Daytime vs. Delayed Eating Among Obese Individuals: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Daytime vs. Delayed Eating Among Obese Individuals (NCT03354169), a randomized na study. The primary outcome is Body Mass (Weight).

2. Clinical Question

3. Trial Design

The registry describes a randomized controlled trial with a crossover model and no masking. The study focused on meal timing among obese individuals. Participants were assigned to eating conditions in which study meals and snacks were consumed during specified daily windows: between 0800 and 1900 for daytime eating, or between 1200 and 2300 for delayed eating. Each condition lasted 8 weeks.

The registry reports enrollment of 38. Thirty participants completed both eating conditions. Six were withdrawn before completing at least two assessment visits. Two participants completed screening and began the first inpatient assessment visit but were withdrawn before completing that visit and were not randomized to begin the intervention. They were not included in data analysis.

A crossover design means participants experience more than one condition, so comparisons may use measurements from the same people under each condition. The registry does not describe the treatment sequence, how the randomization sequence was generated or concealed, whether there was a washout period, or how the analysis accounted for the crossover structure. Those design and analysis details are not reported in the registry record. The posted outcome has 30 observations for each condition, corresponding to the 30 participants who completed both.

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

Analysis population for the primary outcome, as defined in the registry: Thirty participants completed the two eating conditions; six were withdrawn prior to completing at least two assessment visits.

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: All study participants are described as they all were intended to complete both eating conditions. Two were withdrawn after their first assessment visit but before randomization occurred.

6. Primary Endpoint

The registry lists the primary outcome as Body Mass (Weight), measured over pre-post changes between the daytime and delayed eating conditions (each 8 weeks long).

The primary endpoint is change in body mass, measured in kilograms with a calibrated digital scale. The registry describes the outcome as the pre-post changes between the daytime and delayed eating conditions, each lasting 8 weeks. The posted results report a mean change for each condition and a mean difference between conditions.

Weight is a continuous measure: it can take a range of values rather than placing each participant in a category. Reporting the mean change gives a group-level description of the direction and typical size of change in each condition. The standard deviation describes the spread of individual values around that mean. These summaries help readers distinguish the group average from the variation among participants.

Body mass is used to examine whether the two meal-timing conditions were associated with different average changes over their respective study periods. A group mean does not describe every participant’s experience, and the mean difference alone does not show how individual changes were distributed. The registry’s stated endpoint is body mass; other measures mentioned in the study summary, such as adiposity, energy metabolism, and gene expression, are not posted as secondary results in this record.

7. Results Posted in the Registry

• Delayed Eating Condition: mean -2.19 versus -2.11 on control; difference -0.08 (95% CI -1.77 to 1.60), standardized effect d = -0.02; z-test p = 0.924.

8. Statistical Interpretation

9. Statistical Methods Explained

Body mass is a continuous outcome, and the registry reports means and standard deviations for the two eating conditions. A mean is the arithmetic average of the observed values. A standard deviation describes how much those values vary around the mean; it is not the uncertainty in the mean itself. The reported standard deviations were 3.837 kg for daytime eating and 2.724 kg for delayed eating. They describe variation in the condition-specific changes among the participants represented in those summaries.

What does the mean difference represent?

The mean difference is reported as delayed eating minus daytime eating. Its estimate was -0.082 kg. A negative estimate means the reported average change in the delayed condition was lower than the reported average change in the daytime condition, using that subtraction order. It is a contrast of group averages, not a statement about the direction of change for every participant.

What does the confidence interval add?

A confidence interval expresses uncertainty around an estimate. In general, it gives a range of values compatible with the observed data and the assumptions of the statistical procedure. The interval reported for this contrast runs from -1.766 to 1.602 kg. Because it includes zero, the posted data do not distinguish a nonzero difference from no difference at the conventional threshold indicated by the unadjusted p-value. The interval should be read together with the estimate: a value close to zero does not, by itself, make the estimate precise.

How should the p-value be read?

The unadjusted p-value was 0.924. In general, a p-value describes how unusual the data, or results more extreme than the observed result, would be under a specified null model. It is not the probability that the null hypothesis is true, nor does it quantify the chance that the result will be replicated. The record does not report the exact test or model used, so the p-value should not be attributed to a more specific procedure than the registry states.

Why does the crossover structure matter?

In a crossover study, each participant receives more than one condition. This can allow a comparison that accounts for measurements from the same people, which may be correlated. In general, using within-person information can affect both the estimated uncertainty and the analysis. The registry identifies the design as crossover and reports 30 participants completing both conditions, but it does not state how the comparison handled this dependence, the order of conditions, or any period or carryover effects. The analysis approach is therefore not reported in the registry record.

