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Attention-Deficit/Hyperactivity Disorder (ADHD) Phase 4 Continuous Endpoint NCT00776009

Efficacy and Safety of Dex-Methylphenidate Extended Release 30 mg Versus 20 mg in Children (6-12 Years) With Attention-Deficit/Hyperactivity Disorder (ADHD) in a Laboratory Classroom Setting.: Complete Statistical Analysis

This analysis examines a randomized, masked crossover study of dex-methylphenidate extended release at 20 mg and 30 mg versus placebo in children with ADHD. The primary outcome was change in the SKAMP combined score averaged at 10, 11, and 12 hours after dosing.

Trial start: 2008-10  ·  Enrollment: 165  ·  Sponsor: Novartis Pharmaceuticals
Scope of this record

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 Efficacy and Safety of Dex-Methylphenidate Extended Release 30 mg Versus 20 mg in Children (6-12 Years) With Attention-Deficit/Hyperactivity Disorder (ADHD) in a Laboratory Classroom Setting. (NCT00776009), a randomized phase 4 study. The primary outcome is Change From Pre-dose in the Swanson, Kotkin, Agler, M Flynn, and Pelham (SKAMP) Combined Attention and Deportment Scores at 10, 11, and 12 Hour (Averaged) Post-dose.

165
Enrollment
Phase 4
3
Arms
In the primary outcome
-6.52
Mean difference
Dex-Methylphenidate Hydrochloride (Focal
-8.52–-4.52
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00776009
PhasePhase 4
ConditionAttention-Deficit/Hyperactivity Disorder (ADHD)
AllocationRandomized
Design modelCrossover
MaskingQuadruple
Enrollment165
Arms in the primary outcome3
Lead sponsorNovartis Pharmaceuticals
Results postedYes

2. Clinical Question

Population

Children ages 6-12 with attention-deficit/hyperactivity disorder. The intent-to-treat population included randomized patients who took at least one dose of study medication and had at least one post-dose efficacy measurement.

Intervention

Dex-methylphenidate hydrochloride extended release at 20 mg or 30 mg, taken orally once a day for 7 days in the relevant treatment period.

Comparator

Placebo, taken orally once a day for 7 days. The study also compared the two active doses, but the posted primary comparisons are each active dose against placebo.

Primary question

What was the change from pre-dose in the SKAMP combined Attention and Deportment score, averaged over 10, 11, and 12 hours post-dose? The scale rates classroom behaviors, with a negative change indicating improvement.

The central statistical contrast is the posted mean change for each active dose relative to placebo. The registry record describes a laboratory classroom setting and measurements on Day 7 of Weeks 1, 2, and 3. It does not report a direct statistical comparison of the 30 mg dose with the 20 mg dose, so the posted contrasts against placebo should not be read as a formal test of dose versus dose.

3. Trial Design

This was a completed Phase 4, randomized, quadruple-masked, placebo-controlled crossover study with an enrollment of 165 children. The registry record describes a 12-hour laboratory classroom setting and evaluates dex-methylphenidate extended release at 20 mg and 30 mg against placebo. Each listed treatment regimen was taken orally once a day for 7 days. The study's primary outcome was measured on Day 7 of Weeks 1, 2, and 3.

A crossover design means participants receive more than one study condition across treatment periods, so each participant can contribute measurements under multiple conditions. The registry record does not report the treatment sequence, the timing or use of washout periods, or the statistical handling of within-participant correlation and possible carryover. Those details matter because observations from one participant across treatment conditions are not necessarily independent. The displayed arm counts therefore should not be interpreted as proof that the study used three independent parallel groups.

The registry record lists 159 observations for the 20 mg primary outcome, 158 for 30 mg, and 158 for placebo. The stated intent-to-treat population included randomized patients who took at least one dose and had at least one post-dose efficacy measurement. The relationship between the enrollment count and each outcome count is not further explained in the registry record. Dates are recorded as a start in 2008-10 and primary completion in 2008-12. The original sample-size justification and details of the trial's planned statistical analysis are not reported in the registry record.

