Treating Parents With ADHD and Their Young Children Via Telehealth: A Hybrid Type I Effectiveness-Implementation Trial: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Treating Parents With ADHD and Their Young Children Via Telehealth: A Hybrid Type I Effectiveness-Implementation Trial (NCT04240756), a randomized phase 3 study. The primary outcome is Change in Child Impairment.

2. Clinical Question

The clinical question is whether adding stimulant medication for a parent with ADHD to a child-focused treatment strategy is associated with a different child impairment score than the child-focused strategy alone. The registry describes a randomized, parallel-group trial and identifies child impairment as the primary outcome. The posted comparison reports mean CGI scores for the two groups at the week-16 outcome assessment.

3. Trial Design

The registry describes a Phase 3, randomized, single-masked, parallel-group trial with 269 enrolled participants. It is listed as completed. The study start date is 2020-08-06 and the primary completion date is 2025-05-30. The sponsor is the University of Maryland, College Park. The study concerns ADHD and parenting, and its stated aim includes both evaluating a family treatment approach and assessing how telehealth delivery could be implemented in pediatric primary care settings.

One arm combined parent stimulant medication with a child treatment strategy. The other arm used the child treatment strategy without stimulant medication for the parent before behavioral parent training. In both arms, the child strategy included behavioral parent training and a recommendation to the child’s primary care provider for child stimulant medication if the child remained impaired. The registry lists behavioral parent training as a behavioral intervention and extended release mixed amphetamine salts as the drug intervention.

Randomization and parallel-group assignment support a comparison between the assigned strategies, but details such as the allocation procedure and the identity of the masked parties are not reported in the registry record. The total enrollment is 269, while the posted observed week-16 CGI summaries include 60 participants in each arm. The registry says that differences between randomized and analyzed counts arise from loss to follow-up or missing week-16 outcome data. It also says the primary analyses used an intent-to-treat approach with multiple imputation. The original design assumptions, including any planned sample-size justification or interim analyses, 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: Parents were randomized to treatment conditions. Children were enrolled as part of parent-child dyads. Stakeholders and providers participated in baseline assessments and were not assigned to treatment arms.

Week 16 Follow-Up

Week 36 Follow-Up

Baseline

Analysis population for the primary outcome, as defined in the registry: The number analyzed reflects participants with observed child CGI-S data at week 16. Differences from the number randomized in each arm are due to loss to follow-up or missing week-16 outcome data. Primary analyses were conducted using an intent-to-treat approach with multiple imputation.

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.

Population: Participant Flow includes all enrolled participants. Baseline characteristics are reported only for the participant groups for whom each characteristic was collected; measures not collected for a given participant group are reported as not applicable.

6. Primary Endpoint

The registry lists the primary outcome as Change in Child Impairment, measured over Up to 16 weeks post-randomization.

The primary endpoint is registered as change in child impairment, measured with the Clinical Global Impressions—Severity scale. The scale ranges from 1 to 7, and higher scores indicate worse outcomes. The outcome was collected for enrolled parent-child dyads, not for community stakeholders or providers. Its timeframe is up to 16 weeks after randomization, and the registry’s description of the analyzed count refers specifically to observed child CGI-S data at week 16.

A continuous severity score preserves more information about the level of impairment than a simple classification into broad categories. Comparing group means can describe average score differences, while the standard deviation describes how spread out scores are within a group. These are general statistical interpretations of continuous outcomes, not details of an unreported analysis plan.

The registered outcome title refers to change, but baseline CGI values and the precise calculation of change are not reported in the registry record. The posted arm summaries are means and standard deviations, with no separate baseline values or explicit change-score formula. They therefore describe the posted scores and their between-group comparison; they do not allow a reader to reconstruct individual changes or verify how change was calculated. The distinction matters because a follow-up score and a change from baseline are not interchangeable summaries.

7. Results Posted in the Registry

• Child Treatment Strategy: mean 4.04 versus 3.78 on control; difference 0.26 (95% CI -0.04 to 0.56), standardized effect d = 0.31; z-test p = 0.093.

8. Statistical Interpretation

9. Statistical Methods Explained

The outcome is continuous, and the registry identifies the arm summaries as means with standard deviations. A mean describes the average score in a group. A standard deviation describes the spread of individual scores around that group’s mean. These statistics answer different questions: the mean locates the group average, while the standard deviation conveys how variable participants’ scores are. Neither one alone describes the full score distribution.

What does the mean difference represent?

The posted comparison is a mean difference between the child-strategy-only arm and the parent-stimulant-plus-child-strategy arm. Its direction depends on that ordering. A positive value means the first arm’s mean is higher than the second arm’s mean. Because higher CGI scores indicate worse outcomes, the direction of this score difference can be described in relation to the scale. It remains a comparison of group averages, not a statement about every participant’s experience.

