Large-scale Brain Organization During Cognitive Control in ADHD: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Large-scale Brain Organization During Cognitive Control in ADHD (NCT04349917), a randomized phase 4 study. The primary outcome is Resting State Brain Network Organization.

2. Clinical Question

3. Trial Design

This was a phase 4, randomized, double-blind crossover study sponsored by the University of North Carolina, Chapel Hill. The registry lists 37 participants enrolled. The study began on 2016-12-16, reached primary completion on 2020-03-14, and has a completed status.

The crossover structure means that participants in the medication challenge received both methylphenidate and placebo, one in each of two sessions approximately one week apart. The order was randomized and double-blind. This design allows each participant to experience both conditions, so a comparison can potentially use within-participant information. Details of how the sponsor accounted for the paired structure, session order, or possible period effects are not reported in the registry record.

The primary outcome is a continuous measure, reported as a mean with standard deviation. The posted result gives 22 observations for methylphenidate and 22 for placebo. Those condition-specific counts should not be read as a count of distinct participants in a parallel-group trial: the stated design is crossover, with participants receiving both conditions. The record does not explain how the reported outcome counts relate to the overall enrollment, or give a detailed accounting of exclusions and missing outcome data.

Seven outcome measures and 23 analyses are listed in the record. Three secondary outcomes are named: Go/No-go commission rate, omission rate, and response-time variability. The primary outcome timeframe is 1 to 3 hours after intervention. Other details of the original statistical plan and the assumptions used to plan the trial 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.

Before assignment: A total of 47 participants were screened during a behavioral visit. Of those not randomized, 8 did not meet inclusion criteria and 2 withdrew from study.

First Intervention (2-4 Hours)

Reasons for not completing this period:

Washout Period (4-20 Days)

Second Intervention (2-4 Hours)

Analysis population for the primary outcome, as defined in the registry: Participants excluded due to excessive head motion (mean framewise displacement (FD) \> 0.5mm or fewer than 150 timepoints remaining after scrubbing all timepoints with FD \> 0.2mm), incomplete brain coverage, or poor-quality fMRI data. Participants must have good data from both methylphenidate and placebo scan days to be included in this analysis.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Resting State Brain Network Organization, measured over 1 to 3 hours after administration of intervention.

The primary endpoint is resting-state brain network organization, assessed through modularity calculated from functional connectivity estimates collected during functional MRI. Modularity is reported on a scale from -1 to 1. The registry describes higher values as indicating stronger community structure: clusters of brain regions tend to be more strongly connected internally and less connected across clusters.

This measure is used to describe how brain regions are organized into networks. The study’s rationale relates network organization to cognitive control and the ability to respond to changing demands. The registry notes that the meaning of a higher modularity value depends on context: during complex tasks, lower modularity may be preferable, whereas during basic, automatic tasks, higher modularity may be preferable. Thus, a higher value is not inherently a better outcome across every task or state.

The posted endpoint is specifically a resting-state measure, rather than a direct measure of network flexibility while cognitive demands shift. The primary outcome was assessed 1 to 3 hours after administration. The record describes exclusions for excessive head motion, incomplete brain coverage, and poor-quality fMRI data. It states that participants must have good data from both methylphenidate and, but the remaining eligibility text is incomplete in the registry record.

7. Results Posted in the Registry

• Methylphenidate: mean 0.22 versus 0.23 on control; difference -0.01 (95% CI -0.02 to 0.01), standardized effect d = -0.17; z-test p = 0.584.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous, so it is summarized by a mean and standard deviation for each intervention condition. The mean locates the center of the observed values; the standard deviation describes their spread around that center. The registry reports a mean of 0.223 and standard deviation of 0.026 for methylphenidate, and a mean of 0.228 and standard deviation of 0.034 for placebo. These summaries do not show the distribution of individual observations or how closely the two condition measurements were related within participants.

What does the mean difference represent?

The reported mean difference is -0.005. It compares the methylphenidate condition with placebo, with the direction defined by the posted comparison. In general, a mean difference expresses the difference between two condition means in the outcome’s original units. Here the outcome is modularity on the registry’s stated scale. The estimate is a point estimate: it is the single value that best summarizes the observed contrast under the calculation used, but it does not describe all plausible values of the underlying difference.

Why is the crossover structure relevant?

