A Study to Evaluate the Effects of a Dietary Supplement on Children's Health and Development Outcomes.: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study to Evaluate the Effects of a Dietary Supplement on Children's Health and Development Outcomes. (NCT06704178), a randomized na study. The primary outcome is Change Mean Percentile Score in Double Trouble.

2. Clinical Question

The registry describes a study of children's health and development outcomes, including height, weight gain, and cognitive function. Its posted primary result concerns the cognitive measure, not the full range of outcomes listed for the trial. The primary comparison is between the two assigned arms; the record does not report a more detailed primary analysis population or eligibility description. The registry does not report the original sample-size justification or other design assumptions for the trial.

3. Trial Design

This completed study is described as a randomized, parallel-group, placebo-controlled trial of a dietary supplement. The registry lists quadruple masking, while the brief summary calls it double-blind. The registry record does not specify which participants, staff, assessors, or other groups were masked, so the masking description cannot be interpreted in more detail from the record alone.

Participants in the intervention arm took NuBest Tall Growth Protein Powder daily for 6 months; participants in the placebo arm took a placebo product daily for 6 months. The brief summary describes the study as virtual. Parents were to complete questionnaires at baseline and monthly, while children were to undergo cognitive assessments and height and weight measurements at specified intervals. The exact schedule for each assessment beyond the stated baseline and Month 6 primary-outcome timeframe is not reported in the registry record.

The registry lists enrollment of 60 and the study status as completed. The posted primary outcome includes 24 participants in the intervention arm and 21 in the placebo arm. The record does not explain the relationship between the enrollment figure and the numbers contributing to this outcome, nor does it report participant flow, reasons for missing outcome data, or the analysis population definition. The registry lists the start date as 2024-06-12 and primary completion as 2025-02-16.

The study also lists secondary outcomes covering height, weight, parent-reported health and energy, and activity limitations. These outcomes provide broader context for the trial's aims, but the primary statistical result is the Month 6 cognitive-test outcome.

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

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 Change Mean Percentile Score in Double Trouble, measured over Baseline and Month 6.

The primary outcome is titled “Change Mean Percentile Score in Double Trouble.” The registry describes it as assessing improvement in cognitive function using a cognitive test. Participants received a percentile score from 1 to 100, with a higher score indicating a better response. The outcome is specified as a mean, with standard deviation as its measure of dispersion, and a timeframe of baseline and Month 6. Its unit is described as percent change from baseline.

A continuous cognitive score can retain information across the score range rather than reducing results to a simple count of participants who did or did not meet a cutoff. Comparing mean change between randomized arms is intended to describe how the average measured score changed in each group over the stated interval. The interpretation remains tied to this particular test and its recorded score; it does not establish change in every aspect of cognitive function.

The registry does not report the test's administration details, scoring procedures beyond the percentile range, or the specific calculation used to derive the stated percent change. The endpoint title and unit are not fully elaborated in the record, so the precise transformation underlying the posted values is not clear. The result should therefore be read using the outcome definition as registered, without assuming a different scoring or change calculation.

7. Results Posted in the Registry

• Intervention Arm: mean 168.55 versus 129.46 on control; difference 39.09 (95% CI -130.47 to 208.65), standardized effect d = 0.14; z-test p = 0.651.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: it is summarized by a mean and standard deviation in each arm. The recalculated comparison uses those posted summary statistics to estimate the difference between the intervention and placebo means. This is an unadjusted calculation, meaning it does not account for covariates or other factors beyond the group summaries used in the calculation.

For this comparison, the reported arm means are 168.6 and 129.5, and the recalculated mean difference is 39.09. The direction is expressed as intervention minus placebo. A positive estimate means the intervention-arm mean is higher in this contrast; it does not, by itself, establish that the difference is reliable, important, or caused by the supplement. The estimate should be read with its uncertainty interval and with the registry's outcome definition in mind.

General statistical context: a standard deviation describes how dispersed individual measurements are around a group's mean. It is not the uncertainty interval for the mean difference. The standard deviations of 230.4 and 332.8 describe variation in the outcome scores within the two posted groups. The uncertainty in a comparison of means also depends on the number of observations contributing to each group. Large within-group variation relative to the estimated difference generally makes a mean comparison less precise.

The unadjusted recalculation reports a p-value of 0.651. General statistical context: a p-value describes how unusual data at least as incompatible with a specified null model would be, under the assumptions of the test. It is not the probability that the null hypothesis is true, nor the probability that the result occurred by chance. The registry does not report a significance threshold for the sponsor's primary analysis, so the p-value should not be treated as a complete account of the analysis plan or the evidence.