The value 0.26 is an unadjusted recalculation from the posted arm summaries. The corresponding p-value, 0.093, is also unadjusted. The registry does not post an analysis model or an adjusted estimate, and it lists zero analyses. It does say that primary analyses used an intent-to-treat approach with multiple imputation. The details of the model, covariates, handling of repeated measurements, and imputation procedure are not reported in the registry record. It would therefore be inappropriate to assign the recalculated comparison to a particular statistical test or model.

How should the p-value be understood?

In general, a p-value describes how compatible the observed data are with a specified null hypothesis under the assumptions of a statistical model. It is not the probability that the null hypothesis is true, nor does it quantify the size or practical importance of a difference. Here, the posted p-value is unadjusted and comes from a summary-statistic recalculation. The registry does not report the test’s full assumptions or a prespecified decision threshold for this comparison. The p-value should be considered alongside the estimated difference, its confidence interval, the outcome scale, and the missing-data context.

What does a confidence interval add?

In general, a confidence interval gives a range of estimates compatible with the data and the method used to construct the interval. Its width conveys precision: a narrower interval indicates less uncertainty under that method, while a wider one indicates more. The posted interval for the mean difference crosses zero, so it includes both a difference in one direction and a difference in the other direction. Its exact confidence level is not reported in the registry record. The interval is not a range containing a known fixed proportion of individual participant scores; it concerns the estimated group difference.

Why do the standard deviations matter?

For a continuous outcome, the amount of variation within groups affects how precisely a group difference can be estimated. When scores vary more widely, it is generally harder to estimate a mean difference with the same precision and sample size. This is a general statistical principle. The posted standard deviations are 0.793 and 0.898 for the two arms. The trial record does not report the distribution of scores or diagnostic checks, so no conclusion about the shape of the outcome distribution should be inferred from these summaries alone.

What is the role of intent-to-treat analysis?

In general, an intent-to-treat approach aims to analyze participants according to their randomized assignment, preserving the comparison created by randomization. The registry says the primary analyses used this approach with multiple imputation. Multiple imputation is a general method for addressing missing outcome data by using observed information to create plausible values for missing observations and reflecting uncertainty across those imputations. The method depends on assumptions about the missingness process and the imputation model. Those assumptions, the variables used, and the imputed estimates are not reported in the registry record.

The arm means shown for the observed week-16 outcome are based on 60 participants in each arm. The registry explains that these observed counts reflect available week-16 CGI-S data and can differ from the number randomized because of loss to follow-up or missing outcome data. Observed-case summaries and an intent-to-treat analysis using imputation are not necessarily identical estimands or calculations. Without the imputed results and analysis specification, the relationship between them cannot be assessed fully.

What can and cannot be inferred from these methods?

Randomized assignment is a design feature intended to support a fair comparison of assigned strategies. It does not remove uncertainty from sampling variation, missing outcomes, implementation differences, or limitations in reporting. The registry identifies the study as single-masked, but which people were masked is not reported in the registry record. The posted information does not describe a multiplicity strategy for the several outcomes named in the study summary, nor does it report prespecified subgroup analyses or sensitivity analyses. These absences should not be filled in by assuming a conventional analysis plan.

Overall, the available summary statistics support a transparent descriptive comparison, and a simple unadjusted recalculation can quantify that comparison. They do not reproduce the stated primary analysis because the imputed analysis results and its full methods are not reported. For readers, keeping the observed summaries, recalculated inference, and registry-described primary analysis distinct is essential to understanding what each statistic can support.

10. Confidence Intervals and Precision

The posted mean difference is 0.26 points, comparing the child-strategy-only arm with the parent-stimulant-plus-child-strategy arm. Its confidence interval extends from a value below zero to a value above zero. This means the interval includes no difference as well as estimates pointing in either direction. The exact confidence level is not reported in the registry record, so the interval should be described without assuming a particular confidence percentage.

Precision concerns how narrowly the difference is estimated, not whether a result is important or whether a strategy is effective. In general, an interval’s width reflects uncertainty under the method used to calculate it. Here, the interval allows a range of possible differences rather than identifying one value with certainty. The unadjusted p-value is 0.093, but it does not replace the interval: the p-value and interval convey related but distinct information.

The means and interval are based on an unadjusted recalculation from posted summary statistics, while the registry says the primary analysis used intent-to-treat methods with multiple imputation. That analysis’s estimate and interval are not reported in the registry record. The observed outcome counts are 60 per arm, and missing week-16 data or loss to follow-up account for differences from the number randomized. The registry does not report sensitivity analyses that would show how the estimate changes under alternative assumptions about missing data. Consequently, the apparent precision of the observed-summary comparison should not be mistaken for a complete assessment of uncertainty in the stated primary analysis.

