The Effects of Formula Diet on Body Weight, Body Composition, and Biomarkers for Disease Compared to a Standard Diet: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for The Effects of Formula Diet on Body Weight, Body Composition, and Biomarkers for Disease Compared to a Standard Diet (NCT00138645), a randomized phase 4 study. The primary outcome is Percent Change in Body Weight (Completers)..

2. Clinical Question

3. Trial Design

The registry record identifies this as a Phase 4, randomized, single-masked, parallel-group trial, with enrollment of 60. The listed sponsor is Pennington Biomedical Research Center. The record lists the trial status as completed, a start in 2005-04, and primary completion in 2006-05. Details of how randomization was generated or implemented, who was masked, and how masking was maintained are not reported in the registry record.

The two behavioral groups were MicroDiet and Healthy Diet. Both were described as having a 1200 kcal/day prescription. The MicroDiet description specifies meal replacements for two meals each day for Months 1 through 3 and meal plans for the meal not replaced. The Healthy Diet description specifies a traditional food-based diet using the same foods as those meal plans. The registry record's intervention descriptions are not a complete account of all counseling, adherence procedures, or subsequent diet instructions.

The primary outcome is percent change in body weight at 24 weeks, reported for completers. The group summaries include 24 MicroDiet completers and 23 Healthy Diet completers. These outcome counts are distinct from the enrollment figure. The registry record does not explain the flow from enrollment to the completer counts, identify reasons for non-completion, or report an analysis based on all randomized participants.

Secondary outcomes listed include changes in body composition and disease biomarkers at Months 3 and 6, and subjective appetite ratings at Week 2 and Months 1, 2, 3, 4, 5, and 6. Three secondary outcomes are posted, while the registry lists five outcome measures overall. The analysis details for these outcomes are not reported in the registry record. A planned sample-size rationale and the trial's original statistical design assumptions are also 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 Percent Change in Body Weight (Completers)., measured over 24 weeks.

The primary endpoint is percent change in body weight from baseline to week 24 among completers. It is expressed as a change in percent of baseline body weight. This type of measure expresses the change relative to each participant's starting weight rather than as an absolute change in weight units. The registry reports least-squares means for the groups, with standard errors as the measure of dispersion.

Body weight is the outcome named in the endpoint, while body composition, disease biomarkers, health parameters, and appetite are among the other outcomes described in the registry hypotheses or secondary-outcome list. They should not be treated as interchangeable with the primary endpoint. In particular, the primary result alone does not provide the results for those other outcomes.

The endpoint can be used to compare the groups' average reported change over the stated follow-up period. The comparison is based on completers, so it describes the participants included in that reported analysis rather than necessarily all participants enrolled or randomized. The registry record does not report further endpoint details such as the exact handling of measurements outside the stated timeframe or how least-squares means were estimated.

7. Results Posted in the Registry

• Healthy Diet: mean 7.00 versus 7.30 on control; difference -0.30 (95% CI -3.90 to 3.30), standardized effect d = -0.05; z-test p = 0.870.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: it is a numerical measure of percent change in body weight. The posted group summaries are least-squares means, and their accompanying dispersion is reported as a standard error. A mean describes the center of a set of observations, while a standard error describes the uncertainty in an estimated mean. These are different from the spread of individual participant measurements.

What does the mean difference represent?

The comparison is reported as Healthy Diet relative to MicroDiet. Its estimate of -0.3 is obtained from the two posted group means: 7.0 for Healthy Diet and 7.3 for MicroDiet. It represents the estimated difference between the group means on the endpoint's scale, not a difference in individual responses and not an effect for every participant. The sign reflects the stated comparison order; reversing the order would reverse the sign without changing the underlying contrast.

Least-squares means are model-based adjusted means in general statistical usage. The registry identifies the reported parameter as a least-squares mean, but the model terms, covariates, and estimation procedure are not reported in the registry record. It is therefore not possible to describe which adjustments, if any, distinguish these means from simple arithmetic averages.

How should the confidence interval be understood?

A confidence interval expresses uncertainty around an estimate. In general, intervals generated by a procedure with a stated confidence level would cover the target value at that level over repeated use of the procedure, if its assumptions hold. For the mean difference, the posted interval is -3.903 to 3.303. Since the range includes zero, the data do not rule out a zero difference under the interval's calculation. Its endpoints also allow differences in both directions, so the estimate does not pin down the size or direction precisely.

