Examining Tolerance to CNS Stimulants in ADHD: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Examining Tolerance to CNS Stimulants in ADHD (NCT02039908), a randomized phase 4 study. The primary outcome is Number of Dose Changes Required Per Protocol.

2. Clinical Question

3. Trial Design

The registry identifies this as a Phase 4, randomized, quadruple-masked, parallel-group trial of methylphenidate in ADHD. The recorded enrollment is 267. The study began in 2013-04, reached primary completion in 2018-05, and is marked completed. Florida International University is listed as the sponsor.

The Phase 2 comparison was between methylphenidate 7-day dosing and methylphenidate 5-day dosing. The arm descriptions specify 7-day medication dosing during the school year for one group and 5-day dosing with weekend holidays for the other. The primary outcome population is described as all participants who began Phase 2. The reported arm summaries include 124 participants in the 7-day group and 121 in the 5-day group for the primary outcome.

The registry also lists Phase 1 safety groups labeled Medication First and Placebo First, as well as Phase 2 safety groups labeled 7-Day Dosing and 5-Day Dosing. Those labels identify the safety summaries; the registry record does not provide enough detail to infer additional treatment sequencing or explain the relationship among all phases. The exact masking procedures and the original design assumptions are not reported in the registry record.

The central design contrast is the dosing schedule, while the primary outcome records dose increases over the Phase 2 assessment period. Randomization and masking are design features intended to limit bias, but the registry record does not describe how allocation was generated, how masking was maintained, or how adherence was assessed.

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: Because all participants were required to be enrolled in a Summer Treatment Program, some participants withdrew after consenting because they were unable to make the time commitment to the 8-week summer program.

Phase 1-Summer

Reasons for not completing this period:

Phase 2-School Year

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: All participants who began Phase 2 were included in 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 Number of Dose Changes Required Per Protocol, measured over 10 months.

The primary endpoint is the number of dose changes required per protocol, expressed as a mean with a standard deviation. The timeframe is 10 months. According to the registry description, monthly evaluations of medication efficacy were used to determine whether dose adjustments were needed because of anticipated tolerance effects. The reported analysis population consists of all participants who began Phase 2.

This measure is relevant to the study question because the rationale proposes that tolerance might lead to increases in medication dose over time. The endpoint records how many increases were required under the protocol; it does not directly measure tolerance as a biological process. A dose adjustment can reflect a clinical decision made in the study context, and the registry record does not report additional information that would identify the cause of each change.

The group means were 1.79 for 7-day dosing and 1.61 for 5-day dosing. The posted comparison expresses the 5-day group minus the 7-day group as a mean difference of -0.18. The endpoint is therefore a count-like measure summarized using means and standard deviations. Those summaries describe average dose-change burden and variation, but they do not show the distribution of individual participants’ dose changes.

7. Results Posted in the Registry

• Methylphenidate 5-day Dosing: mean 1.61 versus 1.79 on control; difference -0.18 (95% CI -0.46 to 0.10), standardized effect d = -0.16; z-test p = 0.209.

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.

Time to First Dose Increase

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Methylphenidate 5-day Dosing: mean 4.10 versus 3.80 on control; difference 0.30 (95% CI -0.56 to 1.16), standardized effect d = 0.09; z-test p = 0.496.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Methylphenidate 5-day Dosing and the control. The interval gives the range of effects that remain compatible with the data.

Endpoint Medication Dose

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Methylphenidate 5-day Dosing: mean 1.24 versus 1.30 on control; difference -0.06 (95% CI -0.17 to 0.05), standardized effect d = -0.14; z-test p = 0.284.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Methylphenidate 5-day Dosing and the control. The interval gives the range of effects that remain compatible with the data.

The secondary outcomes address two related aspects of dose adjustment: when the first increase occurred and the medication dose at the end of Phase 2. Together with the primary count of required increases, they describe timing and endpoint dose as well as the overall number of increases. These measures are related, but they are not interchangeable; a similar average number of changes does not automatically imply similar timing or endpoint dose.

The posted secondary estimates do not show a consistent large separation between the dosing schedules, and the confidence intervals for both comparisons include zero. This overall pattern is broadly in keeping with the primary result, which also has an interval that includes zero. The secondary findings do not, however, independently establish that the schedules are equivalent or that there is no meaningful difference.

The registry record lists no reported analyses for these secondary outcomes. The posted comparisons are unadjusted, and the record does not state whether multiple testing was considered or whether these outcomes were prespecified in a statistical analysis plan. When several outcomes are examined, the chance of observing an apparently notable result by chance can increase. General statistical explanation: adjustment procedures can address some multiplicity concerns, but the registry record does not report such a procedure.

