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ADHD Phase 3 Continuous Endpoint NCT03247517

Evaluation of SPN-812 (Viloxazine Extended-release Capsule) Low Dose in Adolescents With ADHD: Complete Statistical Analysis

This randomized, placebo-controlled trial evaluated 200mg and 400mg SPN-812 in adolescents with ADHD. The primary outcome was change in ADHD-RS-5 total score from baseline to Week 6, with sponsor-reported analyses showing lower change scores in both dose groups than in the placebo group.

Trial start: 2017-11-02  ·  Enrollment: 310  ·  Sponsor: Supernus Pharmaceuticals, Inc.
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 Evaluation of SPN-812 (Viloxazine Extended-release Capsule) Low Dose in Adolescents With ADHD (NCT03247517), a randomized phase 3 study. The primary outcome is Efficacy of SPN-812 Assessed by Attention-Deficit/Hyperactivity Disorder Rating Scale, 5th Edition (ADHD-RS-5).

310
Enrollment
Phase 3
3
Arms
In the primary outcome
-4.60
Mean difference
200mg SPN-812
-8.51–-0.69
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03247517
PhasePhase 3
ConditionADHD
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment310
Arms in the primary outcome3
Lead sponsorSupernus Pharmaceuticals, Inc.
Results postedYes

2. Clinical Question

Population

Adolescents 12-17 years of age with ADHD were the intended study population. The primary endpoint analysis used an Intent-to-Treat (ITT) population defined as randomized participants who took at least one dose of study medication and had a baseline and at least one post-baseline ADHD-RS-5 assessment.

Intervention

The two active regimens were 200mg SPN-812 and 400mg SPN-812, each described as an oral capsule taken once daily. The registry record identifies SPN-812 as viloxazine extended-release capsule.

Comparator

The comparator was an oral placebo capsule taken once daily. The trial used three parallel groups: placebo, 200mg SPN-812, and 400mg SPN-812.

Primary question

The main question was whether the change from baseline in ADHD-RS-5 total score at Week 6 differed between each SPN-812 group and placebo. The scale assesses ADHD symptomatology; a lower change-from-baseline score, meaning a more negative value, was defined as a better outcome.

The ADHD-RS-5 is a symptom rating measure, not a direct measure of every aspect of functioning or experience. The registry also lists secondary assessments covering clinician-rated improvement, parent and self-reported symptoms, functional impairment, parental stress, and responder status. Those measures broaden the types of outcomes considered, but the primary question is specifically about symptom-score change over the trial's stated six-week period. The registry record does not report the planned sample-size justification or further details about the trial's original statistical design assumptions.

3. Trial Design

This was a completed Phase 3 randomized trial with a parallel-group design and quadruple masking, according to the registry record. Participants were assigned to placebo, 200mg SPN-812, or 400mg SPN-812. Each intervention was described as an oral capsule taken once daily. The registry lists enrollment of 310 participants. The number contributing to the primary endpoint summaries differs by group: 104 for placebo, 94 for 200mg SPN-812, and 103 for 400mg SPN-812. These endpoint counts should not be confused with the overall enrollment figure.

The study began on 2017-11-02, reached primary completion on 2018-10-17, and is recorded as completed. The primary endpoint assessed change from baseline in ADHD-RS-5 total score at Week 6, the stated end of study. The registry defines the ITT population for this endpoint as participants who were randomized, took at least one dose of study medication, had a baseline ADHD-RS-5 assessment, and had at least one post-baseline assessment.

The study title describes it as double-blind, placebo-controlled, and pivotal, while the registry's masking field specifies quadruple masking. Both descriptions are retained as recorded; the registry record does not explain the masking terminology further. It also does not report details such as the method of sequence generation, concealment procedures, stratification factors, adherence rules, or the trial's planned sample-size justification. Those details should not be inferred from the randomized designation or the observed enrollment.

