Effect of Energy Density Over 5 Days in Preschool Children: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effect of Energy Density Over 5 Days in Preschool Children (NCT03010501), a randomized na study. The primary outcome is Differences in Food and Beverage Intake by Energy.

2. Clinical Question

3. Trial Design

The registry describes a randomized, single-masked crossover trial of food energy density in preschool children. The study began in 2016-08 and reached primary completion in 2017-12; its status is completed. The intervention is listed as Food Energy Density, and the record describes three 5-day periods: a baseline condition, a lower-density condition, and a higher-density condition. Their labels are 100%, 80%, and 120% Food Energy Density, respectively.

In a crossover design, participants receive or experience multiple conditions, so each participant may contribute information under more than one condition. In general, this can help comparisons account for stable differences between participants. The registry identifies the model as crossover, but the order of conditions, sequence assignment details, any washout arrangements, and how the analysis accounted for period or sequence effects are not reported in the registry record. Randomization is reported, but the particular randomization procedure is not reported. The record says masking was single; who was masked is not reported in the registry record.

Enrollment was 56. For the primary outcome, each of the three condition summaries reports 49 observations. The registry says that data from one enrolled participant were excluded from the primary analysis for absence from meals on 3 or more days in multiple intervention periods. The record does not explain how that exclusion detail relates to the reported count of 49 for each condition, and the participant flow beyond the stated information is not reported in the registry record. The study is listed under Feeding Behavior. Its phase is recorded as not applicable.

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.

Study Week 1

Reasons for not completing this period:

Study Week 2

Study Week 3

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Data of 1 enrolled participant was excluded from analysis for absence from meals on 3 or more days in multiple intervention periods.

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: The data of one participant was excluded from analysis due to absence from meals on three or more days of each 5-day study period.

6. Primary Endpoint

The registry lists the primary outcome as Differences in Food and Beverage Intake by Energy, measured over Days 1-5 in Weeks 1, 2, and 3.

The primary endpoint is mean daily intake of food and beverages by energy, measured in kilocalories. The registry describes it as differences in daily intake by energy, with observations over Days 1-5 in Weeks 1, 2, and 3. A mean is a summary of the average intake across the observations included in a condition. The reported spread is a standard error, which describes the precision of an estimated mean rather than the range of individual children’s intake.

This endpoint addresses the study’s central question because energy intake is the quantity the investigators set out to compare as food energy density varied. Total daily kilocalories and food energy density are related but distinct: the former describes energy consumed, while energy density describes energy per unit amount of food. A change in one does not, by itself, determine the other. The registry’s hypothesis concerns greater mean daily energy intake under the higher-density condition than under the lower-density condition. It also proposes that intake in those conditions may converge over the 5-day period.

The reported condition means summarize intake over the specified days and weeks. A detailed day-by-day pattern or an estimate of convergence across days is not reported in the registry record. Thus, the posted endpoint summaries speak to average intake across the specified periods, not to the shape of intake over time.

7. Results Posted in the Registry

• 80% Food Energy Density: mean 884.00 versus 956.00 on control; difference -72.00 (95% CI -175.95 to 31.95), standardized effect d = -0.27; z-test p = 0.175.
• 120% Food Energy Density: mean 1,041 versus 956.00 on control; difference 85.00 (95% CI -18.95 to 188.95), standardized effect d = 0.32; z-test p = 0.109.

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.

Differences in Food and Beverage Intake by Energy Density

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
• Result:
  • 80% Food Energy Density: mean 0.93 versus 0.97 on control; difference -0.04 (95% CI -0.10 to 0.02), standardized effect d = -0.29; z-test p = 0.157.
  • 120% Food Energy Density: mean 1.06 versus 0.97 on control; difference 0.09 (95% CI 0.02 to 0.16), standardized effect d = 0.50; z-test p = 0.013.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 80% Food Energy Density and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for 120% Food Energy Density than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The registry posts one secondary outcome, Differences in Food and Beverage Intake by Energy Density, measured in kilocalories per gram. It also records three outcome measures overall, but the other secondary outcome details are not reported in the registry record. The posted secondary measure concerns energy per unit mass, while the primary endpoint concerns total daily energy intake. These outcomes address related but distinct aspects of what children were served and consumed.

Across the posted secondary condition summaries, the mean is lower under the 80% condition and higher under the 120% condition than under baseline. This general pattern is directionally consistent with the intended variation in food energy density. It complements the primary endpoint by describing energy per gram rather than total daily kilocalories; it does not, by itself, explain the daily intake pattern or establish how children’s intake changed over the 5-day periods. The registry reports an overall mixed-model result for this secondary outcome, but model-based estimates and confidence intervals are not reported.

