Promoting Physical Growth and Positive Development in Severely Stunted Guatemalan Children: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Promoting Physical Growth and Positive Development in Severely Stunted Guatemalan Children (NCT02509936), a randomized na study. The primary outcome is Change in Height/Length for Age Z Score.

2. Clinical Question

The question concerns the incremental contribution of the home-based education component against a common background of nutrition support. It is not a comparison of education with no care: both arms received the described national standard of care. The registry describes randomized allocation, but does not report further details about the randomization procedure or the population included in the primary analysis.

3. Trial Design

The registry describes a randomized, single-masked, parallel-group study sponsored by Wuqu' Kawoq, Maya Health Alliance. Enrollment is listed as 324. The study began in 2015-08, primary completion is listed as 2016-10, and its status is completed. The phase is listed as not applicable.

One group received standard-of-care nutrition support, including growth monitoring, a food ration, and a multiple micronutrient powder supplement. The other group received that same support plus home-based nutrition education. The summary describes home-based dietary assessment and individualized parental nutrition education as added components. The intervention-arm description also mentions monthly home visits from a community health promoter. The remaining details of that description are not reported in the registry record.

The primary outcome is continuous: change in height- or length-for-age z score between baseline and 6 months. The posted arm results include 151 participants in standard care and 145 in home-based education. These are the counts reported for the primary outcome; the registry does not explain how they relate to the enrollment figure or identify an analysis population.

Although the study is described as single-masked, who was masked and how masking was maintained are not reported in the registry record. The allocation sequence method, concealment procedures, site count, and protocol details are also not reported. The registry lists secondary outcomes covering development and dietary indicators, while numeric secondary results are posted for dietary measures. Further details about how outcomes were assessed and how follow-up was handled 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.

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 in Height/Length for Age Z Score, measured over Baseline, 6 months.

The primary endpoint is change in height- or length-for-age z score from baseline to 6 months, expressed in z-score units. The registry says the measure uses the WHO Child Growth Reference Standards and defines change as the 6-month score minus the baseline score. A positive change therefore indicates a higher z score at follow-up than at baseline; a negative change indicates a lower score.

A z score expresses a measurement in relation to a reference distribution. Using a common growth reference allows the endpoint to describe children’s growth relative to that standard, rather than reporting height or length alone. The endpoint is continuous, so the posted arm summaries report a mean change and a standard deviation.

The registry identifies this as the primary outcome and gives a 6-month timeframe. It does not report additional rationale for selecting this endpoint, a clinically meaningful threshold for interpreting a change, or a stated primary analysis method. The endpoint addresses physical growth; it does not directly measure the listed cognitive, socioemotional, motor, or language outcomes. Those are separate secondary outcomes in the registry record.

7. Results Posted in the Registry

• Home-based Education: mean 0.05 versus -0.02 on control; difference 0.07 (95% CI -0.04 to 0.18), standardized effect d = 0.15; z-test p = 0.196.

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.

Minimum Diet Diversity

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Home-based Education: 93.1% (135/145) versus 76.2% (115/151) on control; risk difference 16.9 percentage points (95% CI 9.0 to 24.9), risk ratio 1.22 (1.11–1.35); unadjusted two-proportion z-test p = <0.001.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Home-based Education than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Minimum Meal Frequency

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Home-based Education: 89.0% (129/145) versus 86.8% (131/151) on control; risk difference 2.2 percentage points (95% CI -5.2 to 9.6), risk ratio 1.03 (0.94–1.12); unadjusted two-proportion z-test p = 0.561.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Home-based Education and the control. The interval gives the range of effects that remain compatible with the data.

Minimum Acceptable Diet

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Home-based Education: 84.8% (123/145) versus 68.9% (104/151) on control; risk difference 16.0 percentage points (95% CI 6.5 to 25.4), risk ratio 1.23 (1.08–1.40); unadjusted two-proportion z-test p = 0.001.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Home-based Education than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The registry lists secondary outcomes across developmental domains and dietary practices. Numeric results are posted for three dietary indicators: minimum diet diversity, minimum meal frequency, and minimum acceptable diet. The posted comparisons do not present a uniform pattern across all three. The results for diet diversity and minimum acceptable diet are more clearly separated between arms than the result for meal frequency. Numeric findings for the listed cognitive, socioemotional, gross motor, fine motor, receptive language, and expressive language outcomes are not reported in the registry record.

These dietary outcomes provide context about behaviors related to nutrition, but they do not measure the same construct as the primary growth endpoint. Differences in reported dietary indicators therefore cannot be treated as direct confirmation of a change in height- or length-for-age z score. Likewise, the primary result does not resolve whether the dietary indicators differed. Each endpoint addresses a distinct question and has its own uncertainty.