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 participants across both arms and not total events. They illustrate the sample size that a hypothetical study would require under the stated planning assumptions; they are not a reconstruction of the trial’s original design rationale. The original design assumptions and sample-size justification are not reported in the registry record.

The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set at the stated fraction of the observed effect. For planning for 100% of the observed effect, the estimates are 167 participants per arm for 80% power and 224 participants per arm for 90% power. For planning for 75% of the observed effect, the estimates are 297 participants per arm for 80% power and 397 participants per arm for 90% power. For planning for 50% of the observed effect, the estimates are 667 participants per arm for 80% power and 893 participants per arm for 90% power.

In plain terms, the 80% power column gives the planned number per arm for a hypothetical study to have an 80% chance of detecting the specified effect under the assumptions, if that effect and the assumptions are correct. The 90% power column describes the corresponding planning target for a 90% chance. These are prospective planning illustrations, not observed power for the completed trial.

Smaller effects are harder to distinguish from random variation, so detecting them generally requires more participants. That pattern is reflected in the increasing planning estimates as the assumed effect fraction becomes smaller. The curve represents the same planning relationship across effect sizes; it should be read as a design aid under the stated assumptions, not as evidence about the trial’s observed outcome or the certainty of its results.

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 = 0.260; pooled standard deviation σ = 0.847.
2. n = 2 × (1.96 + 0.842)² × 0.847² / 0.260² = 166.6, rounded up to 167 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 <- 0.26                      # observed difference in means
sigma <- 0.847128384602948                     # 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(4240756)
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 = 167 (80% power), 224 (90% power)
 75% of observed effect: n per arm = 297 (80% power), 397 (90% power)
 50% of observed effect: n per arm = 667 (80% power), 893 (90% power)
power.t.test: 167.6 
Simulated power at n = 167 per arm: 0.803 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Multiplicity, Missing Data and Analysis Populations

The study summary names multiple outcomes: child impairment as the primary outcome, child ADHD and externalizing symptoms, time to child stimulant prescription, parental ADHD impairment and symptoms, parenting, and behavioral parent training engagement. The registry reports one outcome measure and zero analyses, and no secondary outcome results are posted. A multiplicity plan specifying how inference across multiple outcomes would be handled is not reported in the registry record. It is therefore not possible to determine whether or how the trial controlled the chance of false-positive findings across a family of tests.

The primary outcome description states that the primary analyses used an intent-to-treat approach with multiple imputation. It also says the reported number analyzed reflects participants with observed child CGI-S data at week 16 and that differences from the number randomized in each arm arise from loss to follow-up or missing week-16 outcome data. This distinction is important: the observed summaries use available outcome information, while the stated primary analysis used a missing-data procedure. The imputation model, assumptions, number of imputations, and analysis estimates are not reported in the registry record.

In general, missing-data methods rely on assumptions about why outcomes are missing and how observed participant information relates to unobserved outcomes. Multiple imputation can account for uncertainty from filling in missing values when its model and assumptions are appropriate, but the name of the method alone does not show whether those assumptions hold. The registry does not report sensitivity analyses exploring alternative missing-data assumptions.

The record describes the primary analysis as intent-to-treat, which generally means retaining participants in their assigned groups for analysis. However, the detailed analysis population, treatment of deviations from assigned strategies, and any additional analysis populations are not reported in the registry record. The posted outcome means should not be presumed to equal the results of the imputed intent-to-treat analysis. These reporting gaps limit assessment of how missingness and multiple outcomes affect the overall interpretation.

14. 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 non-serious adverse event terms

The registry reports serious adverse events for 60 participants at risk in each arm. No serious adverse events were reported in either arm, and deaths were 0 in both. These are counts as recorded; they do not establish that no adverse events of any kind occurred.

For other adverse events, 44 participants were recorded as affected in the parent-stimulant-plus-child-strategy arm, while 0 were recorded as affected in the child-strategy-only arm. The registry does not provide the event terms, severity details, or further information about how these other events were collected. The serious adverse event terms list is empty. The observation period and any rules for event attribution are not reported in the registry record.

These counts should be read as descriptive safety reporting, not as a complete comparison of risk. They do not show the kinds of events, their timing, duration, or clinical context. Zero reported serious events is not proof that an event could never occur, and the difference in other-event counts alone does not establish a causal explanation. The registry record does not provide enough detail to interpret the contrast beyond the reported counts.

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

The posted outcome data show a mean CGI score of 3.78 in the arm receiving parent stimulant medication plus the child treatment strategy and 4.04 in the arm receiving the child strategy alone. The unadjusted mean difference is 0.26 points, with the child-strategy-only arm higher in the stated comparison. Since higher scores indicate worse outcomes, this describes the direction of the observed group averages. It is not a conclusion about every child or a complete estimate from the stated imputed primary analysis.