As with the primary outcome, unadjusted recalculations for individual contrasts should be distinguished from the reported mixed-model analysis. Secondary findings ordinarily carry less weight than the prespecified primary question because they may be exploratory, may represent a broader set of tests, and can be more vulnerable to chance findings when many outcomes or contrasts are examined. General explanation: when multiple hypotheses are tested, the chance of at least one apparently unusual result can increase unless the analysis accounts for multiplicity or the outcomes were prioritized in advance.

The registry does not report a multiplicity adjustment, a hierarchy of secondary hypotheses, or a complete analysis plan, so the degree of planned control over multiple testing is not reported. The secondary outcome can add context to the intervention and the primary endpoint, but it should not be treated as independent confirmation or as a substitute for the primary analysis. The record does not report enough detail to determine the intended inferential role of the secondary result.

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

• Differences in Food and Beverage Intake by Energy Density

9. Statistical Interpretation

10. Statistical Methods Explained

The registry identifies the study as randomized and crossover, and reports a mixed models analysis for the primary outcome. The registry record does not report the full statistical model, the covariance structure, how period or sequence was represented, or how missing observations were handled in that model. The interpretation of an analysis depends on these choices, particularly when observations can be related because participants experience multiple conditions.

What does a mixed model do?

General explanation: a mixed model can represent both systematic effects of interest and correlations among observations. In a crossover study, observations from the same participant may be more alike than observations from different participants. A model that accounts for that dependence can use the structure of the data differently from a calculation that treats condition summaries as unrelated groups. The exact implementation in this trial is not reported in the registry record, so it is not possible to state which specific terms or correlation assumptions produced the sponsor’s result.

The registry reports a mixed models analysis across the three primary conditions and gives p < 0.001, but it does not provide the model-based condition means, pairwise estimates, or confidence intervals. The posted condition means and standard errors therefore do not reveal the sponsor model’s estimates. The difference between the sponsor’s reported result and the unadjusted recalculations cannot be diagnosed from the information in the registry record.

What is an unadjusted recalculation?

General explanation: an unadjusted recalculation compares posted summary statistics without incorporating additional covariates or the full trial model. The pairwise recalculations use the reported condition means and standard errors to describe mean differences and their uncertainty. They are not adjusted estimates from the trial’s mixed model. In particular, a simple comparison of summaries may not represent the participant-level structure or other terms that a crossover analysis could include. The posted results do not provide enough detail to reproduce the sponsor’s model.

A mean difference is an estimate of how far apart two condition means are, with the sign indicating which condition has the larger mean according to the stated contrast. A confidence interval expresses uncertainty around that estimate under the calculation’s assumptions. A p-value measures how compatible the observed data are with a specified null hypothesis under the statistical procedure; it is not the probability that the null hypothesis is true. These general interpretations do not remove the need to distinguish the model-based sponsor analysis from the unadjusted calculations.

Why can estimates differ across methods?

General explanation: methods can differ because they use different assumptions about the data, dependence among observations, missingness, and the comparisons being tested. A crossover model may use participant-level observations and account for their association, while a summary-statistic calculation may not capture all that information. These are possible general reasons for method differences, not findings about what happened in this analysis. The exact reason for the discrepancy is not reported in the registry record. Since the discrepancy flag is true, the sponsor’s own analysis takes precedence over the recalculated pairwise results.

The registry’s p-value is for the reported mixed-model analysis across the three groups. It should not be read as a p-value for each pairwise contrast unless the record explicitly reports those contrasts; it does not. The recalculated pairwise p-values are unadjusted, and the record does not state whether or how the sponsor adjusted for multiple comparisons. Nor does it report whether the stated hypothesis about convergence across the 5-day period was tested with an interaction or another time-related analysis.

What does the standard error describe?

General explanation: a standard error describes the sampling uncertainty of an estimated quantity, such as a mean. It is not the standard deviation of individual observations and does not show how widely children’s intake varied. The primary condition summaries report standard errors of 37.0, 38.0, and 38.0 kilocalories. A reader should not interpret those values as the range of daily intake among participants. Individual-level variability, the distribution of intake, and any diagnostics for the model are not reported in the registry record.

The posted results state that one enrolled participant’s data were excluded from the primary analysis because of absence from meals on 3 or more days in multiple intervention periods. The record does not explain whether other observations were incomplete, how incomplete days were handled, or whether the mixed model used all available observations. The analysis population definition beyond the stated exclusion is not reported in the registry record.

What is not documented?