4. Participant Flow and Accounting

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

Period 1: First Intervention

StageFocalin XR 20 mg First, Then Focalin XR 30 mg, Then PlaceboFocalin XR 30 mg First, Then Placebo, Then Focalin XR 20 mgFocalin XR 30 mg First, Then Focalin XR 20 mg, Then PlaceboPlacebo First, Then Focalin XR 20 mg, Then Focalin XR 30 mgFocalin XR 20 mg First, Then Placebo, Then Focalin XR 30 mgPlacebo First, Then Focalin XR 30 mg, Then Focalin XR 20 mg
STARTED262829272827
COMPLETED262728272627
NOT COMPLETED011020

Reasons for not completing this period:

ReasonFocalin XR 20 mg First, Then Focalin XR 30 mg, Then PlaceboFocalin XR 30 mg First, Then Placebo, Then Focalin XR 20 mgFocalin XR 30 mg First, Then Focalin XR 20 mg, Then PlaceboPlacebo First, Then Focalin XR 20 mg, Then Focalin XR 30 mgFocalin XR 20 mg First, Then Placebo, Then Focalin XR 30 mgPlacebo First, Then Focalin XR 30 mg, Then Focalin XR 20 mg
Withdrawal by Subject001010
Protocol Violation010010

Period 2: Second Intervention

StageFocalin XR 20 mg First, Then Focalin XR 30 mg, Then PlaceboFocalin XR 30 mg First, Then Placebo, Then Focalin XR 20 mgFocalin XR 30 mg First, Then Focalin XR 20 mg, Then PlaceboPlacebo First, Then Focalin XR 20 mg, Then Focalin XR 30 mgFocalin XR 20 mg First, Then Placebo, Then Focalin XR 30 mgPlacebo First, Then Focalin XR 30 mg, Then Focalin XR 20 mg
STARTED262728272627
COMPLETED252727272626
NOT COMPLETED101001

Reasons for not completing this period:

ReasonFocalin XR 20 mg First, Then Focalin XR 30 mg, Then PlaceboFocalin XR 30 mg First, Then Placebo, Then Focalin XR 20 mgFocalin XR 30 mg First, Then Focalin XR 20 mg, Then PlaceboPlacebo First, Then Focalin XR 20 mg, Then Focalin XR 30 mgFocalin XR 20 mg First, Then Placebo, Then Focalin XR 30 mgPlacebo First, Then Focalin XR 30 mg, Then Focalin XR 20 mg
Withdrawal by Subject000001
Protocol Violation101000

Period 3: Third Intervention

StageFocalin XR 20 mg First, Then Focalin XR 30 mg, Then PlaceboFocalin XR 30 mg First, Then Placebo, Then Focalin XR 20 mgFocalin XR 30 mg First, Then Focalin XR 20 mg, Then PlaceboPlacebo First, Then Focalin XR 20 mg, Then Focalin XR 30 mgFocalin XR 20 mg First, Then Placebo, Then Focalin XR 30 mgPlacebo First, Then Focalin XR 30 mg, Then Focalin XR 20 mg
STARTED252727272626
COMPLETED242727272626
NOT COMPLETED100000

Reasons for not completing this period:

ReasonFocalin XR 20 mg First, Then Focalin XR 30 mg, Then PlaceboFocalin XR 30 mg First, Then Placebo, Then Focalin XR 20 mgFocalin XR 30 mg First, Then Focalin XR 20 mg, Then PlaceboPlacebo First, Then Focalin XR 20 mg, Then Focalin XR 30 mgFocalin XR 20 mg First, Then Placebo, Then Focalin XR 30 mgPlacebo First, Then Focalin XR 30 mg, Then Focalin XR 20 mg
Withdrawal by Subject100000

Analysis population for the primary outcome, as defined in the registry: Intent-to-treat population included all randomized patients who took at least 1 dose of study medication and who had at least 1 post-dose efficacy measurement

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.

Only the first 6 of 7 groups are shown.

CharacteristicUnitFocalin XR 20 mg First, Then Focalin XR 30 mg, Then PlaceboFocalin XR 30 mg First, Then Placebo, Then Focalin XR 20 mgFocalin XR 30 mg First, Then Focalin XR 20 mg, Then PlaceboPlacebo First, Then Focalin XR 20 mg, Then Focalin XR 30 mgFocalin XR 20 mg First, Then Placebo, Then Focalin XR 30 mgPlacebo First, Then Focalin XR 30 mg, Then Focalin XR 20 mg
Participants analysed262829272827
Age ContinuousYears9.3 (SD 1.7)9.4 (SD 1.7)10.0 (SD 1.8)9.4 (SD 2.0)9.5 (SD 1.8)9.6 (SD 2.0)
Sex: Female, Male: FemaleParticipants91610101214
Sex: Female, Male: MaleParticipants171219171613
Region of Enrollment: United Statesparticipants262829272827

6. Primary Endpoint

The registry lists the primary outcome as Change From Pre-dose in the Swanson, Kotkin, Agler, M Flynn, and Pelham (SKAMP) Combined Attention and Deportment Scores at 10, 11, and 12 Hour (Averaged) Post-dose, measured over Pre-dose to 10, 11, and 12 hours post-dose.