The confidence interval crosses zero, and the unadjusted p-value is 0.093. Those statistics indicate uncertainty around the recalculated difference; they do not demonstrate equivalence, nor do they establish that one strategy is better. A finding that an estimate is uncertain is different from evidence that two strategies have identical outcomes. The registry does not report a threshold for a clinically important difference, so the practical importance of the point estimate cannot be determined from the posted information alone.

The registry describes a primary intent-to-treat analysis with multiple imputation, but its results and full analytic details are not reported. The available observed summaries include 60 participants per arm, and the record attributes differences from randomized counts to loss to follow-up or missing week-16 outcome data. The distinction between observed summaries and imputed primary analyses limits how far the recalculated comparison can stand in for the trial’s intended analysis.

The registered study also concerns child symptoms and treatment timing, as well as parent outcomes and implementation of telehealth care. Results for those secondary questions are not posted. The findings therefore address only the posted child CGI outcome and do not establish effects on other outcomes, implementation, or longer-term results. They also should not be generalized beyond the population and follow-up information documented in the registry.

16. Why This Trial Matters Statistically

This trial raises a statistical question that is relevant to both clinical researchers and biostatisticians: how to interpret a group comparison when the registered primary analysis and the posted observed summaries are not accompanied by the same level of detail. The registry gives arm means and standard deviations and describes an intent-to-treat analysis using multiple imputation, but does not report the imputed estimate or full analysis specification. Separating those sources of information helps prevent a simple recalculation from being mistaken for the primary analysis.

The endpoint is a continuous severity score, and the direction of its scale matters: higher CGI scores indicate worse outcomes. Reporting the mean difference alongside its interval allows readers to consider both the direction and the uncertainty of the group comparison. The interval crosses zero, illustrating why a point estimate alone is insufficient and why a p-value should not be treated as a measure of effect size or importance.

Missing outcome data are also central to interpretation. The registry identifies observed week-16 counts and explains that loss to follow-up or missing data can reduce those counts, while stating that multiple imputation was used for the primary analyses. This makes transparent reporting of the imputation approach and sensitivity analyses important for assessing whether conclusions depend on assumptions about missingness. Those details are not reported in the registry record.

Finally, the trial’s stated scope spans child outcomes, parent outcomes, and implementation questions, but no secondary results are posted. That gap illustrates the value of distinguishing a registered study question from outcomes for which results are available. Statistical interpretation should remain tied to the outcome, time frame, analysis, and precision that are actually documented.

17. Limitations

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

The posted primary outcome information has important limits. The registry labels the endpoint as change in child impairment, but does not report baseline CGI scores or the exact calculation used to define change. The arm summaries are means and standard deviations for the week-16 outcome; without baseline details, readers cannot independently reconstruct or verify a change score.

The registry reports 60 participants per arm with observed child CGI-S data at week 16, and explains that differences from the number randomized in each arm are due to loss to follow-up or missing outcome data. It states that primary analyses used intent-to-treat methods with multiple imputation, but does not report the imputed estimates, model specification, missingness assumptions, or sensitivity analyses. The unadjusted summary-statistic recalculation is therefore not a replacement for the stated primary analysis.

The record lists one outcome measure and zero analyses, and does not post results for the secondary outcomes named in the study summary. Details of multiplicity handling are not reported. The confidence level for the reported interval, the statistical test underlying the posted unadjusted p-value, and any prespecified threshold for a meaningful difference are also not reported in the registry record.

The trial is described as single-masked, but the masked parties are not identified. Allocation details, eligibility criteria beyond the study’s general population description, and the original sample-size justification are not reported. The follow-up timeframe for the primary outcome is up to 16 weeks after randomization; longer-term outcome results are not reported. Safety reporting does not include other-event terms or details on collection and attribution. These gaps constrain interpretation of the result and its applicability.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Treating Parents With ADHD and Their Young Children Via Telehealth: A Hybrid Type I Effectiveness-Implementation Trial — NCT04240756.
• Registry record last updated 2026-09-16; status last verified 2026-08.
• Results first posted 2026-09-16.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

NCT04240756 is a completed, randomized, single-masked, parallel-group Phase 3 trial sponsored by the University of Maryland, College Park. It enrolled 269 participants and compared parent stimulant medication plus a child treatment strategy with the child treatment strategy alone. The primary outcome was change in child impairment measured by CGI severity scores up to 16 weeks after randomization.

The observed week-16 summaries report mean scores of 3.78 and 4.04, with 60 participants in each arm. The unadjusted recalculated mean difference is 0.26, and its confidence interval crosses zero. The registry says primary analyses used an intent-to-treat approach with multiple imputation, but those analysis estimates and details are not reported. No secondary results are posted. Serious adverse events and deaths were reported as 0 in both arms; other adverse events affected 44 participants in the parent-stimulant arm and 0 in the comparison arm.