The registry lists nine outcome measures and identifies eight secondary outcomes. Reported secondary assessments include clinician-rated improvement and parent- or self-reported measures. The record describes results at Week 6 for some measures and baseline-to-Week-6 change for others. Those outcome-specific definitions matter when interpreting results: the measures do not all represent the same construct or use the same score scale.

4. Participant Flow and Accounting

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

Overall Study

StagePlacebo200mg SPN-812400mg SPN-812
STARTED10498106
COMPLETED967892
NOT COMPLETED82014

Reasons for not completing this period:

ReasonPlacebo200mg SPN-812400mg SPN-812
Adverse Event042
Lost to Follow-up264
Consent withdrawn by caregiver147
Assent/consent withdrawn by subject231
Protocol Violation020
Multiple reasons310

Analysis population for the primary outcome, as defined in the registry: Intent-to-Treat (ITT) Population: The ITT population includes subjects who were randomized, took at least one dose of study medication, have a baseline Attention-Deficit/Hyperactivity Disorder Rating Scale, 5th Edition (ADHD-RS-5) assessment and have at least one post-baseline ADHD-RS-5 assessment.

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: Intent-to-Treat (ITT) Population: The ITT population includes subjects who were randomized, took at least one dose of study medication, have a baseline Attention-Deficit/Hyperactivity Disorder Rating Scale, 5th Edition (ADHD-RS-5) assessment and have at least one post-baseline ADHD-RS-5 assessment.

CharacteristicUnitPlacebo200mg SPN-812400mg SPN-812Total
Participants analysed10494103301
Age, Continuousyears13.8 (SD 1.60)13.9 (SD 1.48)14.0 (SD 1.59)13.9 (SD 1.56)
Age, Customized: 12 to 14 yearsParticipants706364197
Age, Customized: 15 to 17 yearsParticipants343139104
Sex: Female, Male: FemaleParticipants462836110
Sex: Female, Male: MaleParticipants586667191
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants30273289
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants746771212
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants0000
Race (NIH/OMB): American Indian or Alaska NativeParticipants0123
Race (NIH/OMB): AsianParticipants0112
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0000
Race (NIH/OMB): Black or African AmericanParticipants393742118
Race (NIH/OMB): WhiteParticipants635355171
Race (NIH/OMB): More than one raceParticipants2237
Race (NIH/OMB): Unknown or Not ReportedParticipants0000
Region of Enrollment: United Statesparticipants10494103301
ADHD-RS-5 Total Scoreunits on a scale40.5 (SD 6.79)39.9 (SD 7.22)39.4 (SD 7.59)39.9 (SD 7.20)
ADHD-RS-5 Inattentionunits on a scale22.4 (SD 3.67)22.2 (SD 3.66)21.5 (SD 3.60)22.0 (SD 3.65)
ADHD-RS-5 Hyperactivity/Impulsivityunits on a scale18.1 (SD 5.35)17.7 (SD 5.71)17.9 (SD 5.64)17.9 (SD 5.55)

6. Primary Endpoint

The registry lists the primary outcome as Efficacy of SPN-812 Assessed by Attention-Deficit/Hyperactivity Disorder Rating Scale, 5th Edition (ADHD-RS-5), measured over Baseline and Week 6 (End of Study).

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

The primary endpoint was change from baseline in ADHD-RS-5 total score at Week 6, the end of study. ADHD-RS-5 is an ADHD-specific rating scale designed and validated to assess current ADHD symptomatology. It contains 18 items corresponding to the 18 DSM-5 symptoms of ADHD. Each item is rated on a four-point scale from 0, meaning never or rarely, to 3, meaning very often. The total is calculated by adding the item responses; the registry gives the possible total-score range as 0-54, with higher scores indicating more severe symptoms.

Change from baseline focuses the comparison on how scores shifted during the study rather than only on the score at the final assessment. The registry defines lower change scores, below 0, as a better outcome. In the posted primary results, all three group means are negative, indicating decreases from baseline on average. The relevant comparison is not simply whether each group changed, but whether the change differed between each active-treatment group and placebo.