The registry record does not report the original sample-size justification, the target effect used for planning the trial, or the trial’s original power assumptions. It does not report an interim-analysis plan, stopping rules, details of model diagnostics, or a complete statistical analysis plan. These omissions limit independent assessment of the analysis choices; they do not show that any particular procedure was or was not used. The separate planning illustrations based on the observed effects are not the trial’s original design assumptions and should not be confused with the sponsor’s analysis.

11. Confidence Intervals and Precision

The unadjusted recalculation for the 80% condition versus baseline gives a mean difference of -72.0 kilocalories, with a 95% confidence interval from -176.0 to 31.95. For the 120% condition versus baseline, the estimated mean difference is 85.0 kilocalories, with a 95% confidence interval from -18.95 to 189.0. Both intervals include zero. This means the posted summary-statistic comparisons do not pin down a difference in one direction with high precision; the compatible values span both sides of no difference.

General explanation: a confidence interval represents a range of values compatible with the data and the method’s assumptions at the stated confidence level. It is not a guarantee that the true effect lies in the interval, nor does it describe the spread of individual children’s intake. Wider intervals indicate greater uncertainty about the estimated difference. The interval’s meaning also depends on the calculation used. These are unadjusted recalculated intervals, not intervals from the reported mixed model.

The sponsor’s reported mixed-model result has p < 0.001, but its estimate and confidence interval are not reported in the registry record. A small p-value alone does not indicate how large or precisely estimated the modeled effect is. The discrepancy between the reported analysis and the recalculations makes it especially important not to substitute the recalculated intervals for model-based precision. The record does not provide enough model output to assess the precision of the sponsor’s condition-specific estimates or to identify which contrasts account for its overall result.

For the secondary outcome, the registry likewise reports an overall mixed-model p-value but no model-based estimate or confidence interval. The unadjusted pairwise recalculations have their own intervals, but those do not resolve the missing model-based precision. The registry record therefore allows a descriptive appraisal of the posted summaries and unadjusted estimates, while precision under the sponsor’s analysis remains incompletely documented.

12. Planning a Similar Trial: Sample Size

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

The planning estimates are participants per arm, not total events. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning row uses the stated fraction of the observed effect as the effect to detect. The original trial’s own sample-size assumptions and justification are not reported in the registry record; these planning calculations are separate illustrations based on the posted effect estimates.

Read a row as a hypothetical planning scenario: if a future comparison aims to detect the effect size specified for that row, the entries give the estimated participants per arm for 80% power and for 90% power under the stated assumptions. In general, power describes the chance that a statistical procedure will detect an effect of the specified size if that effect is present and the assumptions hold. The 90% column represents a higher target chance of detection than the 80% column, and it consequently requires a larger planned sample under the same assumptions.

The rows that plan for smaller effects require more participants, because a smaller difference is harder to distinguish from sampling variation. The estimates are based on observed effects, which are uncertain and may not match the effect a future study aims to detect. These figures are planning illustrations, not observed power for this completed trial. They do not show the probability that the trial’s findings are correct, and they should not be read as a retrospective measure of the trial’s success.

Because the illustration uses equal allocation between two arms and reports participants per arm, it is not a direct description of the crossover design or its original analysis plan. The registry record does not report the original design’s sample-size rationale, or enough detail to translate these two-arm illustrations into the design assumptions used for the trial.

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 = -72.000; pooled standard deviation σ = 262.523.
2. n = 2 × (1.96 + 0.842)² × 262.523² / -72.000² = 208.7, rounded up to 209 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 <- -72                      # observed difference in means
sigma <- 262.523332296388                     # 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(3010501)
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 = 209 (80% power), 280 (90% power)
 75% of observed effect: n per arm = 372 (80% power), 497 (90% power)
 50% of observed effect: n per arm = 835 (80% power), 1,118 (90% power)
power.t.test: 209.7 
Simulated power at n = 209 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

The sponsor’s reported primary analysis is a mixed models analysis across the three conditions, with p < 0.001. The registry does not give a model-based estimate, confidence interval, or detailed contrast results. The simple unadjusted recalculations from the posted means and standard errors produce different pairwise conclusions: their intervals include zero, and their unadjusted p-values are not close to the reported overall p-value. This is a discrepancy between the reported analysis and the summary-statistic recalculations, not a basis for replacing one with the other.

The sponsor’s analysis takes precedence. It is the analysis reported for the trial, and the recalculations do not reproduce the stated mixed-model result. Because the model specification and underlying participant-level data are not reported in the registry record, the source of the discrepancy cannot be established from these summaries. It would be inappropriate to infer that the sponsor’s analysis used any particular adjustment, covariance structure, or set of model terms.