ElementRegistry entry
Result typeLeast Squares Mean
Measure of spreadStandard Error
UnitScores on a scale
Endpoint classificationContinuous Endpoint

The primary endpoint is change from pre-dose in the SKAMP combined Attention and Deportment score, averaged over measurements at 10, 11, and 12 hours after dosing. The registry describes SKAMP as a 13-item rating scale for classroom manifestations of ADHD. Its Attention and Deportment subscales contain 7 and 6 items, respectively; their combined score ranges from 0 to 78. Ratings reflect both the frequency and quality of specific behaviors, with 0 representing normal behavior with no impairment and 6 representing maximum impairment on each rating item. A negative change from pre-dose indicates improvement on this scale.

This measure is relevant to the stated laboratory classroom question because it captures rated behavior during classroom tasks, including behavior related to attention and deportment. Averaging the specified late post-dose ratings gives a summary of the endpoint across those assessment hours rather than a result from a single hour. The registry reports least-squares means and standard errors for change. The endpoint is a continuous score, so its mean describes the average change in the analyzed group; it does not show how individual children responded or how many crossed a threshold for meaningful change. A threshold defining clinical importance is not reported in the registry record.

7. Results Posted in the Registry

Mean difference: Dex-Methylphenidate Hydrochloride (Focalin XR) 20 mg

-6.52

95% CI: -8.52 to -4.52

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-7.1-4.2-1.41.44.37.1Dex-Methylphenidate Hydrochlo… (n=159)Dex-Methylphenidate Hydrochlo… (n=158)Placebo (n=158)Scores on a scale (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Dex-Methylphenidate Hydrochlo…Dex-Methylphenidate Hydrochlo…-12-9.31-6.76-4.21-1.670.88mean difference vs control (95% CI)

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 outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Change From Pre-dose in the Swanson, Kotkin, Agler, M Flynn, and Pelham (SKAMP) Attention Score at 10, 11, and 12 Hour (Averaged) Post-doseContinuous EndpointMean difference-2.27 (-3.38 to -1.16)78 per arm
Change From Pre-dose in the Swanson, Kotkin, Agler, M Flynn, and Pelham (SKAMP) Deportment Score at 10, 11, and 12 Hour (Averaged) Post-doseContinuous EndpointMean difference-3.34 (-4.51 to -2.17)41 per arm
Change From Pre-dose in the Permanent Product Measure of Performance of Measurement (PERMP) Math Test-Attempted Score at 10, 11, and 12 Hours (Averaged) Post-doseContinuous EndpointMean difference18.99 (10.48 to 27.50)65 per arm

Change From Pre-dose in the Swanson, Kotkin, Agler, M Flynn, and Pelham (SKAMP) Attention Score at 10, 11, and 12 Hour (Averaged) Post-dose

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Dex-Methylphenidate Hydrochlo…Dex-Methylphenidate Hydrochlo…-5.05-3.96-2.88-1.80-0.710.37mean difference vs control (95% CI)

Change From Pre-dose in the Swanson, Kotkin, Agler, M Flynn, and Pelham (SKAMP) Deportment Score at 10, 11, and 12 Hour (Averaged) Post-dose

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Dex-Methylphenidate Hydrochlo…Dex-Methylphenidate Hydrochlo…-6.07-4.76-3.46-2.16-0.850.45mean difference vs control (95% CI)

Change From Pre-dose in the Permanent Product Measure of Performance of Measurement (PERMP) Math Test-Attempted Score at 10, 11, and 12 Hours (Averaged) Post-dose

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Dex-Methylphenidate Hydrochlo…Dex-Methylphenidate Hydrochlo…-2.945.5914233140mean difference vs control (95% CI)

The secondary endpoints follow a broadly consistent pattern across the posted summaries. For both active doses, the SKAMP Attention and Deportment changes are negative, while placebo changes are positive. For the two PERMP math outcomes, the active-dose changes are positive and the placebo mean change is near zero or negative. These directions are consistent with the primary endpoint's pattern when each outcome's scale and direction are considered. All posted unadjusted comparisons against placebo have p-values <0.001.