For that reason, the secondary results carry less inferential weight than a clearly prespecified, fully reported analysis would. They are best treated as descriptive context for the primary dose-change result. Their pattern can inform questions for future research, but they should not be used to claim a confirmed schedule effect or a confirmed absence of one.

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

• Time to First Dose Increase
• Endpoint Medication Dose

9. Statistical Interpretation

10. Statistical Methods Explained

The primary endpoint is continuous in the registry’s statistical classification and is summarized by a mean and standard deviation. A mean describes the average number of dose increases in a group. A standard deviation describes how spread out participant-level values are around that group mean. It is not a confidence interval and does not directly express the precision of the mean difference.

What does the mean difference represent?

The comparison is oriented as 5-day dosing minus 7-day dosing. The group means are 1.61 and 1.79, respectively, and the posted difference is -0.18. A negative value therefore means the observed average was lower in the 5-day group. This is a difference between group averages, not a statement about the change experienced by every participant. Individual outcomes may vary substantially within each group.

How should the confidence interval be read?

A confidence interval describes the range of values reasonably compatible with the observed data under the statistical method used. For the primary comparison, the interval extends from -0.461 to 0.101. Since zero lies within that interval, the data do not give a precise estimate that rules out no mean difference. The interval also indicates that the estimated contrast is uncertain in both direction and magnitude. General statistical explanation: an interval is not a guarantee that the true value lies within its endpoints, and it does not by itself determine whether an effect matters clinically.

What does the p-value add?

The unadjusted p-value for the primary comparison is 0.209. A p-value describes how unusual data at least as incompatible with a specified null model would be if that model were correct, according to the test used. It is not the probability that the null hypothesis is true, nor is it a measure of effect size. The registry record does not report the test specification or any adjusted p-values. The p-value should be read alongside the estimate and confidence interval rather than as a stand-alone verdict.

Why can a mean and standard deviation be incomplete?

The endpoint counts dose increases, so its possible values are count-like even though the registry classifies the outcome as continuous and reports a mean and standard deviation. General statistical explanation: count outcomes can have asymmetric distributions, and participants’ values may be more variable than a simple model assumes. Over-dispersion means that observed variability exceeds what a model’s assumed distribution would predict; if present, it can affect standard errors and confidence intervals. The registry record does not report the outcome distribution, a check for over-dispersion, or a model that would allow these features to be assessed. This is a limitation in what can be inferred about the analysis, not evidence that the reported method was inappropriate.

The posted comparison is an unadjusted group comparison based on summary statistics. No covariate-adjusted model, repeated-measures model, or other analysis specification is reported in the registry record. Monthly assessments are described for dose decisions, but that description alone does not establish how the repeated measurements were handled statistically. The registry lists zero analyses and gives no reported analyses for the secondary outcomes. Consequently, the posted results support interpretation of the reported summaries, but they do not reveal the full analytic workflow.

Randomization is intended to make treatment groups comparable on average, while masking is intended to reduce the influence of treatment knowledge on behavior or assessment. Those design features do not remove all uncertainty, and they do not resolve missing-data concerns or guarantee that the analysis population matches the population initially enrolled. The registry record does not report allocation procedures, masking details, adherence, or the handling of participants with incomplete outcome data.

For the primary endpoint, the record identifies the analysis population as participants who began Phase 2. It does not state whether the analysis followed an intention-to-treat principle, how protocol deviations were handled, or whether any imputation was used. Those details matter because missing outcomes or exclusions can affect the comparability established by randomization. They cannot be inferred from the group summaries alone.

11. Confidence Intervals and Precision

The primary mean difference is -0.18, with a 95% confidence interval from -0.461 to 0.101. This interval crosses zero: values consistent with the posted data include a lower mean number of dose increases with 5-day dosing, no average difference, and a higher mean with 5-day dosing. The point estimate is therefore not precise enough to settle the direction of the average difference.

The interval also conveys uncertainty about magnitude. Its endpoints are not identical to the point estimate, and the estimate should not be described as a definitive measurement of the schedule effect. The reported standard deviations, 1.16 for 7-day dosing and 1.08 for 5-day dosing, show variation in participant outcomes around the group means. They do not replace the confidence interval for the comparison.

The registry record does not report a clinically important difference threshold. Statistical compatibility with zero therefore cannot be translated into a conclusion that any possible difference is unimportant. Likewise, the interval does not establish equivalence. That would require an explicit equivalence framework and a prespecified margin, neither of which is reported in the registry record.