The condition-specific means and standard deviations are descriptive summaries. The posted comparison gives a mean difference, confidence interval, and unadjusted p-value. The registry lists no posted analyses, and the calculation method for the comparison is not reported. These limitations matter because details of the model and its assumptions are needed to fully evaluate how the interval and test were obtained.

10. Confidence Intervals and Precision

The mean difference in body-mass change was -0.082 kg, with a 95% confidence interval from -1.766 to 1.602 kg. The estimate is close to zero, but the interval is wide in relation to that estimate and covers both negative and positive differences. Thus, the posted estimate alone is not a precise indication of the direction or size of the contrast.

In general, a confidence interval reflects sampling uncertainty under the assumptions of the method used. It is not a range containing every individual participant’s change, and it does not guarantee that the true value lies within the interval. Its interpretation depends on the analysis model. The specific model and method used to calculate this interval are not reported in the registry record.

The interval includes zero, and the unadjusted p-value is 0.924. Together, these statistics indicate that the posted comparison does not identify a clear difference between conditions. They do not demonstrate equivalence or rule out potentially meaningful differences. The endpoints of the interval allow a range of interpretations, so the estimate should be read with that uncertainty in mind.

The result is based on the 30 participants who completed both conditions. The record does not state how missing data were handled or whether the analysis included any participants beyond those with completed condition data. That missing information limits assessment of whether the reported precision reflects all randomized participants or only those with available measurements.

11. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm, not total event counts. They are illustrations based on the observed effect, not the original design assumptions for the trial; those original assumptions are not reported in the registry record. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. For each scenario, the effect to detect is the stated fraction of the observed effect.

For 100% of the observed effect, the illustration gives 25,848 participants per arm for 80% power and 34,603 participants per arm for 90% power. For 75% of the observed effect, the figures are 45,952 and 61,517 participants per arm, respectively. For 50% of the observed effect, they are 103,392 and 138,412 participants per arm.

In general, power is the probability that a study’s statistical test will detect an effect of a specified size if that effect is present, under the planning assumptions. The 80% and 90% columns describe different target probabilities for detecting the assumed effect. A smaller target effect requires more participants to detect under otherwise unchanged assumptions. These figures are planning illustrations, not observed power. They should not be read as a recommendation for a future study without considering its design, outcome, and assumptions.

12. How the Sample Size Is Derived

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

Formula

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

Worked calculation for this trial

1. Observed difference Δ = -0.082; pooled standard deviation σ = 3.327.
2. n = 2 × (1.96 + 0.842)² × 3.327² / -0.082² = 25,847.9, rounded up to 25,848 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 <- -0.0819999999999999                      # observed difference in means
sigma <- 3.32741739040957                     # 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(3354169)
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 = 25,848 (80% power), 34,603 (90% power)
 75% of observed effect: n per arm = 45,952 (80% power), 61,517 (90% power)
 50% of observed effect: n per arm = 103,392 (80% power), 138,412 (90% power)
power.t.test: 25848.8 
Simulated power at n = 25,848 per arm: 0.807 (20000 replicates)

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

13. Multiplicity, Missing Data and Analysis Populations

The registry lists four outcome measures but reports zero posted analyses and zero posted secondary results. The primary outcome is body-mass change. The registry record does not provide a complete analysis plan describing which outcomes were tested, how hypotheses were prioritized, or whether any adjustment for multiple comparisons was planned or performed. The posted p-value is identified as unadjusted.

Multiplicity arises when several outcomes, comparisons, or analyses are examined. In general, conducting more tests can increase the chance of at least one apparently notable result by chance. Whether and how that issue applies depends on the prespecified outcomes and analysis plan, which are not reported in the registry record. The available information does not support conclusions about whether multiplicity was controlled.

The record reports 30 participants completing both eating conditions and six withdrawn before completing at least two assessment visits. It separately describes two participants who were withdrawn before randomization and were not included in data analysis. The approach to missing measurements, including any imputation, exclusion criteria after randomization, or sensitivity analyses, is not reported in the registry record.

The record does not state whether the primary analysis followed an intention-to-treat, per-protocol, or other analysis population. It also does not explain how the crossover structure, condition sequence, or incomplete assessments were handled statistically. Without these details, readers cannot determine whether the posted comparison represents all randomized participants or only those with complete measurements, beyond the reported completion counts.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent non-serious adverse event terms

The serious adverse event figures report zero events among 36 participants at risk in the daytime eating group and zero among 36 at risk in the delayed eating group. The non-randomized participant group also had zero serious events among two participants at risk. Deaths were reported as zero in each group.