The sponsor-reported result is identified as Multiple t-tests. A t-test is a method for comparing means under its assumptions; the registry record does not provide enough detail to identify all aspects of the sponsor's implementation. In particular, the record does not say whether adjustments were made for multiple testing, which specific tests were included in that analysis, or how missing outcome values were handled. The reported sponsor analysis and the recalculation should not be assumed to be identical procedures.

General statistical context: a confidence interval conveys a range of estimates compatible with the data and the method used, under the method's assumptions. It is not a guarantee that the true difference lies in the displayed range. The interval reported for the recalculation runs from -130.5 to 208.7. The registry does not state the confidence level or full method used for that interval, so these details cannot be inferred from the result alone.

Over-dispersion is a concern when observed variation is larger than a model assumes. General statistical context: if a model understates variability, its standard errors can be too small and its uncertainty intervals too narrow. Here the outcome is continuous and the posted standard deviations are large, but the registry does not report a model-based dispersion assessment. It would not be justified to assert that over-dispersion was present or that a particular method was used to address it.

The recalculation is based on posted group summary statistics, rather than participant-level observations. It therefore cannot independently check individual records, confirm the outcome derivation, adjust for baseline scores, or reproduce any covariate-adjusted analysis. Whether the sponsor's analysis used participant-level data or a particular adjustment is not reported in the registry record.

General statistical context: randomization supports a comparison between assigned groups, but it does not remove uncertainty in the observed estimates, ensure complete follow-up, or resolve ambiguity about outcome measurement. Those questions require details about trial conduct and analysis. The registry record does not report participant flow, analysis-population definitions, or the treatment of missing data. Consequently, the reported group counts and summary measures are the basis for interpreting this result, while other analysis details remain unknown.

Finally, multiple outcomes and analyses create a multiplicity issue: as more hypotheses are tested, the chance of at least one apparently unusual result can increase if tests are considered together without an appropriate plan. General statistical context: methods such as prespecified outcome hierarchies or multiplicity adjustments can address that concern, but no such plan or adjustment is reported for this trial. The registry lists 72 outcome measures and 339 analyses, and 67 secondary outcomes are posted. Those counts alone do not establish which analyses were planned, how they were related, or how any multiplicity was handled.

10. Confidence Intervals and Precision

The recalculated mean difference is 39.09, with a confidence interval from -130.5 to 208.7. The interval is broad and includes zero, so the estimate is not precise enough to settle the direction of the mean difference. Its lower limit is compatible with a negative intervention-minus-placebo contrast, and its upper limit is compatible with a positive contrast. The point estimate should be read as one estimate within a much wider range of uncertainty.

General statistical context: a confidence interval describes uncertainty around an estimate under the assumptions of the method used. It is not a range of individual participant scores, and it does not mean that every value in the interval is equally likely. The registry does not report the confidence level or full interval method for this recalculation, which limits further interpretation of its formal coverage properties.

The observed standard deviations, 230.4 in the intervention arm and 332.8 in the placebo arm, are large compared with the estimated difference. The outcome groups include 24 and 21 participants, respectively. Together, the posted variability and group sizes help explain why the mean-difference estimate has substantial uncertainty. The interval should not be narrowed or treated as decisive simply because the point estimate is positive.

Precision is distinct from importance. The registry record does not report a threshold for a meaningful difference on the Double Trouble score, so the interval cannot be judged against a stated importance criterion. The record also does not give the confidence interval for the sponsor-reported analysis. The sponsor's reported result and the unadjusted recalculation therefore offer different forms of information, and the posted record does not explain their difference.

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 describe participants per arm for this continuous-outcome comparison. The note that time-to-event displays give total events does not apply to this outcome; the listed figures are participants per arm, not total events across the trial. The values are planning illustrations based on the observed effect, rather than a record of the trial's actual design requirements.

The stated 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. The planning rows cover 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. The registry's original sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the estimated participants per arm under those assumptions for a design intended to have 80% power to detect the specified effect. The 90% power column gives the corresponding per-arm planning number for a design intended to have 90% power. In general, power is the probability of detecting an effect of the assumed size under the planning model and assumptions; it is not a description of what happened in this completed trial.

The displayed figures increase as the assumed fraction of the observed effect gets smaller. This reflects a general planning principle: smaller effects are harder to distinguish from random variation, so more participants are needed under otherwise unchanged assumptions. The observed trial enrollment and the posted primary-outcome group sizes should not be confused with these hypothetical planning counts. These calculations are not observed power.