Uncertainty also reflects the analysis details that are not reported, including the statistical test, missing-data handling, and any adjustment for multiple outcomes. The posted interval is useful for describing precision of the reported comparison, but it should be interpreted within those limits. The secondary comparisons also have confidence intervals that include zero, which is consistent with uncertainty rather than a precise separation between schedules.

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.

The planning figures are participants per arm, not total events. They are illustrations based on the observed effect rather than the original trial design. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. For each outcome, the effect to detect is set to the stated fraction of the observed effect. The original trial’s own design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the planned number of participants per arm under those assumptions for a design with an 80% probability of detecting the specified effect if that effect is the true one and the model assumptions hold. The 90% power column applies the same idea with a higher target probability, which requires more participants per arm under otherwise matching assumptions. These are planning quantities, not descriptions of the enrollment or analysis population.

Rows for smaller fractions of the observed effect require larger planned group sizes. This is the general relationship reflected in the figures: smaller differences are harder to distinguish from random variation, so more participants are generally needed to detect them at the same power and significance level. The display uses the observed estimate as a starting point, so the planning results depend on that estimate and on the stated statistical assumptions.

These figures are not observed power. They are hypothetical planning illustrations and do not tell whether the completed trial had an adequate design or whether its result is true. They should not be treated as a retrospective explanation of the primary finding. The original design rationale is not reported in the registry record.

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 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 = -0.180; pooled standard deviation σ = 1.121.
2. n = 2 × (1.96 + 0.842)² × 1.121² / -0.180² = 609.1, rounded up to 610 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 <- -0.18                      # observed difference in means
sigma <- 1.12120746199778                     # 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(2039908)
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 = 610 (80% power), 816 (90% power)
 75% of observed effect: n per arm = 1,083 (80% power), 1,450 (90% power)
 50% of observed effect: n per arm = 2,437 (80% power), 3,262 (90% power)
power.t.test: 610 
Simulated power at n = 610 per arm: 0.801 (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

The registry lists one primary outcome and two secondary outcomes. It reports no analyses for the secondary outcomes, and the registry record does not describe a multiplicity strategy. It is therefore not reported whether the investigators adjusted significance thresholds, used a hierarchical testing plan, or treated the secondary outcomes as exploratory. Unadjusted secondary p-values, where posted, should be interpreted cautiously because examining multiple outcomes can increase the chance of a nominally notable result.

The primary analysis population is described as all participants who began Phase 2. The record does not explain whether this population was defined before analysis, whether participants were excluded after beginning Phase 2, or whether the analysis followed an intention-to-treat principle. It also does not report how missing outcome values were handled, whether participants with incomplete follow-up were included, or whether imputation or sensitivity analyses were conducted.

These omissions matter because the target population and missing-data approach affect what a group comparison estimates. If availability of outcome data differs across groups or relates to the outcome, a complete-case summary may not represent the randomized groups in the same way. This is general statistical context; the registry record does not establish whether such a problem occurred in this trial.

The record does not report a statistical analysis plan, interim analyses, stopping rules, model diagnostics, or adjusted analyses. None should be inferred from the reported endpoint descriptions. Without these details, the posted summaries can be described and compared, but a full assessment of multiplicity control, missing-data bias, and adherence to a prespecified analysis cannot be made.

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 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: hospitalized (0.8%).

The registry reports serious adverse events separately for Phase 1 and Phase 2 groups. In Phase 1, the Medication First group had 1 serious adverse event among 129 at risk, and the Placebo First group had 0 among 138 at risk. In Phase 2, the 7-Day Dosing group had 1 among 121 at risk, and the 5-Day Dosing group had 1 among 124 at risk. Deaths were reported as 0 in each of these groups.

“Hospitalized” is the listed top serious-event term, reported as 0.8%. The registry record does not provide further detail in the posted term summary about event circumstances or whether the event was judged related to study medication. Counts of serious adverse events should not be interpreted as evidence of causation, and the group labels and at-risk denominators should be retained when reading them.

These safety figures are descriptive registry reports. The record does not provide a comparative statistical analysis of serious adverse events, and the counts alone cannot establish that one dosing schedule has a different safety profile. The absence of a reported death in these groups does not address other safety outcomes or establish overall safety.

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

The result answers a limited question: how the mean number of dose increases recorded over the 10-month primary assessment differed between the methylphenidate 7-day and 5-day schedules among participants who began Phase 2. The posted estimate is a mean difference of -0.18, with a 95% confidence interval from -0.461 to 0.101. The interval includes zero, and the unadjusted p-value is 0.209. The data do not provide a statistically clear separation between group means.