The secondary outcomes extend the assessment from combined classroom behavior to the attention and deportment subscales and to math-task performance. They provide related but distinct measures, rather than independent replications of the primary endpoint. The repeated outcome pattern may be informative, but its interpretation depends on the measurement definitions, analysis methods, and planned testing strategy. The registry record does not list sponsor-reported analyses for the secondary outcomes, and the displayed comparisons are simple unadjusted recalculations.

Unadjusted secondary results carry less weight when several outcomes and comparisons are examined, because the chance of seeing small p-values somewhere among many tests can increase. No multiplicity adjustment or prespecified hierarchy is reported in the registry record. The record also does not describe whether the secondary endpoints were confirmatory or exploratory. They should therefore be treated as supportive descriptions of the posted results, not as a set of independent, confirmatory claims. Their consistency with the primary outcome does not remove uncertainty about the crossover analysis, missing data, or clinical importance.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary SKAMP combined score, the posted least-squares mean change was -2.02 for 20 mg, -4.47 for 30 mg, and 4.5 for placebo. Because a negative change indicates improvement, the estimates describe different average directions of change across the treatment conditions. The recalculated, unadjusted mean difference versus placebo was -6.52 for 20 mg, with an interval from -8.516 to -4.524, and -8.97 for 30 mg, with an interval from -10.98 to -6.965. Both posted unadjusted p-values are <0.001.

These contrasts describe the posted summary statistics; they are not a substitute for a complete crossover analysis. The estimates were recalculated from posted group summaries, using approximate standard deviations inferred from standard errors. The registry record reports no analyses in its analyses listing, and it does not give a sponsor-reported test or adjusted model result for these comparisons. The registry's description of the endpoint as a least-squares mean does not supply the model specification or enough detail to reconstruct a crossover model. The recalculated contrasts should therefore be read as simple, unadjusted comparisons, not as a reproduction of an undocumented sponsor model.

The intervals for both active-dose contrasts do not include zero, and the unadjusted p-values are small. Those features indicate that the observed summary-statistic differences are not close to zero under the simple comparison used for recalculation. They do not establish that the contrast is free of bias, that all modeling assumptions are met, or that the size of the difference is important to children or families. Clinical importance thresholds are not reported in the registry record. The numerical estimates also do not provide a direct comparison between the active doses, so they cannot establish that one dose is superior to the other.

Interpretation is limited by the record's missing detail on sequence, carryover, analysis model, missing-data handling, and multiplicity. The crossover design makes within-participant analysis especially relevant, while the recalculated estimates use unadjusted summary-statistic methods. The trial's posted results describe average scale changes in the defined intent-to-treat population under a controlled classroom assessment. They do not by themselves characterize effects in other settings, longer-term outcomes, or every participant's experience.

10. Statistical Methods Explained

What does a least-squares mean describe?

A mean is an average across observations. A least-squares mean is an average estimated from a statistical model, often adjusted for terms included in that model. The registry labels the primary endpoint and secondary continuous outcomes as least-squares means, but the model terms and estimation details are not reported in the registry record. The posted values are therefore best described using the registry's label, without assuming which covariates or crossover terms were included. For a continuous outcome, a group mean summarizes the central average change; it does not show the distribution of individual changes.

What is the standard error?

The registry reports standard errors as the dispersion measure for the least-squares means. A standard error describes the estimated uncertainty in a mean, rather than the spread of individual participant measurements. A smaller standard error generally indicates a more precise estimate under the analysis used. It cannot, on its own, show whether the analysis accounts appropriately for the crossover structure. The primary standard errors are 0.717 for 20 mg, 0.724 for 30 mg, and 0.723 for placebo.

How should the mean differences be read?

The posted comparisons express an active-dose mean relative to the placebo mean. A negative difference for the SKAMP endpoint is in the direction of a lower change score for the active condition; because negative change indicates improvement, the sign needs to be understood alongside the scale definition. The recalculated contrasts are unadjusted and use the posted summary statistics. In this calculation, standard deviations are approximated from the posted standard errors. This is a simple summary-statistic approach, not a fit of the study's original crossover analysis. The corresponding p-values are unadjusted and should not be taken as evidence that a multiplicity plan was followed.

Why does the crossover structure matter?