In general, a crossover study measures participants under more than one condition. Because the same person contributes data under each condition, a paired analysis can use the relationship between that person’s two measurements. The within-person correlation can affect the uncertainty of the estimated contrast. If only separate condition means and standard deviations are available, that correlation cannot be reconstructed from those summaries alone. The registry’s primary outcome shows 22 observations for each condition, but does not report the paired covariance or explain in the listed analysis how the crossover pairing was handled.

The registry lists a two-sided t-test. A two-sided test evaluates departures in either direction rather than only a prespecified increase or decrease. The listed analysis gives p = 0.532, but its entry does not state the test parameter or provide a confidence interval. The registry does not report further details about the model, the pairing structure, or adjustments for session order or period. Those details should not be inferred from the study’s design description.

How should the recalculation be understood?

The recalculated comparison is an unadjusted calculation from the posted summary statistics. It reports a mean difference of -0.005, a 95% confidence interval from -0.023 to 0.013, and p = 0.584. In general, a recalculation from summary statistics can help readers understand the scale and precision of a contrast, but it may not reproduce a sponsor analysis that uses participant-level data or design-specific modeling. It is not evidence that the registry’s listed analysis used the same calculation. The registry marks no discrepancy between the posted analysis and the recalculation.

The recalculation also reports d = -0.165. In general, a standardized mean difference expresses a contrast relative to a standard deviation, making the estimate dimensionless. Its value depends on the standardization method and does not replace the original-unit mean difference or its confidence interval. It should be read alongside the original scale and the study design, not as a stand-alone clinical interpretation.

What does the confidence interval add?

In general, a confidence interval gives a range of values compatible with the observed data under the assumptions of the calculation. The reported interval extends from -0.023 to 0.013 and includes zero. It therefore includes no difference as well as values in either direction. The interval is useful for seeing uncertainty that a point estimate alone does not convey. It does not guarantee that the true effect lies inside the interval, nor does it account for possible biases or unreported design features.

The registry reports several outcomes and analyses, but does not report a multiplicity adjustment or a detailed hierarchy of confirmatory and exploratory tests. In general, when many outcomes or comparisons are tested, the chance of at least one apparently notable result can increase unless the analysis plan accounts for the number of tests. The number of listed outcomes alone does not show which procedures were planned or applied. Those statistical-plan details are not reported in the registry record.

10. Confidence Intervals and Precision

The recalculated mean difference is -0.005, with a 95% confidence interval from -0.023 to 0.013. This interval is the main guide to the precision of the estimated contrast. It spans values below and above zero, so the posted result remains compatible with a lower mean under methylphenidate, little or no difference, or a higher mean under methylphenidate. The point estimate by itself does not distinguish among those possibilities.

In general, a confidence interval represents uncertainty about an estimate under the statistical method’s assumptions. A narrower interval indicates greater precision for the contrast being estimated; a wider interval indicates less precision. It does not account automatically for systematic bias, missing-data problems, or a mismatch between the calculation and the study design. Here, the registry does not report whether the listed analysis incorporated the crossover pairing, and the unadjusted recalculation is based on posted summary statistics rather than a reported paired covariance.

The sponsor’s reported test has p = 0.532, while the unadjusted recalculation has p = 0.584. Neither number describes the size of the effect or its practical meaning. The confidence interval gives more direct information about the range and direction of estimates compatible with the recalculation. The outcome scale is modularity, whose interpretation depends on context; therefore, numerical precision alone does not establish whether a difference is meaningful for brain organization or behavior.

11. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm, not total events. The illustration assumes a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. It considers effects set at 100%, 75%, and 50% of the observed effect. The original trial’s own design assumptions and sample-size justification are not reported in the registry record.

For planning around 100% of the observed effect, the figures are 576 participants per arm for 80% power and 770 participants per arm for 90% power. For 75% of the observed effect, they are 1,023 participants per arm for 80% power and 1,369 participants per arm for 90% power. For 50% of the observed effect, they are 2,301 participants per arm for 80% power and 3,080 participants per arm for 90% power.

In plain terms, 80% power describes a design that would have an 80% chance of detecting the specified effect under the stated assumptions; 90% power raises that target chance to 90%. The higher target generally calls for more participants for the same assumed effect. Smaller assumed effects also need more participants, as the planning figures illustrate. These values are planning illustrations based on the observed effect, not observed power and not evidence about the probability that the study’s finding is true.