The overall p-value should be interpreted as the result of the reported analysis, not as an estimate of the difference between any one pair of conditions. The missing model-based estimates prevent assessment of the size and precision of the sponsor’s condition-specific effects. The recalculations remain useful as a transparent, limited check on the posted summary statistics, provided their unadjusted nature and their lower priority relative to the sponsor’s own analysis remain clear.

15. Multiplicity, Missing Data and Analysis Populations

The registry reports an overall mixed-model analysis across three primary conditions and gives p < 0.001. It does not report the model-based pairwise contrasts, a testing hierarchy, or whether the reported overall test was the sole primary inferential test. The record also does not say whether the investigators adjusted for multiple comparisons when assessing individual conditions or outcomes. The unadjusted pairwise recalculations are not multiplicity-adjusted and should not be interpreted as though such an adjustment had been made.

Multiplicity matters when several hypotheses are examined. General explanation: the more tests considered, the greater the opportunity for at least one result to appear statistically notable by chance, if all null hypotheses were true. An analysis plan may address this through a prespecified hierarchy or an adjustment method. Whether either approach was used for this trial is not reported in the registry record. The overall p-value and the unadjusted pairwise results therefore answer different questions and cannot be combined into a single unqualified claim about all condition comparisons.

The primary analysis population description says data from one enrolled participant were excluded because of absence from meals on 3 or more days in multiple intervention periods. The registry reports 49 observations for each primary condition, but does not provide a full participant flow or explain how those counts relate to the stated exclusion. The handling of any other missed meals, incomplete intervention periods, or missing daily observations is not reported in the registry record. The reasons for missing information beyond the stated exclusion are also not reported.

The analysis population definition beyond the stated exclusion, any imputation method, and the assumptions about missing data are not reported in the registry record. The record does not state whether all randomized participants were included in the sponsor’s mixed model or whether the analysis followed another population definition. These omissions limit assessment of how the incomplete or excluded observations might affect the result; they do not establish that a particular missing-data method was used or that the reported result is biased.

The record does not report an interim-analysis plan, stopping rules, or the original statistical analysis plan. It is therefore not possible to determine from the registry whether these details were prespecified, amended, or considered in the reported analysis. Their absence from the record should be described as unreported rather than interpreted as evidence that no such procedures existed.

16. 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 0% reporting threshold.

The adverse-event entries list 56 participants at risk in each of the 80%, 100%, and 120% Food Energy Density groups. For each condition, the registry reports 0 serious adverse events, 0 other adverse events, and 0 deaths. No serious adverse-event terms are listed.

These figures describe what was entered in the registry for the listed groups. They do not establish that no symptoms or other events occurred outside the categories or reporting process represented by those entries. The record does not provide event definitions, the method or timing of safety monitoring, or a narrative explaining whether events were actively sought. It also does not explain how the adverse-event group counts relate to the crossover structure or to the number analyzed for the primary endpoint.

General explanation: a recorded zero means that no events in that category were reported in the registry entry; it is not proof that an intervention has no risk. Safety summaries are also affected by how events are defined, collected, attributed, and reported. The registry’s figures should therefore be read as the posted event counts, without extending them to unreported outcomes or broader claims about safety.

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

The registry describes a controlled comparison of food energy density and reports that mean daily energy intake was numerically lowest in the lower-density condition and highest in the higher-density condition, with baseline between them. The sponsor’s mixed-model analysis across the conditions is reported as p < 0.001. Together, these registry entries describe the posted pattern and the reported overall statistical result. They do not provide the sponsor model’s condition-specific effect estimates or confidence intervals, so the magnitude and precision of the modeled differences cannot be read from the reported p-value alone.

The unadjusted recalculations offer a separate view based on the posted condition summaries. Their pairwise estimates are uncertain, with confidence intervals that include zero. Because the sponsor’s analysis and these recalculations differ, the sponsor’s own analysis takes precedence; the recalculations should not be used to overrule it. The registry does not provide enough detail to explain the discrepancy or to determine which condition contrasts underlie the overall mixed-model result.

The study’s stated hypothesis also concerned whether intake in the higher- and lower-density conditions would begin to converge across the 5-day period. Condition means summarized over Days 1-5 in Weeks 1, 2, and 3 do not show the day-by-day trajectory. A specific test or estimate of convergence is not reported in the registry record. Accordingly, the posted summaries do not establish whether intake converged over time.

These results do not establish a general effect beyond the participants and conditions described in the registry, and they do not answer questions about other populations, foods, settings, or longer-term outcomes. General explanation: statistical significance and practical importance are different concepts. A p-value alone does not quantify the size of an effect or its relevance in a particular setting. The registry does not report a threshold for a meaningful change in daily intake, so the clinical or practical importance of the reported result is not established by the posted statistical information.