These are registry counts over the record’s reported safety information. A zero count means no serious adverse events were recorded for that group in the posted figures; it does not establish that an event could not occur. The safety groups list 36 at risk for each randomized condition, while the primary outcome reports 30 participants completing both conditions. The record does not explain the relationship between these safety denominators and the outcome population.

Other adverse events were reported for six of 36 at risk in each eating-condition group and two of two non-randomized participants. The registry does not provide serious adverse event terms. These counts should be kept separate from the primary body-mass comparison: they do not determine whether the mean weight changes differed.

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

The posted results describe mean body-mass changes of -2.107 kg in the daytime eating condition and -2.189 kg in the delayed eating condition among 30 participants who completed both conditions. The estimated mean difference was -0.082 kg, with a 95% confidence interval from -1.766 to 1.602 kg. The unadjusted p-value was 0.924. Taken together, the estimate is close to zero, while the interval leaves substantial uncertainty about the contrast’s direction and size.

These results do not establish that the two conditions are equivalent. Equivalence requires a prespecified margin defining which differences would be considered sufficiently small, along with an analysis designed to assess that question. Such a margin and an equivalence analysis are not reported in the registry record. Likewise, a result that does not identify a difference does not prove that no difference exists.

The result concerns the registry’s primary endpoint and the participants with completed condition data. It does not establish what would happen in other populations, under other meal schedules, or over other periods. The study summary mentions adiposity, energy metabolism, and gene expression as areas of interest, but secondary results for these outcomes are not posted in the record.

The registry supports a cautious description of the observed averages and uncertainty, not a medical recommendation or a claim that one eating condition is superior. Interpretation is also limited by missing details about the statistical model, handling of missing measurements, and crossover analysis.

16. Why This Trial Matters Statistically

This trial is statistically interesting because its crossover design compares two eating conditions experienced by participants, rather than assigning separate groups to experience only one condition. In general, measurements from the same participant may be related. A suitable analysis can account for that relationship, but the registry does not report how the crossover structure was incorporated in the primary comparison.

The posted mean difference is small in magnitude, while its confidence interval spans negative and positive values. This illustrates why a point estimate should not be read without its uncertainty. A near-zero estimate is not equivalent to proof of no effect, particularly when the interval is broad enough to include contrasting possibilities.

The record also shows how sample-size planning can be sensitive to the effect chosen for detection. Its planning illustrations use fractions of the observed effect, and the participant counts increase as the target effect becomes smaller. Because these are planning calculations rather than the trial’s original design assumptions, they cannot explain why the trial enrolled its reported number of participants.

Finally, the difference between the outcome completion count and the safety denominators, together with unreported analysis and missing-data details, highlights the importance of understanding who contributes to each result. These issues are central to evaluating precision and the population to which a reported estimate applies.

17. Limitations

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

The registry does not report the statistical model or test used to estimate the primary mean difference, or whether the analysis accounted for repeated measurements within participants in the crossover design. It also does not describe the condition sequence, any washout period, or how period and carryover effects were considered. These omissions make it difficult to assess the assumptions behind the interval and p-value.

The reported primary outcome includes 30 participants completing both conditions. Six participants were withdrawn before completing at least two assessment visits, while two participants were withdrawn before randomization and excluded from data analysis. The handling of missing outcome data and the primary analysis population are not reported. The safety denominators are 36 for each randomized condition, and the registry does not explain how those denominators relate to the primary outcome population.

The record does not report the original sample-size justification, analysis plan, multiplicity approach, or any interim analyses. It lists four outcome measures but no posted analyses or secondary results. The registry does not give confidence intervals for the condition-specific means, and no adjusted primary estimate is posted. These limitations constrain conclusions about the precision and robustness of the primary comparison.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Daytime vs. Delayed Eating Among Obese Individuals — NCT03354169.
• Registry record last updated 2025-11-21; status last verified 2025-11.
• Results first posted 2025-11-21.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The registry record describes NCT03354169, a randomized, unmasked crossover study of daytime versus delayed eating among obese individuals. The two conditions each lasted 8 weeks, with meals and snacks scheduled between 0800 and 1900 or between 1200 and 2300. Thirty participants completed both conditions.

The primary outcome was change in body mass. Mean changes were -2.107 kg during daytime eating and -2.189 kg during delayed eating. The mean difference was -0.082 kg, with a 95% confidence interval from -1.766 to 1.602 kg and an unadjusted p-value of 0.924. The registry also reports zero serious adverse events in each group. Details of the primary analysis and missing-data handling are not reported in the registry record.