A symptom rating scale provides a structured way to assess a target clinical domain consistently across participants and trial groups. It does not, by itself, establish how every individual participant changed, nor does it encompass every possible effect on functioning or quality of life. The registry's other outcome measures address some additional domains, but they do not replace the prespecified role of the primary endpoint. The record does not report additional details about the scale's administration, assessor training, or the clinical threshold for a meaningful individual change.

7. Results Posted in the Registry

Mean difference: 200mg SPN-812

-4.60

95% CI: -8.51 to -0.69

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-20.3-17.7-15.2-12.7-10.2-7.7Placebo (n=104)200mg SPN-812 (n=94)400mg SPN-812 (n=103)units on a scale (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)200mg SPN-812400mg SPN-812-9.62-7.56-5.49-3.42-1.350.71mean 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
Effect of SPN-812 Assessed by Clinical Global Impression-Improvement (CGI-I) ScaleContinuous EndpointMean difference-0.50 (-0.82 to -0.18)82 per arm
Effect of SPN-812 Assessed by Conners 3rd Edition - Parent Short Form (C3-PS)Continuous EndpointMean difference-0.70 (-3.70 to 2.30)3,687 per arm
Effect of SPN-812 Assessed by Weiss Functional Impairment Rating Scale-Parent Report (WFIRS-P)Continuous EndpointMean difference-0.08 (-0.20 to 0.04)447 per arm

Effect of SPN-812 Assessed by Clinical Global Impression-Improvement (CGI-I) Scale

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)200mg SPN-812400mg SPN-812-0.99-0.78-0.57-0.35-0.140.07mean difference vs control (95% CI)

Effect of SPN-812 Assessed by Conners 3rd Edition - Parent Short Form (C3-PS)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)200mg SPN-812400mg SPN-812-6.47-4.59-2.71-0.821.062.95mean difference vs control (95% CI)

Effect of SPN-812 Assessed by Weiss Functional Impairment Rating Scale-Parent Report (WFIRS-P)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)200mg SPN-812400mg SPN-812-0.26-0.19-0.13-0.07-0.000.06mean difference vs control (95% CI)

The secondary outcomes extend beyond the primary ADHD-RS-5 total score to clinician-rated improvement, parent- and self-reported measures, functional impairment, parental stress, symptom subscales, and responder status. This range provides context across several assessment types, but each measure has its own scale, meaning, and analysis. A secondary outcome should not be treated as if it were another version of the primary endpoint.

Across the posted secondary results, evidence is not uniform. Some active-versus-placebo comparisons have confidence intervals that include or touch zero, while some other reported comparisons have intervals that do not include zero. The overall pattern therefore adds context but does not establish a consistent difference across every secondary measure. These results should be interpreted in relation to their endpoint definitions and analysis methods, rather than combined into a single generalized claim.

The primary endpoint remains the central confirmatory question identified by the registry. Secondary measures can help show whether the primary result is accompanied by patterns in other domains, but their statistical weight depends on how they were planned and analyzed. When many outcomes and comparisons are tested, the chance of at least one apparently notable result can increase. Adjustments for multiple testing can address that concern, but the registry record does not report whether adjustments were used for the secondary analyses.

For this reason, unadjusted secondary p-values carry less weight as stand-alone evidence than the reported primary analysis. A result on a secondary measure may be useful for describing the pattern of observations, but it should not be read as a definitive independent confirmation without the analysis plan and multiplicity procedures. The registry record also does not report all details needed to assess the hierarchy, prespecification, or role of each secondary outcome. The most cautious reading is to treat the secondary results as supportive descriptive context around the primary comparison.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The primary endpoint summaries show mean ADHD-RS-5 change scores of -11.4 in the placebo group, -16.0 in the 200mg SPN-812 group, and -16.5 in the 400mg SPN-812 group. Because lower change scores were defined as better, the active-group means represent larger decreases than the placebo mean. The sponsor-reported mixed models for repeated measures (MMRM) analyses estimated a least square mean difference of -4.5 for 200mg SPN-812 versus placebo, with a 95% confidence interval from -8.4 to -0.6 and p = 0.023. For 400mg SPN-812 versus placebo, the reported difference was -5.1, with a 95% confidence interval from -8.9 to -1.3 and p = 0.009.