The secondary comparisons are unadjusted. When multiple outcomes are examined, some apparently notable results can occur by chance even if no underlying effect is present. This general multiplicity concern means that individual secondary p-values carry less weight than a result specified in advance as primary, especially when the analysis plan and any correction procedure are not reported. The registry does not report adjusted secondary analyses or a multiplicity strategy.

The secondary results can be viewed as exploratory signals that may motivate further evaluation, not as a replacement for the primary finding or as a comprehensive account of development. The absence of posted numeric developmental results is especially important: the registry’s list of outcomes alone does not establish what those outcomes showed. Interpretation should remain limited to the specific posted dietary comparisons and the uncertainty around them.

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

• Cognitive Development
• Socioemotional Development
• Gross Motor Development
• Fine Motor Development
• Receptive Language Development
• Expressive Language Development
• Minimum Diet Diversity
• Minimum Meal Frequency

9. Statistical Interpretation

10. Statistical Methods Explained

The primary measure is continuous, and the registry describes each arm using a mean change and a standard deviation. The mean gives the group’s average change, while the standard deviation describes how dispersed individual changes are around that average. A group mean is not a claim that every participant experienced that change. The registry’s reported mean difference compares the home-based education mean with the standard-of-care mean.

What does the confidence interval express?

A confidence interval describes the range of values reasonably compatible with the observed estimate under the statistical method used. A narrower interval indicates greater precision; a wider interval indicates more uncertainty. For the primary contrast, the posted interval crosses zero. Zero represents no difference between the arm means, so the interval includes a no-difference value as well as values on either side. That is why the point estimate’s positive direction should not be read in isolation.

The interval is not a range containing a known proportion of individual children’s outcomes. It concerns uncertainty in the estimated group contrast. Its interpretation also depends on the analysis method and assumptions. The registry does not report the full primary statistical analysis plan or enough detail to evaluate all those assumptions.

How should the p-value be read?

A p-value measures how compatible the observed data are with a specified null model, assuming that model and the analysis assumptions hold. The primary unadjusted p-value is 0.196. This does not give the probability that the null hypothesis is true, and it does not measure the size or importance of the estimated difference. It also does not show that the groups are equivalent. For the secondary dietary outcomes, the posted unadjusted p-values describe each comparison individually and do not account for the full set of outcomes.

Why does the type of outcome matter?

The primary growth outcome is continuous, whereas the posted diet outcomes are counts of participants meeting specified indicators. For a continuous outcome, the mean difference summarizes separation in average values. For a binary indicator, a risk difference describes the difference between the proportions meeting the indicator in the two groups. These quantities answer different questions and should not be compared as if they shared one scale. Ratios such as risk ratios and odds ratios are also measures of binary-outcome association, but they use different scales from a risk difference.

The registry posts risk differences and other comparison measures for its dietary results. The posted comparisons are unadjusted, and the registry does not report fitted models or covariate-adjusted analyses. Unadjusted comparisons are easier to interpret as direct contrasts of the posted group summaries, but they do not address possible differences in prognostic characteristics or other sources of variation beyond random assignment.

What does over-dispersion mean in general?

In general, over-dispersion occurs when observed variability is greater than a statistical model expects. For count or binary data, a model that understates variability can make uncertainty appear too small and can produce intervals or tests that are too optimistic. This is a general statistical concern, not a reported finding for this trial. The registry does not report an over-dispersion assessment or enough modeling detail to determine whether it was considered.

The registry labels the primary parameter as a mean and its spread as a standard deviation. It does not report the distribution of individual changes, tests of model assumptions, or an alternative robust analysis. The simple unadjusted comparison therefore should be understood as a summary-based estimate, not as evidence that every possible analytical concern has been addressed.

What can and cannot be inferred from randomization?

Randomized allocation is intended to make groups comparable on average at the point of assignment, including for characteristics that may not be measured. It supports a causal interpretation when allocation is implemented appropriately and when follow-up and analysis preserve the randomized comparison. The registry does not report sequence generation, allocation concealment, adherence, crossover, or detailed analysis-population rules. It is not possible from the record to assess those features fully.

Statistical significance is not the same as clinical importance, and neither is the same as certainty. The primary estimate, its interval, and its p-value should be considered together. The secondary indicators add context but are subject to multiplicity and are not a substitute for the primary outcome. No adjusted secondary analyses are reported in the registry record.

11. Confidence Intervals and Precision

The primary mean difference is 0.07 z-score units, with a confidence interval that extends from a negative value to a positive value and crosses zero. This interval indicates uncertainty about the direction and size of the underlying mean contrast. The point estimate favors greater average change in the home-based education arm, but values consistent with a modest contrast in either direction remain compatible with the interval.

Precision is affected by the amount of information in the outcome data and by variability. The posted standard deviations, 0.45 in standard care and 0.48 in home-based education, describe spread within each arm. They are not themselves confidence intervals and do not show the precision of the group difference. The interval around the comparison is the relevant summary for uncertainty in that contrast.