The adverse-event entries report no serious or other adverse events and no deaths in the listed groups. Those entries are limited to the registry’s reporting and should not be taken as proof that all possible harms were excluded. The findings describe a short-term feeding study with specified energy-density conditions, not a recommendation about what children should eat.

18. Why This Trial Matters Statistically

This trial raises several important statistical issues in a compact setting. First, the crossover structure means the observations may be related within participant. General explanation: methods that represent this dependence can yield different uncertainty estimates and tests from calculations that compare condition summaries without the full participant-level model. The registry reports a mixed-model analysis, but does not provide its specification or model-based effect estimates. That makes it difficult for readers to assess the reported result fully or reproduce it.

Second, the registry’s overall mixed-model p-value differs in statistical implication from the unadjusted pairwise recalculations. This illustrates why an overall test, pairwise estimates, and model-based confidence intervals are not interchangeable. The sponsor’s analysis takes precedence, but the missing model output limits interpretation of which comparisons matter and how precisely they were estimated. The discrepancy should be made visible rather than concealed by presenting only one set of results.

Third, the endpoint has a time dimension: the stated aim concerns daily intake over 5-day periods, and the hypothesis includes possible convergence across days. Overall summaries do not answer a question about changing patterns over time. A reader would need the relevant day-specific estimates or a reported time-related model to assess that hypothesis; these are not reported in the registry record.

Finally, the record illustrates the distinction between planning and retrospective interpretation. Sample-size illustrations based on observed effects can help describe the scale of a future study under stated assumptions, but they do not recover the original design rationale or determine whether the completed study was adequately planned. The registry does not report its original sample-size justification. Clear reporting of model estimates, uncertainty, missing-data handling, multiplicity decisions, and the time pattern would make the results easier to assess without requiring readers to infer details from a single p-value.

19. Limitations

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

The registry record does not report the full mixed-model specification, model-based condition estimates, or model-based confidence intervals. Because the reported overall p-value and unadjusted recalculations differ, the absence of those details prevents a clear explanation of the discrepancy and limits assessment of the sponsor’s estimated effects. The sponsor’s analysis takes precedence, but its effect sizes and precision cannot be evaluated from the reported p-value alone.

The crossover design is identified, but sequence assignment details, the condition order, period effects, and any washout arrangements are not reported in the registry record. The record also does not explain who was masked under the single-masked designation. Without these details, readers cannot assess how the design’s features were handled or how they might bear on interpretation.

The stated hypothesis about convergence across the 5-day period is not accompanied by day-specific estimates or a reported test of the time pattern. The endpoint summaries combine observations across the specified days and weeks, so they do not establish how intake changed from day to day. The registry record also does not explain the relation between the stated exclusion of one participant and the reported 49 observations for each condition, or give a complete account of missing observations.

The original sample-size justification, the statistical analysis plan, any multiplicity procedure, and any interim-analysis plan are not reported in the registry record. Only one secondary outcome is posted, although the record indicates three outcome measures overall. The unadjusted secondary comparisons and the sponsor’s overall result should therefore be interpreted with the uncertainty around multiplicity and reporting completeness in mind. These are limitations of the information reported; they do not demonstrate that unreported procedures were absent.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Effect of Energy Density Over 5 Days in Preschool Children — NCT03010501.
• Registry record last updated 2019-07-11; status last verified 2019-07.
• Results first posted 2019-07-11.
• 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.

23. Record Summary

The registry describes a completed randomized, single-masked crossover study of food energy density in preschool children, with enrollment of 56. Children were studied under baseline 100%, lower 80%, and higher 120% Food Energy Density conditions over three 5-day periods. The primary outcome was mean daily energy intake in kilocalories during Days 1-5 in Weeks 1, 2, and 3.

The primary condition summaries report 49 observations per condition. The registry states that one enrolled participant was excluded from the primary analysis because of absence from meals on 3 or more days in multiple intervention periods. The sponsor reports a mixed-model analysis across the conditions with p < 0.001, but does not report model-based estimates or confidence intervals. Unadjusted recalculations from the posted summary statistics differ from the sponsor’s reported analysis; the sponsor’s own analysis takes precedence.

One secondary outcome, energy intake per gram, is posted. The record does not report the original sample-size justification, full analysis details, a multiplicity procedure, or a day-specific assessment of the convergence hypothesis. Adverse-event entries report 0 serious adverse events, 0 other adverse events, and 0 deaths in each listed condition.