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 = 39.090; pooled standard deviation σ = 282.658.
2. n = 2 × (1.96 + 0.842)² × 282.658² / 39.090² = 820.8, rounded up to 821 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 <- 39.09                      # observed difference in means
sigma <- 282.658477137471                     # 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(6704178)
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 = 821 (80% power), 1,099 (90% power)
 75% of observed effect: n per arm = 1,460 (80% power), 1,954 (90% power)
 50% of observed effect: n per arm = 3,284 (80% power), 4,396 (90% power)
power.t.test: 821.7 
Simulated power at n = 821 per arm: 0.805 (20000 replicates)

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

13. Analyses Reported by the Sponsor

The registry's sponsor-reported analysis is labeled Multiple t-tests and identifies the comparison as a superiority test. Its result entry gives a p-value but does not include an estimate or confidence interval. The unadjusted recalculation from the posted summary statistics gives a mean difference of 39.09, a confidence interval from -130.5 to 208.7, and a p-value of 0.651.

The sponsor-reported p-value differs from the recalculated p-value. The registry record does not explain the difference, and it does not provide enough methodological detail to establish whether the analyses used the same assumptions, data handling, or test implementation. The recalculation uses the posted arm-level summary statistics and is not a reproduction of the sponsor's full analysis.

The registry does not flag a discrepancy between the reported result and the recalculation. The sponsor's analysis should therefore be understood as the analysis reported by the trial sponsor, while the recalculation is a separate, unadjusted check based on posted summaries. Neither result supplies the missing detail about the analysis plan, multiple testing, or handling of missing values.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 72 outcome measures and 339 analyses, and 67 secondary outcomes are posted. These counts show that the record covers more than the single primary outcome discussed in the main comparison. They do not, on their own, identify which analyses were planned in advance, which were exploratory, or how outcomes and tests were organized.

The sponsor's primary result is labeled Multiple t-tests, but the registry does not report whether that analysis included a correction for multiple comparisons. It also does not report a prespecified testing hierarchy, a multiplicity adjustment method, or how the primary endpoint was protected from the effects of testing multiple outcomes. Without those details, the potential influence of multiple testing on the interpretation cannot be assessed from the registry record.

Missing-data handling is not reported in the registry record. The posted primary outcome includes 24 participants in the intervention arm and 21 in the placebo arm, while the listed enrollment is 60. The record does not explain the difference, identify missing outcome counts, report reasons for missingness, or state whether any imputation or other missing-data method was used. The figures alone do not establish why some enrolled participants are not included in the posted outcome summaries.

The analysis populations are also not reported in the registry record. It is not stated whether the primary result includes all randomized participants, only participants with available outcome data, or another defined group. The registry does not provide a participant-flow account or enough information to assess adherence to assigned treatment. These omissions limit assessment of how the posted results relate to randomization and to the full enrolled population.

General statistical context: multiplicity and missing data can affect how confidently results are interpreted. Their effects depend on the study's prespecified plan, the number and relationships of tests, the amount and reasons for missingness, and the methods used to address them. Those particulars cannot be inferred from the counts of outcomes and analyses or from the arm summaries alone.

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.

The adverse-event record lists 30 participants at risk in each arm. It reports 0 serious adverse events in the intervention arm and 0 in the placebo arm, with 0 deaths in each arm. The record also lists 0 other adverse events in each arm. These are the posted counts for the registry's stated safety categories.

These figures describe what was recorded in the registry; they should not be read as proof that no adverse events occurred outside the recorded categories or reporting period. The registry does not provide further details about how adverse events were defined, collected, assessed, or followed over time. It also does not explain why the at-risk counts differ from the participant counts in the posted primary-outcome result.

A zero count in a trial record is a count, not a guarantee about safety. The safety figures should be considered alongside the trial's size, duration, and reporting detail, without extending them beyond the participants and outcomes represented in the record.

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

The posted primary result compares mean change in a cognitive-test percentile score between the intervention and placebo arms at baseline and Month 6. The recalculated difference is 39.09 in the intervention-minus-placebo direction. The interval from -130.5 to 208.7 is wide and includes both negative and positive values, indicating substantial uncertainty about the direction and size of the contrast.

The result concerns the registered Double Trouble measure and the participants contributing to its posted summaries. It does not, by itself, establish what happened on every other health or development outcome. The registry lists outcomes concerning height, weight, parent-reported health and energy, and activity limitations, but the primary comparison should not be generalized to all of them.