The primary unadjusted p-value of 0.196 is consistent with the interval crossing zero, but it should not replace the interval-based interpretation. Neither a p-value nor an interval establishes whether a difference matters to children or families. The registry does not report a threshold for meaningful change, a non-inferiority or equivalence margin, or an adjusted primary analysis.

The secondary dietary results have their own intervals, which also express uncertainty in the respective comparisons. Their interpretation is further limited by the number of outcomes examined and the absence of reported multiplicity adjustment. The registry does not provide numerical results for the listed developmental outcomes. Overall, the primary estimate is not precise enough to distinguish confidently between no mean difference and a positive mean contrast of the size suggested by its point estimate.

12. Planning a Similar Trial: Sample Size

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

The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design calculations. Each row considers planning for the full observed effect, 75% of the observed effect, or 50% of the observed effect. Each power column gives participants per arm for 80% power or participants per arm for 90% power. These figures apply to participant outcomes; the accompanying assumption states that time-to-event calculations, if present, would instead give total events. The outcomes in this record are not time-to-event outcomes.

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 the stated fraction of the observed effect. The original trial’s design assumptions, including its original target effect and sample-size justification, are not reported in the registry record.

Power is the chance, under a specified model and effect assumption, of detecting an effect at least as large as the one used for planning. The 80% column means planning for an 80% chance under those assumptions; the 90% column uses a higher target chance. The calculations show that planning for a smaller effect requires more participants per arm. This is not observed power: it is a prospective planning illustration using the observed effect as its starting point, not a measure of how likely the completed study was to find its result.

The figures should not be read as evidence that the trial was adequately or inadequately sized under its original plan. They are sensitive to the assumed effect and planning method, and the registry does not report whether the original design used these assumptions. They are most useful for understanding how a future study’s required size changes when the target effect is reduced.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 0.070; pooled standard deviation σ = 0.465.
2. n = 2 × (1.96 + 0.842)² × 0.465² / 0.070² = 692.5, rounded up to 693 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 <- 0.07                      # observed difference in means
sigma <- 0.464935808604208                     # 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(2509936)
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 = 693 (80% power), 928 (90% power)
 75% of observed effect: n per arm = 1,232 (80% power), 1,649 (90% power)
 50% of observed effect: n per arm = 2,771 (80% power), 3,709 (90% power)
power.t.test: 693.5 
Simulated power at n = 693 per arm: 0.804 (20000 replicates)

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

14. Multiplicity, Missing Data and Analysis Populations

The registry names one primary outcome and multiple secondary outcomes. Examining several outcomes creates a multiplicity issue: as the number of statistical tests increases, the chance of at least one apparently unusual result can also increase, even when the tests are considered under a common null model. This is a general statistical issue, not evidence that any particular posted result is false.

A prespecified strategy can address multiplicity by defining which outcomes are confirmatory, setting an order for testing, or adjusting inference across a family of comparisons. The registry record does not report whether such a strategy was planned or used. The posted secondary comparisons are unadjusted, and the developmental results listed as secondary outcomes are not reported in the registry record. This makes the dietary p-values less conclusive than a single, prespecified primary comparison.

Information about missing data is also limited. The registry gives the counts used for the primary outcome and the dietary outcomes, but does not report reasons for missing measurements, the amount or pattern of missingness, or how missing outcomes were handled. The enrollment figure is 324, while the posted primary arm counts are 151 and 145; the record does not explain the relationship between these counts. No explanation should be inferred from the difference alone.

The analysis populations are not described in detail. The registry does not state whether results use an intention-to-treat population, a per-protocol population, or another defined set, nor does it describe handling of participants who did not adhere to their assigned intervention. The primary analysis method and any covariate adjustment are not reported. These omissions limit assessment of the robustness of the comparisons and of whether the analyses preserve the benefits of randomized assignment.

The record also does not report interim analyses, stopping rules, or a complete statistical analysis plan. Their absence from the registry record should be read as missing documentation, not as evidence that a particular procedure was or was not used.

15. Safety Results

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

Other (non-serious) adverse events

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

The registry reports zero serious adverse events among 163 participants at risk in the standard-of-care arm and zero among 161 participants at risk in the home-based education arm. It also reports zero other adverse events among the same arm-specific counts at risk. These figures describe what was recorded in the registry for the stated risk groups.

Zero reported events does not establish that no adverse events occurred outside the observation or reporting system, nor does it guarantee that an event is impossible. The record does not provide event definitions, surveillance procedures, timing, severity details beyond the serious-event category, or reasons for the risk-group counts. Death counts are not reported in the registry record. No serious adverse-event terms are listed.