This does not establish that the schedules have identical effects. The interval remains compatible with differences in either direction, and the registry record does not provide an equivalence margin or a prespecified threshold for clinical importance. Nor does the result establish that tolerance did or did not occur. The endpoint counts dose increases required under the protocol; it is not a direct biological measure of tolerance, and the cause of individual dose changes is not reported.

The findings are also not a direct test of long-term academic performance or the long-term course of ADHD, even though those topics appear in the study rationale. The primary timeframe is 10 months, and the registered primary outcome is dose changes. The secondary outcomes extend the description to first dose increase and endpoint dose, but their unadjusted nature and absent analysis details limit the strength of conclusions from them.

In short, the posted data describe average dose outcomes in the registered groups and show uncertainty around the estimated differences. They do not establish benefit, lack of benefit, equivalence, or a causal mechanism beyond the randomized comparison of the dosing schedules as reported. Any broader interpretation would require information and outcomes not reported in the registry record.

17. Why This Trial Matters Statistically

This trial raises a statistical question about how a dosing schedule is evaluated when the proposed process—tolerance—is not measured directly. The primary endpoint uses dose increases as an observable indicator related to the study rationale. Statistical interpretation must keep that distinction clear: a difference in recorded adjustments would describe the endpoint, not necessarily identify the underlying mechanism.

The primary comparison also illustrates why estimates and confidence intervals matter more than a binary reading of a p-value. The point estimate favors fewer mean increases in the 5-day group, but the interval includes zero and extends in both directions. The result is not a precise demonstration of a schedule difference, and it is not evidence that the schedules are equivalent. Presenting both magnitude and uncertainty helps keep conclusions proportionate to the data.

The secondary outcomes are useful because timing and endpoint dose can complement a count of dose increases. At the same time, multiple outcomes require clarity about prespecification and multiplicity. The registry record does not report those analytic details, so the additional comparisons are informative descriptively but should not be treated as separate confirmatory evidence.

Finally, this record shows the importance of transparent reporting. Population definitions, missing-data handling, analysis plans, and design assumptions affect how confidently readers can interpret results. When these details are not reported in the registry record, careful readers can still describe the observed estimates, but should avoid extending them beyond the registered endpoints and follow-up.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record does not report a detailed statistical analysis plan, the original sample-size justification, allocation procedures, or how masking was implemented. It also does not report how adherence to the dosing schedules was assessed. These omissions limit assessment of the design and its execution beyond the listed randomized, quadruple-masked, parallel-group features.

The primary analysis population is described as participants who began Phase 2, but the record does not explain how this population relates to all randomized participants or how missing data and protocol deviations were handled. The analysis sample sizes differ from the overall recorded enrollment, and the registry does not provide a participant-flow account that would explain the transitions among enrollment, phases, and endpoint analyses. No total or cause of missing outcomes should be inferred from the posted summaries.

The primary outcome is a count-like measure summarized using means and standard deviations. The record does not report participant-level distributions or diagnostics that would show whether the summaries capture the outcome well. It also does not explain the decision rules used to determine that a dose increase was required, beyond the description of monthly efficacy evaluations.

The reported primary period is 10 months, and the secondary endpoint dose is reported at the end of the Phase 2 school year. The registry record does not provide a longer-term follow-up result for these outcomes. The trial’s registered dose measures therefore do not directly resolve questions about long-term academic outcomes or the long-term course of ADHD discussed in the rationale. These limits constrain interpretation of what the trial can establish, without implying that the observed analysis is invalid.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Examining Tolerance to CNS Stimulants in ADHD — NCT02039908.
• Registry record last updated 2020-06-09; status last verified 2020-05.
• Results first posted 2019-09-17.
• 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

NCT02039908 is a completed Phase 4 randomized, quadruple-masked, parallel-group study sponsored by Florida International University. It compared methylphenidate on a 7-day dosing schedule with a 5-day schedule that included weekend holidays during the school year. Recorded enrollment was 267.

The primary outcome was the number of dose increases required over 10 months among participants who began Phase 2. The mean difference for 5-day versus 7-day dosing was -0.18, with a 95% confidence interval from -0.461 to 0.101 and an unadjusted p-value of 0.209. The interval includes zero, so the posted comparison does not establish a clear difference between group means.

Secondary outcomes were time to first dose increase and endpoint medication dose. Their posted comparisons are unadjusted, and no secondary analyses are reported in the registry record. The record does not provide the original design assumptions, a full analysis plan, or details of missing-data handling.