In a crossover trial, outcomes from the same participant under different treatment conditions are related. A suitable analysis usually needs to represent that dependence, as well as any relevant period or sequence effects. Treating each condition's summary as if it came from separate, unrelated groups can omit information about within-participant comparisons and may misstate uncertainty. The registry identifies the study as crossover but does not report the sequence, periods beyond the listed measurement weeks, washout details, model, or treatment of carryover. The recalculated summary comparisons cannot recover those missing details. This is why the posted estimates and their recalculated intervals are informative descriptions but should not be confused with a complete trial analysis.

What does a p-value add?

A p-value describes how compatible the observed data are with a specified null model, under the assumptions of the test. The posted comparison values are unadjusted p-values, each reported as <0.001. They do not measure the probability that the null hypothesis is true, the probability that the finding will replicate, or the clinical importance of a score difference. Their interpretation also depends on the statistical method and assumptions. The exact test used for sponsor-reported comparisons is not reported in the registry record, and the displayed p-values accompany recalculated simple comparisons.

What is over-dispersion, and is it relevant?

Over-dispersion is a general statistical issue in which observed variability is greater than a model's assumptions allow. It is important for outcomes whose variability is modeled through a count or probability distribution, because underestimated variability can make standard errors too small. The primary SKAMP endpoint is continuous, and the record does not describe a dispersion model or report an over-dispersion diagnostic. It would not be appropriate to assert that over-dispersion occurred in this trial. More generally, a model should represent the outcome's variability and the dependence created by repeated measurements; the record's missing model details prevent assessing those choices.

What can be inferred from the reported analysis count?

The registry lists zero analyses in its analyses listing. This does not mean that no statistical work was performed; it means the registry record does not post analyses in that listing. The outcome summaries and the recalculated comparisons can still be described, but a full account of prespecified models, estimands, covariate adjustment, missing-data procedures, or analysis populations is not reported in the registry record. Without those details, readers should distinguish descriptive summaries and unadjusted recalculations from a sponsor's complete inferential analysis.

11. Confidence Intervals and Precision

The recalculated primary mean difference for 20 mg versus placebo is -6.52, with interval endpoints -8.516 and -4.524. For 30 mg versus placebo, it is -8.97, with endpoints -10.98 and -6.965. These intervals communicate uncertainty around the estimated contrasts: values closer to the endpoints are less precisely distinguished from the estimate than the single point estimate suggests. Both intervals lie on the negative side of zero. The registry record does not state the confidence level for these recalculated intervals, so a confidence level should not be assigned to them.

Precision is distinct from importance. An interval can describe uncertainty around an average difference without establishing whether that difference matters clinically. The registry record does not report a threshold for a clinically important change on the SKAMP combined score. It also does not provide participant-level distributions in the stated results, so the intervals do not describe how much responses varied among children.

The interval calculations use simple, unadjusted summary-statistic methods, with approximate standard deviations inferred from standard errors. In a crossover study, within-participant correlation can affect the uncertainty of treatment contrasts. Because the registry record does not report the full analysis model or correlation information, the recalculated intervals may not represent the precision from an appropriately specified crossover model. The posted unadjusted p-values are <0.001 for both active-dose comparisons, but p-values and intervals from the same simple calculation do not resolve the missing model details or multiplicity questions.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect3141
75% of the observed effect5473
50% of the observed effect122163
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect205010020050040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Standard deviation was approximated from model-based standard errors, so treat it as rough. Calculated for the comparison: Dex-Methylphenidate Hydrochloride (Focalin XR) 20 mg.

The sample-size estimates are planning illustrations based on the observed effect, not the trial's original design calculation. For these continuous outcomes, the estimates are participants per arm, not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is set to the stated fraction of the observed effect: 100%, 75%, or 50%. The original trial's own sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the estimated participants per arm for a design with an 80% chance of detecting the target effect at the stated significance level, if the planning assumptions hold. The 90% power column describes the corresponding estimate for a 90% chance. These are prospective design calculations, not measures of how much power the completed study actually had; this is not observed power.

Each row represents planning for a different fraction of the observed effect. A smaller target effect requires more participants to detect under the same assumptions, because a smaller signal is harder to distinguish from sampling variation. These estimates use the observed effect as their starting point, so they should not be treated as an independent confirmation of the result or as evidence that the original trial was designed around these exact assumptions. They are illustrations to help readers understand how assumed effect size and desired power relate to participant requirements.