These results describe group-average differences at the stated endpoint, under the sponsor's reported analysis. They do not mean that every participant experienced a decrease or that the same size of change occurred across participants. The confidence intervals express uncertainty around the estimated average differences; their width indicates that the true difference compatible with the data could be smaller or larger than the point estimate. The record labels both comparisons as superiority analyses. The statistical results alone do not establish the clinical importance of the differences, and the registry does not report a threshold for interpreting their clinical importance.

Simple unadjusted recalculations from the posted arm summaries estimate differences of -4.6 for 200mg SPN-812 versus placebo and -5.1 for 400mg SPN-812 versus placebo. These are close to the sponsor's reported estimates. The recalculated intervals and p-values are not substitutes for the sponsor's model-based results: the sponsor's MMRM analysis takes precedence for interpreting the trial's own primary analysis. The recalculations use posted summary information and do not reproduce the trial's participant-level model.

The registry's secondary results are mixed across measures. Some comparisons have intervals that include or touch zero, while others have reported differences with intervals excluding zero; the pattern varies by measure and dose. These secondary comparisons should be read as supporting or exploratory context rather than as a set of equally definitive findings. The registry record does not report whether or how statistical multiplicity was handled, so unadjusted secondary p-values should not be treated as if they accounted for testing multiple outcomes and comparisons.

Interpretation is also bounded by the endpoint population and time point. The primary endpoint is defined at Week 6 and the ITT definition requires at least one post-baseline assessment. The record does not report the missing-data handling details, the number of participants with missing endpoint assessments, or additional sensitivity analyses. Those omissions limit what can be concluded about the influence of incomplete outcome data. The findings should therefore be described as the posted short-term group comparisons, not as a complete account of longer-term outcomes or individual responses.

10. Statistical Methods Explained

The primary endpoint is a continuous score-change measure. A continuous outcome can take a range of values rather than representing only event categories. In this trial the value is change in ADHD-RS-5 total score from baseline to Week 6. Negative changes indicate decreases from baseline, and the registry states that lower change scores represent a better outcome. The arm summaries are least square means with standard errors, rather than raw individual observations.

What does a least square mean represent?

A least square mean is a model-based estimate of a group mean. Unlike a simple arithmetic average calculated directly from all observed values, it can reflect the statistical model used to account for repeated measurements and other modeled features. The registry reports primary least square mean differences from mixed models for repeated measures. The record does not list all model terms, covariance structures, or other implementation details, so those should not be assumed. The arm-level posted summaries and the sponsor's model-based contrast are related but are not interchangeable calculations.

What does the treatment contrast mean?

A mean difference compares the average outcome in an active group with the average in the placebo group. A negative primary-endpoint difference favors the active group under the registry's definition, because lower change scores are considered better. The reported primary contrasts are least square mean differences, with corresponding confidence intervals and p-values. The model-based contrasts are the sponsor's own analysis results; simple recalculations from posted summaries are unadjusted and do not reproduce the sponsor's repeated-measures model.

Why use a repeated-measures model?

Repeated-measures methods are designed for outcomes measured more than once per participant. In general, such models use information from the repeated observations to estimate change and compare groups while accounting for the fact that measurements from the same participant are related. Their estimates depend on the model specification and the assumptions used for incomplete observations. The registry names MMRM for the primary comparisons, but does not report the detailed specification or missing-data assumptions. It is therefore possible to explain the method's general purpose without attributing unreported model choices to this trial.

What do the standard errors tell the reader?