The safety figures should be read as reported counts, not as a complete assessment of risk. They do not by themselves establish comparative safety, particularly when the registry does not describe how events were collected or adjudicated.

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

The primary result is an estimate of the difference in mean change in height- or length-for-age z score between children assigned to home-based education plus standard care and children assigned to standard care. Its point estimate is positive, but the confidence interval crosses zero and the unadjusted p-value is 0.196. The posted evidence is therefore uncertain about the direction and size of the underlying difference.

This does not mean that the two approaches are equivalent. The registry does not report an equivalence margin or a design intended to establish equivalence. It also does not mean that a difference is impossible: the interval includes positive contrasts. The result should be read as limited precision rather than as proof of no difference.

The primary endpoint is a growth measure, not a direct measure of cognition, language, motor function, or social and emotional development. Although those developmental outcomes are listed as secondary outcomes, their numeric results are not reported in the registry record. The posted dietary indicators address additional but distinct questions and cannot establish an effect on the primary growth endpoint.

The result also does not show which component of the home-based program might account for any observed contrast. The intervention combines standard support with education and home visits, and the study compares that package with standard support alone. The record does not provide component-specific comparisons or detailed information about implementation and adherence.

Finally, the registry result is not a complete account of all possible benefits and harms. The posted adverse-event counts are limited, and details about ascertainment and deaths are not reported. Conclusions should stay within the reported outcomes, comparisons, and their uncertainty; the record does not support medical advice or a broader claim about what families should choose.

17. Why This Trial Matters Statistically

This trial is statistically instructive because it separates a clear directional estimate from a precise conclusion. The primary point estimate favors greater mean change in the home-based education arm, while its interval crosses zero. Reading both together avoids treating the estimate’s direction as certainty or treating a non-small p-value as proof of no difference.

The intervention is an addition to standard care, not a contrast with no nutrition support. That distinction matters for interpreting the estimand: the primary comparison concerns the added home-based education package against a shared standard-of-care background. It is not an estimate of the effect of nutrition support as a whole.

The record also illustrates why outcome families must be considered together. Growth, dietary indicators, and developmental measures concern related but nonidentical domains. The posted dietary findings may add context, but unadjusted secondary comparisons carry greater risk of chance findings when multiple outcomes are examined. A list of developmental outcomes is not a substitute for their results.

Finally, the distinction between planning and observed results is important. The sample-size illustrations are based on the observed effects and specified planning assumptions; they are not the original design justification and not observed power. The trial’s original assumptions and several analysis details are not reported in the registry record. Keeping those limitations visible helps prevent retrospective planning calculations or incomplete registry documentation from being mistaken for evidence about the trial’s original design.

18. Limitations

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

Several limitations arise from what the registry record does not describe. The age range, detailed eligibility criteria, number of sites, randomization method, allocation concealment, and identity of the masked group are not reported. The study is described as involving severely stunted Guatemalan children, but the record does not give enough detail to assess how representative the enrolled population was.

The intervention description is incomplete: the summary identifies home-based dietary assessment and individualized parental education, while the arm description is truncated after mentioning detailed support during monthly home visits. The record therefore does not fully document intervention content, delivery, adherence, or variation in implementation. These gaps make it difficult to assess how reproducible the intervention was.

The posted primary analysis counts do not match the enrollment figure, and the record does not explain the relationship between them. Reasons for missing data, the analysis population, and methods for handling missing outcomes are not reported. The registry also does not provide an analysis plan, covariate-adjusted results, or a stated meaningful-change threshold. These omissions constrain evaluation of the primary estimate and its clinical relevance.

Numeric results are posted for only some of the listed secondary outcomes, and secondary comparisons are unadjusted. A multiplicity strategy is not reported. Safety reporting is limited to counts, without detailed event definitions or ascertainment information; death counts are not reported in the registry record. These limitations apply to interpretation of the posted record and should not be taken as proof that unreported procedures or information did not exist elsewhere.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Promoting Physical Growth and Positive Development in Severely Stunted Guatemalan Children — NCT02509936.
• Registry record last updated 2019-11-26; status last verified 2019-11.
• Results first posted 2019-11-26.
• 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, single-masked, parallel-group study with enrollment of 324. It compared national standard-of-care growth support with the same support plus home-based nutrition education among severely stunted Guatemalan children. The primary outcome was change in height- or length-for-age z score from baseline to 6 months.

The posted primary mean difference was 0.07 z-score units, with an interval crossing zero and an unadjusted p-value of 0.196. Posted secondary numeric results concern three dietary indicators; developmental outcome results are not reported in the registry record. The record reports zero serious and zero other adverse events in each arm’s stated risk group, while death counts are not reported.

Important details about the original sample-size justification, analysis populations, missing data, multiplicity, and statistical plan are not reported in the registry record. Interpretation is therefore limited to the posted summaries and their uncertainty.