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 = -0.005; pooled standard deviation σ = 0.030.
2. n = 2 × (1.96 + 0.842)² × 0.030² / -0.005² = 575.2, rounded up to 576 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 <- -0.005                      # observed difference in means
sigma <- 0.0302654919008431                     # 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(4349917)
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 = 576 (80% power), 770 (90% power)
 75% of observed effect: n per arm = 1,023 (80% power), 1,369 (90% power)
 50% of observed effect: n per arm = 2,301 (80% power), 3,080 (90% power)
power.t.test: 576.1 
Simulated power at n = 576 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. Analyses Reported by the Sponsor

The registry’s reported analysis is a two-sided t-test with p = 0.532. It does not include a posted estimate or confidence interval in that analysis entry. An unadjusted recalculation from the posted outcome summaries gives a mean difference of -0.005, a 95% confidence interval from -0.023 to 0.013, and p = 0.584. The registry marks no discrepancy between the analyses.

The recalculation is a simple summary-statistic comparison. The study is described as a crossover, but the registry does not give the within-participant covariance or sufficient detail to determine whether the listed sponsor test accounted for pairing, session order, or period effects. The recalculated test therefore should not be assumed to reproduce the sponsor’s analysis. If the record marked a discrepancy, the sponsor’s own analysis would take precedence; in this case, no discrepancy is marked. The two p-values are close in their broad interpretation, but neither alone establishes the magnitude, importance, or clinical meaning of a difference.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists seven outcome measures and 23 analyses, and names three secondary outcomes: Go/No-go commission rate, omission rate, and response-time variability. It does not report a multiplicity adjustment, a testing hierarchy, or which analyses were designated confirmatory versus exploratory. Without those details, the relationship between the many listed analyses and the primary result cannot be fully assessed. The count of analyses alone does not establish that any particular adjustment was required or omitted in the original analysis.

Missing-data handling is also not described in detail. The primary-outcome description excludes participants for excessive head motion, incomplete brain coverage, or poor-quality fMRI data. It gives thresholds of mean framewise displacement > 0.5mm or fewer than 150 timepoints remaining after scrubbing all timepoints with framewise displacement > 0.2mm. The population text then states that participants must have good data from both methylphenidate and, but ends before the criterion is complete. The record does not give a full account of exclusions, missing scans, or how incomplete paired measurements were handled.

The outcome summaries list 22 observations for each condition, while overall enrollment is 37. The record does not explain the difference between those counts or provide a participant flow for the primary outcome. It also does not state whether the analysis population was defined by intention to treat, per protocol, or another rule. These analysis-population details are not reported in the registry record.

Because this is a crossover study, the analysis may need to address the fact that each participant received both conditions. The registry does not describe how pairing, treatment order, or period effects were modeled. In general, these features can affect estimation and uncertainty in crossover analyses. The method used to address them is not reported in the registry record, so the posted summary does not allow an independent assessment of those modeling choices.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent non-serious adverse event terms

The registry reports serious adverse events for 35 participants at risk in the methylphenidate group and 36 at risk in the placebo group. No serious adverse events are reported for either condition, and deaths are reported as 0 in both groups. These are the registry’s serious-event figures; they do not by themselves establish that no adverse effects occurred.

The record separately lists other adverse events affecting 11 participants at risk in the methylphenidate group and 9 at risk in the placebo group. These are not serious adverse events and should not be combined with the serious-event counts. The registry does not provide event terms for the serious-event category because none are listed, and it does not give further detail about the nature, timing, or severity of the other events. The safety counts are descriptive registry entries and should be interpreted within the reported follow-up and participant counts.

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

The primary result describes a small observed difference in resting-state modularity between the methylphenidate and placebo conditions: the reported means are 0.223 and 0.228, respectively, and the recalculated difference is -0.005. The confidence interval, from -0.023 to 0.013, includes zero and allows values in either direction. The registry’s listed two-sided test has p = 0.532; the unadjusted recalculation has p = 0.584.

These numbers do not establish that the conditions differ, nor do they prove that the conditions are equivalent. A result that does not provide clear evidence of a difference can reflect a small underlying contrast, uncertainty, limitations in measurement, or other features of the analysis. The registry record does not report an equivalence margin or a non-inferiority framework, so the result should not be described as demonstrating equivalence.