The study is randomized and placebo-controlled, which establishes the intended comparison between assigned arms. However, the registry does not report participant flow, analysis-population definitions, missing-data methods, or enough detail about the sponsor's test to determine how those matters affected the posted result. The outcome's stated unit and title also leave the precise score-change calculation unclear.

The registry does not report a threshold for a meaningful difference on this measure. Statistical uncertainty and practical importance are separate questions: an estimate's size cannot be judged as meaningful without a relevant interpretation standard, and a p-value alone cannot supply one. The posted result should therefore be described as an uncertain comparison of group averages, not as a broad conclusion about children's cognitive development or health.

The registry's safety entries report zero serious adverse events and zero deaths in both arms, as well as zero other adverse events. Those counts are limited to the record's reporting and do not establish a general safety conclusion. Taken together, the primary efficacy result and safety counts describe the posted trial data, while important details needed for broader interpretation remain unreported.

17. Why This Trial Matters Statistically

This trial illustrates why a point estimate should not be read without its uncertainty. The recalculated mean difference is positive, but the confidence interval extends below and above zero. That contrast between a single estimate and a broad range is central to statistical interpretation: the data provide an estimate, but the estimate is not precise enough to settle the direction of the underlying difference.

The posted standard deviations are much larger than the mean difference, and the primary outcome summaries include 24 participants in one arm and 21 in the other. This makes it useful to consider both variability and group size when reading the comparison. A difference between means can appear substantial as a point estimate while remaining uncertain when individual measurements vary widely.

The trial also offers an example of why registry analyses need context. The sponsor's result is reported as Multiple t-tests, while a separate unadjusted recalculation uses the posted summaries. The p-values differ, and the record does not explain why. The registry lists many outcomes and analyses, but does not report a multiplicity plan or enough information to reconstruct how the sponsor's tests were conducted.

Finally, the trial's outcome and reporting definitions matter. The primary endpoint is described as percent change from baseline, while its title refers to change in mean percentile score. The exact calculation is not further explained. Attention to such details helps keep interpretation connected to what was actually measured and reported, rather than to a broader claim about children's health or development.

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 leaves several trial-specific questions unresolved. It does not report participant eligibility details, so the population represented by “children” cannot be characterized more narrowly. It lists enrollment of 60, while the posted primary outcome includes 24 participants in the intervention arm and 21 in the placebo arm, but it provides no participant-flow explanation or reasons for the difference.

The endpoint description also has limits. It identifies a Double Trouble percentile score, a range of 1 to 100, and a higher score as a better response, but does not describe test administration or give the exact calculation behind the stated percent change from baseline. The title and unit are not fully reconciled in the registry record.

The sponsor-reported result is labeled Multiple t-tests, but details needed to evaluate it are not reported: the specific test implementation, any covariate adjustment, multiplicity handling, missing-data methods, analysis populations, and confidence interval for the sponsor's result. The registry also does not explain why its reported p-value differs from the recalculated p-value.

The posted primary summaries are based on relatively small outcome groups with large standard deviations, and the recalculated interval is broad. The registry does not report the confidence level or full method for that interval. It also does not provide a threshold for a meaningful difference on the outcome.

For safety, the record gives counts but not detailed definitions, collection methods, or follow-up procedures. These limitations do not determine the direction of the result; they define what can and cannot be concluded from the registry record.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: A Study to Evaluate the Effects of a Dietary Supplement on Children's Health and Development Outcomes. — NCT06704178.
• Registry record last updated 2025-07-24; status last verified 2025-07.
• Results first posted 2025-07-24.
• 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

The registry describes a completed, randomized, parallel-group, placebo-controlled study of NuBest Tall Growth Protein Powder in children. The intervention and placebo were taken daily for 6 months. The record lists quadruple masking and describes the trial as virtual; its brief summary calls it double-blind.

The primary outcome is mean change in the Double Trouble cognitive-test percentile score from baseline to Month 6. The posted group means are 168.6 for 24 participants in the intervention arm and 129.5 for 21 participants in the placebo arm. The unadjusted recalculation estimates a mean difference of 39.09, with a confidence interval from -130.5 to 208.7 and a p-value of 0.651.

The registry lists 60 enrolled participants, 72 outcome measures, and 339 analyses. It reports zero serious adverse events and zero deaths in both arms. Details about participant flow, missing data, analysis populations, multiplicity, and the original sample-size justification are not reported in the registry record.