The comparison statistics include a pooled standard deviation of 6.303 and an effect-size estimate of -0.048. These are comparison-scale summaries accompanying the posted result. The standard deviation concerns variation in observations, whereas the standard errors of 1.3 attached to each group mean describe uncertainty in those means. The comparison calculation labels the pooled standard deviation as approximate; the posted results do not provide participant-level data to independently assess that approximation.

What does the p-value add?

The unadjusted p-value is 0.87. In general, a p-value measures compatibility between the observed data and a specified null model, assuming the model and analysis are appropriate. A large p-value is not evidence that the null is certainly true, and a small p-value would not by itself establish clinical importance. Here, the estimate and confidence interval are also important: they show the range of differences that remain compatible with the posted result.

The p-value is explicitly unadjusted. Whether the primary test was selected in advance, whether other tests were considered in a common family, and whether any multiplicity procedure was used are not reported in the registry record. The registry record also does not report the full statistical analysis plan, model assumptions, or any interim analyses.

What can be inferred from the analysis population?

The endpoint is explicitly described as being for completers. This means the reported group summaries concern those included as completers, rather than a stated analysis of all randomized participants. In general, restricting analysis to completers can affect how well a randomized comparison preserves the balance created by randomization if completion is related to participant characteristics or outcomes. Whether that occurred cannot be determined from these summary statistics. Reasons for missing outcome data, methods for handling missingness, and sensitivity analyses are not reported in the registry record.

Randomization is listed, but its sequence generation, concealment, and implementation are not described. Single masking is also listed without specifying who was masked. These design details matter when judging possible bias, but cannot be reconstructed from the group estimates. The posted result is best interpreted as the registry's completer-based comparison, with the design and analysis details that remain unreported kept distinct from what the estimates directly show.

10. Confidence Intervals and Precision

The estimated mean difference in percent change in body weight is -0.3 for Healthy Diet relative to MicroDiet. Its 95% confidence interval runs from -3.903 to 3.303. This interval is the central evidence about precision: it spans zero and includes possible differences in either direction. The posted estimate is therefore not precise enough to determine that the group means differ, or to establish that any difference is negligible.

Precision concerns how narrowly the data locate an estimate, not whether an estimate is important. A confidence interval is not a guarantee that the true value lies within its endpoints. In general, it describes uncertainty under the statistical procedure and its assumptions. The registry record does not report the full model or all assumptions used to obtain the interval, so the interval should be interpreted as the posted analysis's uncertainty statement rather than as a complete account of model validity.

The group means are based on 24 MicroDiet and 23 Healthy Diet completers. The registry does not report why these participants, rather than the full enrollment of 60, are represented in the endpoint summaries. If missing outcome data or completion are related to the outcome, the interval's sampling uncertainty alone would not capture that concern. The registry record does not provide missing-data sensitivity analyses.

The standard errors for the group means are 1.3 in each arm. They are not the same as the confidence interval for the between-group difference. The uncertainty about the contrast is summarized directly by its own interval, which is the appropriate range to use when describing the estimated group comparison.

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 sample-size figures are planning illustrations based on the observed effect, not the trial's original design calculation. For this continuous outcome, the figures are participants per arm, not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row considers an effect to detect stated as a fraction of the observed effect. The effect fractions are 100%, 75%, and 50% of the observed effect.

The 80% power column gives the planned number of participants per arm for a design that would have an 80% chance of detecting the selected effect under those assumptions, if that effect were the true one and the statistical model were appropriate. The 90% power column gives the corresponding per-arm planning figure for a 90% chance under the same conditions. For the 100% fraction, the figures are 6,931 participants per arm for 80% power and 9,278 for 90% power. For 75% of the observed effect, they are 12,321 and 16,494. For 50% of the observed effect, they are 27,722 and 37,112.

Smaller effects require more participants to distinguish them from random variation at the same significance level and target power. The displayed calculations use the observed effect as their starting point; they do not establish that this is the effect the trial was designed to detect. These figures are not observed power. The registry record does not report the trial's own sample-size justification or original design assumptions, so the planning display should not be read as evidence that the trial was adequately or inadequately sized under its original protocol.