Modularity describes network organization, not symptoms or cognitive performance directly. The registry notes that the interpretation of higher modularity depends on context: lower modularity may be preferable during complex tasks, while higher modularity may be preferable during basic, automatic tasks. The primary endpoint was measured at rest, so it does not directly show how network organization changes as cognitive demands shift. The broader hypotheses about changes in cognitive control and their relationship to behavior and symptoms cannot be resolved from this primary outcome alone.

The findings also do not establish whether methylphenidate improves or worsens ADHD symptoms or functioning. No medical conclusion should be drawn from the modularity comparison alone. The posted result is limited to the registered endpoint, the reported outcome counts, and the statistical information available in the registry record.

17. Why This Trial Matters Statistically

This study is statistically interesting because it combines a randomized, double-blind crossover design with a brain-imaging measure of network organization. In general, crossover designs can make within-person comparisons useful when participants can receive each condition, because each participant can serve as their own comparator. That advantage depends on appropriate analysis and adequate data from both conditions. The registry does not report enough detail to determine how the sponsor’s analysis handled pairing and session-related effects.

The endpoint also highlights why measurement interpretation matters. Modularity summarizes the degree of community structure in functional connectivity, but the registry explicitly describes its meaning as context-dependent. A larger value is not automatically better. The fact that the primary endpoint is a resting-state measurement also matters: it is related to the study’s broader interest in cognitive control, but it is not itself a direct measure of network flexibility while task demands change.

The reported difference and interval demonstrate the distinction between an estimate and the uncertainty around it. The mean difference is -0.005, while the interval ranges from -0.023 to 0.013. Reporting both helps readers avoid treating a point estimate or p-value as a complete account of the result. At the same time, the incomplete reporting of the crossover analysis, outcome exclusions, multiplicity procedures, and analysis populations limits how much can be concluded from the registry entry.

The study therefore offers a useful example of how design, measurement, analysis, and reporting jointly shape interpretation. The numerical result is only one part of that assessment; context and precision are essential.

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.

Several limitations are specific to the information recorded for this study. The primary endpoint is resting-state modularity, while the broader research question concerns adapting brain networks to changing cognitive control demands. A resting-state endpoint does not directly quantify that adaptation during task shifts. The registry also notes that the interpretation of higher modularity depends on context, so the direction of a numerical difference does not have a simple universally favorable meaning.

The crossover design makes within-participant analysis relevant, but the registry does not report whether the listed t-test accounted for pairing. It also does not state how treatment order or period effects were handled, or provide the within-participant covariance needed to assess a paired contrast from the posted summaries. This limits assessment of the analysis method from the registry entry alone.

The primary-outcome population description includes fMRI quality exclusions and ends mid-sentence after stating that participants must have good data from both methylphenidate. The record does not give a complete explanation of the eligibility text, the missing-data approach, or the full participant flow. Overall enrollment is 37, while the outcome summaries report 22 observations for each condition; the reason for that difference is not described.

The registry lists seven outcome measures and 23 analyses but does not report multiplicity procedures or a detailed statistical plan. It also does not report the original sample-size justification, the sponsor’s full effect estimate and confidence interval, or a complete description of analysis populations. These reporting gaps constrain interpretation; they do not, by themselves, show that the study or analysis was improperly conducted.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Large-scale Brain Organization During Cognitive Control in ADHD — NCT04349917.
• Registry record last updated 2021-01-12; status last verified 2020-04.
• Results first posted 2021-01-12.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT04349917 is a completed, phase 4 randomized, double-blind crossover study sponsored by the University of North Carolina, Chapel Hill. It enrolled 37 children with ADHD. Participants in the medication challenge received methylphenidate and placebo in separate sessions approximately one week apart, with randomized order.

The primary outcome was resting-state brain network modularity measured 1 to 3 hours after administration. The reported means were 0.223 for methylphenidate and 0.228 for placebo, with a recalculated mean difference of -0.005 and a 95% confidence interval from -0.023 to 0.013. The registry lists a two-sided t-test with p = 0.532; the unadjusted recalculation gives p = 0.584. The record does not provide full details of crossover analysis, missing-data handling, or multiplicity procedures.