A standard error describes the estimated sampling uncertainty of a mean or model estimate. It is not the spread of individual participant values. A smaller standard error generally indicates a more precise estimate, all else equal, while a larger one indicates more uncertainty about the estimated mean. Standard errors for the primary arms are posted as 1.37, 1.45, and 1.38 for placebo, 200mg SPN-812, and 400mg SPN-812, respectively. The record does not provide individual participant data or standard deviations for those arms. The recalculated pooled standard deviations are therefore approximations derived from the posted standard errors and group sizes.

How should p-values be read?

A p-value describes how compatible the observed data are with a specified null hypothesis under the assumptions of the analysis. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. The sponsor reports primary p-values of 0.023 and 0.009 for the two active-versus-placebo contrasts. The unadjusted recalculations use a simpler comparison based on summary statistics. They are not a replacement for the sponsor's analysis and do not account for all features that may be represented in the model-based result.

The registry reports superiority comparisons for the primary endpoint. A superiority analysis evaluates whether the data support a difference in the specified direction or a nonzero contrast under the stated analysis. The reported confidence intervals and p-values describe the strength and precision of evidence within that analysis. They do not, on their own, answer whether a difference is important to participants, or whether the observed pattern applies to outcomes outside the study's population and timeframe.

Why can over-dispersion matter?

Over-dispersion is a general issue that arises when observed variability is greater than a model assumes. If a model understates variability, its standard errors can be too small and uncertainty may appear less than it is. This concept is especially relevant to count or event outcomes, although model choice depends on the outcome and design. The primary endpoint is continuous, and the registry does not report an over-dispersion assessment. It should not be assumed that over-dispersion affected the primary analysis.

In general, statistical methods should match the outcome's structure, the study design, and the way observations are collected. Randomized parallel-group allocation supports comparison of groups, while repeated assessment motivates methods that account for within-participant measurements. The registry identifies those broad design and analysis features, but does not report the full statistical analysis plan, all model specifications, or sensitivity analyses. Those details are not reported in the registry record.

11. Confidence Intervals and Precision

The sponsor's primary analysis reports a 95% confidence interval from -8.4 to -0.6 for the 200mg SPN-812 versus placebo difference, and from -8.9 to -1.3 for the 400mg SPN-812 versus placebo difference. Each interval lies below zero. In the direction defined by the registry, negative differences correspond to lower change scores in the active group than in placebo. The point estimates are -4.5 and -5.1, respectively.

A confidence interval is a range of values produced by a statistical procedure that, under its assumptions, reflects uncertainty in an estimate. It helps readers assess precision: a narrower interval indicates more precision than a wider interval, while a wider interval leaves more uncertainty about the magnitude. The interval is not a range containing every participant's response, and it does not mean that all values inside it are equally likely. Nor does an interval alone determine clinical importance.

The primary intervals give a sense of how uncertain the average group contrasts remain. Their negative limits are closer to zero than their more negative limits, so the estimates are compatible with a range of magnitudes. The registry does not report a threshold for a clinically meaningful difference on this endpoint. Statistical separation from zero should therefore not be treated as a direct measure of practical importance.

The recalculated unadjusted intervals are based on posted summary statistics and approximate standard deviations, whereas the sponsor's intervals come from MMRM. The sponsor's analysis is the relevant trial analysis. Differences between the two approaches can arise because a model-based repeated-measures contrast is not the same as a simple calculation from endpoint summaries. The recalculated intervals are useful as a check on the broad scale of the posted results, not as an independent replacement or validation of the sponsor's model.

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 effect146196
75% of the observed effect259347
50% of the observed effect583781
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1002005001,0002,00040%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: 200mg SPN-812.

The planning illustrations show participants per arm for 80% power and participants per arm for 90% power. These are not total sample sizes. They use the stated planning assumptions: a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set at the specified fraction of the observed effect. The trial's own original design assumptions and sample-size justification are not reported in the registry record.