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 = -0.300; pooled standard deviation σ = 6.303.
2. n = 2 × (1.96 + 0.842)² × 6.303² / -0.300² = 6,930.3, rounded up to 6,931 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 <- -0.3                      # observed difference in means
sigma <- 6.30347346926897                     # 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(138645)
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 = 6,931 (80% power), 9,278 (90% power)
 75% of observed effect: n per arm = 12,321 (80% power), 16,494 (90% power)
 50% of observed effect: n per arm = 27,722 (80% power), 37,112 (90% power)
power.t.test: 6931.3 
Simulated power at n = 6,931 per arm: 0.798 (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 record lists one primary endpoint and three secondary outcomes as posted. The broader outcome description includes body composition, disease biomarkers, and appetite ratings, while the trial hypotheses also mention health parameters such as blood pressure and lipids. The record lists five outcome measures overall. The primary comparison's p-value is unadjusted. Whether tests across the primary and secondary outcomes were treated as a family, and whether any correction for multiple testing was planned or used, are not reported in the registry record.

Multiplicity matters because examining multiple outcomes or time points can increase the chance of at least one apparently unusual result by chance. In general, adjustment procedures can change the threshold or interpretation for a collection of tests. No particular procedure should be assumed for this trial. The registry record does not report a multiplicity plan, a prespecified testing hierarchy, or results for all the listed secondary assessments in the registry record for this analysis.

The primary outcome is reported for completers, with 24 in MicroDiet and 23 in Healthy Diet. Enrollment was 60. The registry record does not report participant flow, reasons for missing outcomes, the number originally randomized to each arm, or a detailed definition of completer. It also does not report how missing measurements were handled, whether imputation was used, or whether sensitivity analyses assessed alternative missing-data assumptions.

Because the primary analysis is identified as completer-based, its population differs in description from an analysis of all randomized participants. In general, a randomized analysis population can help retain the comparison created by random assignment, while a completer analysis may be affected if completion relates to outcomes or participant characteristics. The posted summaries do not establish whether such effects occurred. The registry record does not report an intention-to-treat analysis, interim analyses, or the trial's full statistical analysis plan.

14. 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 lists 30 participants at risk for serious adverse events in each group. It reports 0 serious adverse events in MicroDiet and 0 in Healthy Diet. For other adverse events, it also lists 30 participants at risk in each group and 0 events in each group. No serious adverse event terms are listed. Death counts are not reported in the registry record.

These figures describe the adverse-event counts and at-risk denominators recorded for the two groups. A recorded count of zero is not proof that no event could occur, and it does not establish that the interventions have no risks. The registry information does not provide event definitions, collection procedures, exposure time, severity details for other events, or additional safety analyses. The groups' at-risk figures should not be substituted for the completer counts used in the primary endpoint analysis, since they describe a different part of the record.

The safety figures are limited to the registry's reported counts. They do not establish a comparative safety profile or account for events that may not have been captured or reported. No medical conclusion should be drawn from the absence of recorded events alone.

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

The primary result is a comparison of average percent change in body weight among completers at 24 weeks. The posted means are 7.3 for MicroDiet and 7.0 for Healthy Diet, with an estimated mean difference of -0.3 for Healthy Diet relative to MicroDiet. The confidence interval spans -3.903 to 3.303, and the unadjusted p-value is 0.87. Taken together, these statistics do not establish a difference in the group means, while leaving a range of possible differences compatible with the estimate.

This result does not establish that the diets are identical. The interval includes zero but also extends to values on either side of zero. Nor does the result establish equivalence: the registry record does not report an equivalence margin or a non-inferiority objective. A conclusion about equivalence would require a suitably defined margin and analysis, not simply a non-significant test.

The result does not show whether MicroDiet or Healthy Diet affected body composition, biomarkers, blood pressure, lipids, or appetite. Those are separate questions named in the hypotheses or secondary-outcome descriptions. The primary body-weight result cannot be used as a substitute for results on those outcomes. The information available for the primary comparison also does not establish effects beyond the 24-week timeframe.

The estimate applies to the reported completers. The registry record does not explain the outcome counts relative to enrollment or report missing-data analyses, so the extent to which the result represents all randomized participants cannot be determined from these registry entries. Details such as the masking roles, randomization procedure, analysis model, and multiplicity approach are also not reported in the registry record. These limits affect how broadly and confidently the estimate can be interpreted, without changing what the posted completer-based comparison says.

