participant comparisons, but valid inference depends on accounting for the relationship among repeated observations and considering treatment order and period-related effects. The record does not report those analysis details. This makes the design label important: the displayed comparisons should not automatically be treated as independent parallel-group estimates.

The result also illustrates why effect estimates and uncertainty are more informative than a p-value alone. The low dosage comparison has an interval that includes zero, while the medium and high dosage intervals are below zero. At the same time, the registry does not report a meaningful-change threshold or a multiplicity strategy. A statistical distinction among comparisons does not by itself determine clinical relevance or resolve the risk of selective emphasis across several tests.

Finally, the study summary emphasizes response variability and broader neuropsychological questions, but the posted primary endpoint is a symptom-rating total score. The contrast between broad aims and the available primary result is a useful reminder to match conclusions to the endpoint actually reported. Results for outcomes that are not posted cannot be inferred from the symptom-score summaries.

17. 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's brief summary describes 45 children with ADHD-Combined Type, 45 children with ADHD-Predominantly Inattentive Type, and 45 normal controls as recruitment plans, while the recorded enrollment is 96. The record does not explain how that narrative relates to enrollment or the four reported condition summaries. This makes the recruited population and the relationship between the narrative cohorts and analyzed outcome groups difficult to reconstruct from the registry record alone.

The description of the primary endpoint specifies measurement at the end of each week over 4 weeks, but the posted results do not identify whether each condition mean reflects a particular week, an average across weeks, or another summary. There are no posted week-specific estimates or treatment-by-time results. This limits interpretation of whether the reported differences were stable across the measurement period.

Although the record describes intent-to-treat analysis with imputation, the missing-data amount, imputation method, and sensitivity analyses are not reported in the registry record. The crossover sequence, washout, carryover, period effects, adherence, and within-participant correlation are also not reported. These gaps prevent a full assessment of how the posted comparisons account for the design and incomplete observations.

The record does not report a prespecified statistical analysis plan, original sample-size justification, or multiplicity adjustment. The reported confidence intervals and p-values therefore need to be read without confirmation of the planned analysis hierarchy or whether the analysis model addressed the crossover structure. No meaningful-change threshold is reported, and no secondary outcome measures are posted despite the broader aims described in the study summary. These limitations restrict the conclusions to the available symptom-score summaries and their stated comparison estimates.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Response Variability in Children With Attention Deficit Hyperactivity Disorder (ADHD) — NCT01238822.
• Registry record last updated 2012-04-04; status last verified 2012-04.
• Results first posted 2012-04-04.
• 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.

21. Record Summary

The registry record describes a completed Phase 4 randomized, quadruple-masked crossover trial of placebo and three methylphenidate dosage conditions, with enrollment recorded as 96. The primary endpoint was the Vanderbilt ADHD Rating Scales total score across all 18 symptom items, with a stated range of 0-54 and assessments scheduled over 4 weeks.

Mean scores were 26.54 for placebo, 25.0 for low dosage, 18.94 for medium dosage, and 18.46 for high dosage. The posted mean differences versus placebo were -1.54 for low dosage, -7.6 for medium dosage, and -8.08 for high dosage. The record describes an intent-to-treat population with imputation, but does not report the imputation details, crossover analysis methods, original design assumptions, or multiplicity handling.