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 = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

  1. Observed difference Δ = -6.520; pooled standard deviation σ = 9.064.
  2. n = 2 × (1.96 + 0.842)2 × 9.0642 / -6.5202 = 30.3, rounded up to 31 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -6.52                      # observed difference in means
sigma <- 9.06445341193515                     # 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(776009)
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 = 31 (80% power), 41 (90% power)
 75% of observed effect: n per arm = 54 (80% power), 73 (90% power)
 50% of observed effect: n per arm = 122 (80% power), 163 (90% power)
power.t.test: 31.3 
Simulated power at n = 31 per arm: 0.791 (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 multiple outcomes, treatment comparisons, time points, or analysis choices. Each additional test can add opportunities for a result to appear noteworthy by chance. This study lists a primary SKAMP combined score and secondary SKAMP Attention, SKAMP Deportment, and PERMP math outcomes. The primary and secondary measurements are made across several post-dose hours, and the posted comparisons contrast each active dose with placebo. The registry record does not report a multiplicity adjustment, testing hierarchy, or procedure for controlling the overall false-positive risk. The posted p-values are unadjusted, so they should not be interpreted as if a family-wide adjustment had been applied.

The registry identifies an intent-to-treat population: randomized patients who took at least one dose and had at least one post-dose efficacy measurement. This definition excludes randomized participants without a dose or without any post-dose efficacy measurement from the stated analysis population. The record does not report the number excluded under each criterion, the amount or pattern of missing outcome data, or the method used to handle missing measurements. It also does not describe whether all analyses followed the same population definition.

For a crossover study, missing observations can affect within-participant comparisons, and missingness in one period may have different implications from missingness across all periods. The registry record does not report whether imputation, a likelihood-based method, or another missing-data approach was used. The exact statistical model, treatment of period and sequence, and handling of carryover are also not reported in the registry record. These omissions limit assessment of whether the reported means and recalculated contrasts address the intended trial question without bias.

The record lists zero analyses in its analyses listing. That does not establish that the study lacked a prespecified analysis plan; it means the plan is not reported in the registry record. A protocol, analysis plan, and sponsor-reported inferential results would be needed to evaluate prespecification, multiplicity control, and analysis-population decisions in detail.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Dex-Methylphenidate Hydrochloride (Focalin XR) 30 mg01650.0%
Dex-Methylphenidate Hydrochloride (Focalin XR) 20 mg11650.6%
Placebo01650.0%
Participants with at least one serious adverse event
Serious adverse events by armDex-Methylphenidate Hydrochlo…0.0%Dex-Methylphenidate Hydrochlo…0.6%Placebo0.0%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

ArmParticipants affected of at risk
Dex-Methylphenidate Hydrochloride (Focalin XR) 30 mg10 of 165
Dex-Methylphenidate Hydrochloride (Focalin XR) 20 mg8 of 165
Placebo0 of 165

Most frequent serious adverse event terms

Event termOrgan systemDex-Methylphenidate Hydrochloride (Focalin XR) 30 mgDex-Methylphenidate Hydrochloride (Focalin XR) 20 mgPlacebo
Peritonsillar abscessInfections and infestations0 of 1651 of 1650 of 165

Most frequent non-serious adverse event terms

Event termOrgan systemDex-Methylphenidate Hydrochloride (Focalin XR) 30 mgDex-Methylphenidate Hydrochloride (Focalin XR) 20 mgPlacebo
Decreased appetiteMetabolism and nutrition disorders10 of 1658 of 1650 of 165

Serious events with the highest arm-level rate: peritonsillar abscess (0.6%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry lists 165 participants at risk for serious adverse events in each of the 30 mg, 20 mg, and placebo groups. It records zero serious adverse events for 30 mg, one for 20 mg, and zero for placebo. A serious adverse event term, peritonsillar abscess, is listed at 0.6%; the record does not identify the treatment group for that term in the listed information. Deaths are not reported in the registry record.

These figures are counts within the registry's stated at-risk groups. They do not establish that a difference between treatment conditions is statistically meaningful, particularly in a crossover study where exposure and participant overlap require careful interpretation. The record does not provide a detailed account of event timing, duration, relatedness, or the method used to compare safety across conditions. The listed counts should be read as descriptive registry reporting, not as a complete comparative safety analysis.