Power is the probability, under a particular assumed effect and statistical model, of detecting that effect at the chosen significance level. The 80% and 90% columns describe different target probabilities under the planning assumptions: the 90% target generally requires more participants per arm than the 80% target. The illustrations vary the assumed effect from the full observed effect to 75% and 50% of that effect. When a smaller effect is the target, more participants are needed because a smaller signal is harder to distinguish from random variation.

The values are planning illustrations based on effects observed in this trial. They are not evidence about the study's original recruitment plan, nor do they show how likely this completed trial was to produce a statistically significant result. They are not observed power. They show how hypothetical group sizes change under the stated assumptions and effect scenarios. The sample-size calculation applies to a two-arm comparison; it does not mean that the whole three-group trial used those per-arm numbers.

For the primary endpoint, the illustrations are separate for the 200mg and 400mg comparisons with placebo. Their values depend on the observed contrast used as the planning effect. A reader should focus on the stated assumptions and the direction of change across effect scenarios, rather than treating any one illustrated size as a recommended or definitive design size. Trial-specific planning details beyond the assumptions listed for these illustrations are 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 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 = -4.600; pooled standard deviation σ = 14.013.
  2. n = 2 × (1.96 + 0.842)2 × 14.0132 / -4.6002 = 145.7, rounded up to 146 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 <- -4.6                      # observed difference in means
sigma <- 14.0126414864783                     # 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(3247517)
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 = 146 (80% power), 196 (90% power)
 75% of observed effect: n per arm = 259 (80% power), 347 (90% power)
 50% of observed effect: n per arm = 583 (80% power), 781 (90% power)
power.t.test: 146.6 
Simulated power at n = 146 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.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Mixed Models for Repeated MeasuresLeast Square Mean Difference -4.5-8.4 to -0.60.023
Mixed Models for Repeated MeasuresLeast Square Mean Difference -5.1-8.9 to -1.30.009

The sponsor's reported primary analysis used mixed models for repeated measures and estimated least square mean differences. For 200mg SPN-812 versus placebo, the reported difference was -4.5, with a 95% confidence interval from -8.4 to -0.6 and p = 0.023. For 400mg SPN-812 versus placebo, it was -5.1, with a 95% confidence interval from -8.9 to -1.3 and p = 0.009. The registry classifies both comparisons as superiority analyses.

The unadjusted recalculations from the posted arm summaries estimate differences of -4.6 and -5.1 for the same comparisons. These are simple calculations using summary statistics, and the primary endpoint's recalculated pooled standard deviations are approximations derived from standard errors. The recalculations are not the sponsor's analysis and do not reproduce the repeated-measures model. Their role is to provide a basic comparison with the reported results, not to supplant them.

The recalculated estimates are close to the sponsor's reported estimates, and the registry's discrepancy indicator is false. No discrepancy is flagged in the record. For interpretation of the trial's own results, the sponsor's MMRM estimates, confidence intervals, and p-values take precedence over the simplified recalculations. The registry does not report enough model detail to independently reproduce the sponsor's analysis from the posted summaries.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when several outcomes, treatment comparisons, or analysis choices are examined. With repeated testing, the chance of finding at least one apparently notable result can increase even if there is no true difference on any particular measure. Statistical procedures can control or otherwise address this issue, but the appropriate approach depends on which findings are intended to be confirmatory and how the tests are organized.

The registry lists multiple secondary outcomes and comparisons of each active group with placebo. It reports p-values for the primary endpoint and several secondary analyses, but does not report whether a multiplicity adjustment was applied, which outcomes were included in any adjustment, or whether a testing hierarchy was used. Thus, secondary p-values should be regarded as unadjusted unless the record states otherwise. The record does not provide enough information to conclude that multiplicity was or was not handled in the trial's full statistical plan.

Missing-data handling is also important for a repeated-measures endpoint. The primary endpoint population is defined as randomized participants who took at least one dose, had a baseline ADHD-RS-5 assessment, and had at least one post-baseline assessment. This definition indicates that the reported ITT population is not simply every randomized participant; the listed eligibility conditions require some observed outcome information.