More generally, a p-value is not a measure of treatment benefit, and the observed group means do not identify what any one participant experienced. The appropriate statistical reading is narrower: the reported average contrast is close to zero, its interval is broad enough to include differences in either direction, and the result does not resolve the full set of trial hypotheses.

16. Why This Trial Matters Statistically

This trial illustrates why an estimated group difference should be read alongside its confidence interval. The mean difference is -0.3, but the interval from -3.903 to 3.303 makes clear that the estimate is uncertain and compatible with multiple possible contrasts. A p-value of 0.87 alone would not convey that range or show whether the data rule out effects that might matter in a particular context.

It also demonstrates the importance of keeping the analysis population in view. The primary result is explicitly for completers, with 24 MicroDiet and 23 Healthy Diet participants, while total enrollment is 60. The distinction does not prove that the estimate is biased, but it makes participant flow and missing-data methods relevant to interpretation. Those details are not reported in the registry record.

The registry hypothesis covers several kinds of outcomes, including body weight, body composition, biomarkers, health parameters, and appetite. A single primary outcome estimate cannot resolve all of these questions. With multiple outcomes or time points, prespecified analysis and multiplicity handling are important for interpreting the collection of results; those methods are not reported in the registry record.

Finally, the planning illustration makes a useful distinction between an observed estimate and a design target. It uses fractions of the observed effect and explicit assumptions, rather than documenting the original rationale for enrollment. This emphasizes that post hoc planning figures are not a replacement for a trial's own prospective sample-size justification. The registry record does not report that original justification.

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 primary outcome is described for completers, and its reported group counts are 24 and 23 against enrollment of 60. Participant flow, group-specific enrollment or randomization counts, reasons for not appearing in the endpoint analysis, and missing-data handling are not reported in the registry record. The relationship between the completer analysis and the full randomized population therefore cannot be assessed from the posted summary statistics.

The record identifies randomization and single masking but does not report the randomization method, allocation concealment, who was masked, or whether masking was maintained. It identifies least-squares means but does not report the model, covariates, assumptions, or full analysis plan. The comparison uses an approximate pooled standard deviation, and participant-level data are not available in the registry record to evaluate that approximation independently.

The result concerns percent change in body weight at 24 weeks. It does not supply the findings for the listed secondary outcomes, nor does it establish effects outside the stated endpoint timeframe. Multiplicity methods, any interim analyses, and the primary endpoint's prespecification details are not reported in the registry record. The record also does not report an equivalence or non-inferiority margin, which limits any interpretation that would claim the diets are equivalent.

The intervention descriptions identify the prescribed energy intake and some meal-replacement details, but further information about adherence, exposure, and implementation is not reported in the registry record. Safety reporting lists no serious or other adverse events in the stated at-risk groups, but definitions and ascertainment methods are not reported. These gaps do not negate the posted result; they constrain how fully its reliability, generalizability, and scope can be evaluated.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: The Effects of Formula Diet on Body Weight, Body Composition, and Biomarkers for Disease Compared to a Standard Diet — NCT00138645.
• Registry record last updated 2016-02-08; status last verified 2016-01.
• Results first posted 2009-06-10.
• 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 a completed, randomized, single-masked, parallel-group Phase 4 trial sponsored by Pennington Biomedical Research Center, with enrollment of 60. It compares the behavioral interventions MicroDiet and Healthy Diet. Both are described with a 1200 kcal/day prescription, while MicroDiet includes meal replacements during Months 1 through 3.

The primary endpoint is percent change in body weight from baseline to week 24 among completers. Posted least-squares means are 7.3 for MicroDiet and 7.0 for Healthy Diet, with an estimated difference of -0.3, a 95% confidence interval from -3.903 to 3.303, and an unadjusted p-value of 0.87. The result does not establish a difference between group means and remains compatible with differences in either direction.

The primary outcome counts are 24 and 23 completers. Missing-data methods, the original sample-size rationale, detailed analysis methods, and multiplicity procedures are not reported in the registry record. Serious and other adverse-event counts are 0 in each group among 30 participants at risk per group.