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

The posted results describe average changes in a classroom behavior scale and related attention, deportment, and math-task measures after study treatment. On the primary SKAMP combined score, the active-dose means are negative and the placebo mean is positive; by the registry's definition, negative change indicates improvement. The recalculated unadjusted comparisons against placebo have intervals on the negative side of zero and p-values <0.001. These are features of the posted summary data, not a complete account of the sponsor's statistical analysis.

What the numbers do not establish is equally important. They do not quantify a clinically important threshold, show how individual participants responded, or determine whether the average differences translate into outcomes outside the laboratory classroom setting. The registry record describes assessments at 10, 11, and 12 hours post-dose, but it does not support conclusions about other times, longer-term outcomes, or settings not studied. Nor do the separate comparisons against placebo establish a direct difference between 20 mg and 30 mg.

Interpretation also depends on design and analysis details that are not reported in the registry record. The crossover sequence, washout arrangements, model, missing-data procedures, and multiplicity approach are not stated. The displayed comparisons are recalculated from summary statistics using approximate standard deviations and do not account for undocumented crossover-model features. These estimates can help describe the posted pattern, but the missing information limits a full evaluation of precision and bias.

The safety listing gives serious adverse event counts by stated treatment group, but event counts alone cannot establish comparative risk or explain causality. The record also does not report deaths. Overall, the registry results are best understood as summary observations from a specific pediatric laboratory-classroom trial, with statistical uncertainty and analysis limitations kept distinct from clinical conclusions.

17. Why This Trial Matters Statistically

This trial illustrates several issues that arise when interpreting clinical evidence from a crossover design. The same participant can contribute outcomes under more than one condition, making within-participant dependence central to the analysis. A simple comparison of treatment-specific summaries can be easy to interpret, but it does not necessarily reproduce the information or uncertainty from a crossover model. Here the registry identifies the design, while leaving the sequence, model, and related analysis details unreported.

It also illustrates why scale direction matters. A negative SKAMP change denotes improvement, while the PERMP outcomes count attempted or correctly answered math items, so their directions need to be understood according to their own definitions. A sign cannot be interpreted without knowing what the measure represents. Similarly, a small unadjusted p-value is not a measure of clinical importance, and it does not address the effect of examining multiple endpoints and comparisons.

Finally, registry completeness affects how far results can be interpreted. Posted means, standard errors, and adverse event counts communicate useful descriptive information, but details about missing data, multiplicity, and the sponsor's full analysis are not reported in the registry record. Keeping those distinctions visible helps separate what the posted data describe from what would require a prespecified analysis or additional reporting.

18. Limitations

This trial-specific interpretation has several limitations. The study is a crossover trial, but the registry record does not report treatment sequence, washout details, period effects, carryover assessment, or the model used to estimate treatment contrasts. The displayed comparisons are recalculated, unadjusted summary-statistic estimates with approximate standard deviations derived from standard errors. They do not account for within-participant correlation unless that information is represented in the posted summaries, and such representation is not explained.

The registry record lists zero analyses in its analyses listing. It does not report the original statistical analysis plan, sponsor-reported comparison tests, missing-data methods, or multiplicity handling. The intent-to-treat population definition is stated, but participant flow into each outcome analysis and the amount of missing data are not given. The sample-size calculations are planning illustrations based on observed effects, not a report of the trial's original design justification.

The primary outcome is measured in a laboratory classroom setting at specified late post-dose hours. The registry record does not provide a clinical-importance threshold or participant-level distributions, limiting interpretation of the average score difference. The safety listings are descriptive and do not provide sufficient detail on event timing, relatedness, or comparative analysis. These limitations mean the posted summaries can be described, but a full assessment of the study's design implementation and inferential results is not possible from the registry record alone.

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22. Record Summary

NCT00776009 is a completed Phase 4 randomized, quadruple-masked, placebo-controlled crossover study of dex-methylphenidate extended release at 20 mg and 30 mg in children ages 6-12 with ADHD. The registry reports enrollment of 165 and a laboratory classroom setting. The primary endpoint is change from pre-dose in the SKAMP combined score averaged at 10, 11, and 12 hours post-dose. The posted group means and recalculated unadjusted comparisons show negative primary-score contrasts against placebo for both active doses, with p-values <0.001. The record does not report the full crossover analysis, multiplicity approach, missing-data methods, or original sample-size justification. The posted results therefore support description of the observed summaries but leave important aspects of the planned and executed statistical analysis unclear.

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