The registry names MMRM for the primary analysis, but does not report the model's missing-data assumptions, how participants with incomplete measurements were handled, the amount or pattern of missing endpoint data, or sensitivity analyses. General descriptions of MMRM cannot fill those trial-specific gaps. The record also does not report whether the analysis included any imputation, or how intercurrent events were addressed. Those details are not reported in the registry record.

Without those particulars, readers cannot assess from the registry alone how robust the primary estimates are to different assumptions about missing outcomes, or how much the reported analysis population differs from the randomized population. These limitations do not negate the posted analysis; they define the boundaries of what can be concluded from the available record.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo01040.0%
200mg SPN-8122992.0%
400mg SPN-81201050.0%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo0.0%200mg SPN-8122.0%400mg SPN-8120.0%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Placebo0 of 104
200mg SPN-8120 of 99
400mg SPN-8120 of 105

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
Placebo22 of 104
200mg SPN-81239 of 99
400mg SPN-81250 of 105

Most frequent serious adverse event terms

Event termOrgan systemPlacebo200mg SPN-812400mg SPN-812
Thermal burnInjury, poisoning and procedural complications0 of 1041 of 990 of 105
SyncopeNervous system disorders0 of 1041 of 990 of 105

Most frequent non-serious adverse event terms

Event termOrgan systemPlacebo200mg SPN-812400mg SPN-812
SomnolenceNervous system disorders8 of 10413 of 9915 of 105
HeadacheNervous system disorders10 of 10410 of 9913 of 105
NauseaGastrointestinal disorders3 of 1047 of 997 of 105
Decreased appetiteMetabolism and nutrition disorders0 of 1045 of 999 of 105
FatigueGeneral disorders1 of 1044 of 996 of 105

Serious events with the highest arm-level rate: thermal burn (1.0%), syncope (1.0%).

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's serious adverse event summaries list 0 affected participants in the placebo group, 2 in the 200mg SPN-812 group, and 0 in the 400mg SPN-812 group. The corresponding numbers at risk are 104, 99, and 105. The record also identifies Thermal burn and Syncope among the top serious adverse event terms, each listed as 1.0%. It does not provide a fuller event-level account in the registry record used for this summary.

Other adverse events were reported for 22 participants in the placebo group, 39 in the 200mg group, and 50 in the 400mg group, with respective group counts at risk of 104, 99, and 105. These counts describe participants affected, not a comparison adjusted for exposure duration or other factors. Deaths were listed as 0 in all three groups.

These figures should be read as descriptive summaries. They do not by themselves establish whether an event was caused by an intervention, whether groups differ reliably in safety, or how event severity and timing compare. The registry record does not supply a detailed narrative or longer-term safety follow-up in the registry record.

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

The posted primary results show lower mean ADHD-RS-5 change scores in both SPN-812 groups than in the placebo group at Week 6. The sponsor's reported MMRM comparisons estimate negative differences for both doses, with confidence intervals below zero. This is a description of the trial's group-level results under its reported primary analysis. It does not establish that every participant improved, or that each participant's change was similar to the group average.

A statistically distinguishable group average is not the same as a judgment about clinical importance. The registry defines the direction of a better outcome but does not provide a threshold for the smallest clinically meaningful difference on ADHD-RS-5. Readers therefore should not interpret a p-value as a measure of benefit size or as a substitute for a clinical importance standard.

The endpoint covers ADHD symptom ratings through Week 6. It does not by itself answer questions about durability beyond the recorded timeframe, outcomes not measured, or the experiences of individuals outside the study's defined population. The registry's secondary assessments add other perspectives, but their results are not uniformly aligned and the record does not state the multiplicity procedures that would clarify their inferential status.

The findings are also bounded by the analysis population and the reporting detail available. The ITT endpoint population required baseline and post-baseline assessments, while the registry does not report the full missing-data approach or sensitivity analyses. The sponsor's analysis is the primary source for the trial contrasts; recalculated summary-statistic comparisons are only an approximation and do not reproduce the model.

Accordingly, the posted record supports a description of short-term average differences between randomized groups on the named symptom scale. It does not alone settle the clinical meaning of those differences, characterize every safety outcome, or establish results over time periods and populations not represented in the registry record.

18. Why This Trial Matters Statistically

This trial is statistically informative because it combines randomized parallel groups with a defined symptom-scale endpoint and reports both group summaries and model-based comparisons. The primary endpoint is change from baseline, making the treatment contrasts interpretable in the direction specified by the registry. Reporting confidence intervals alongside p-values also allows readers to consider uncertainty and estimated magnitude rather than relying on a significance label alone.

The record illustrates why the analysis method matters. The sponsor's primary MMRM contrasts are model-based, while recalculations from posted arm summaries are unadjusted approximations. Their closeness gives a basic check on scale and direction, but it does not make the methods equivalent. Model-based analyses can reflect repeated measurements and other specifications that cannot be reconstructed from a few summary values.

The secondary outcomes also illustrate a common interpretive challenge: multiple outcomes can broaden the clinical picture, while simultaneously making isolated p-values harder to interpret without a stated multiplicity plan. The registry does not report how that issue was handled. Similarly, naming an ITT population does not resolve questions about missing observations; the population definition and model assumptions both matter for understanding who contributed information and how incomplete data were treated.

Finally, planning illustrations derived from observed effects are distinct from a trial's original design calculations. They can show how hypothetical participant requirements change with the target effect and power, but they do not reveal why the trial enrolled its observed number of participants. The registry does not report the original sample-size justification. Separating observed findings, model-based inference, and hypothetical planning is essential to a statistically careful reading of the record.

19. Limitations

The registry record does not report the original sample-size justification, detailed statistical analysis plan, or model specifications beyond naming MMRM for the primary comparisons and ANCOVA for some secondary results. Without those details, readers cannot verify all analysis choices or determine the intended role of each reported outcome. The record also does not report whether multiplicity adjustments were applied.

The primary endpoint summaries are based on group counts of 104, 94, and 103, while overall enrollment is 310. The record defines the endpoint analysis population using baseline and post-baseline assessment requirements, but does not report the number or reasons for missing measurements, the handling of incomplete observations, or sensitivity analyses. Those omissions limit assessment of potential missing-data effects.

The posted recalculations use summary statistics rather than participant-level data. The primary endpoint's pooled standard deviations are approximate, and the calculations do not reproduce the sponsor's repeated-measures model. The registry does not provide enough detail to independently reconstruct that model or evaluate all of its assumptions.

The reported primary endpoint covers Week 6. The registry entries summarized in the registry record do not establish longer-term outcomes. The record also does not provide a clinical importance threshold for ADHD-RS-5 change, so statistical evidence and practical importance cannot be equated. Secondary outcomes span different measures and constructs, but the multiplicity plan and outcome hierarchy are not reported.

These are limitations of the information available in the registry record, not findings that the trial necessarily lacked particular procedures. Unreported details should not be treated as proof that they were absent.

20. Related Tutorials

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23. Record Summary

NCT03247517 is a completed Phase 3 randomized, quadruple-masked, parallel-group trial of 200mg and 400mg SPN-812 versus placebo in adolescents with ADHD. The registry lists enrollment of 310. The primary endpoint was change from baseline in ADHD-RS-5 total score at Week 6.

The sponsor reported MMRM least square mean differences versus placebo of -4.5 for 200mg and -5.1 for 400mg, with 95% confidence intervals from -8.4 to -0.6 and -8.9 to -1.3, respectively. Both active-group comparisons were labeled superiority analyses. Secondary results varied across measures, and the registry does not report multiplicity procedures or detailed missing-data assumptions.

The registry record does not report the original sample-size justification, full statistical plan, or enough model detail for independent reproduction of the sponsor's analyses. Results describe the reported group comparisons at the stated endpoint and should be interpreted within those limits.

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