This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for The Personalized Nutrition Study (NCT04145466), a randomized na study. The primary outcome is Weight Change.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT04145466 |
| Phase | NA |
| Condition | Weight Loss |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Single |
| Enrollment | 145 |
| Arms in the primary outcome | 4 |
| Lead sponsor | Pennington Biomedical Research Center |
| Results posted | Yes |
2. Clinical Question
Population
Participants in a randomized study of a genetically informed weight-loss approach. The registry record lists Weight Loss as the condition and reports enrollment of 145. The population description and further eligibility details are not reported in the registry record.
Intervention
A high-fat diet or a high-carbohydrate diet, with participants categorized as Fat Responders or Carbohydrate Responders. The arm descriptions assign each responder category to each of the two diets.
Comparator
The posted primary comparisons use Fat Responders (1), the high-fat diet arm, as the reference. The other arms are Carbohydrate Responders (1) on a high-fat diet, Fat Responders (2) on a high-carbohydrate diet, and Carbohydrate Responders (2) on a high-carbohydrate diet.
Primary question
How did mean weight change from baseline to 12 weeks compare between each of the other three arms and Fat Responders (1)? The study description also frames a broader question: whether people classified as carbohydrate responders or fat responders lose more weight on the diet hypothesized to suit that category. A direct statistical test of that broader responder-by-diet question is not reported in the registry record.
The stated hypotheses concern whether genetic responder classification relates to weight loss on diets differing in carbohydrate and dietary fat content. The registry record describes a randomized controlled trial intended to test those hypotheses. Its posted results present four arm means and three comparisons against one reference arm. Those comparisons help describe differences among the assigned groups, but they do not by themselves establish whether the relationship between responder classification and diet assignment differs across diets. That distinction matters when interpreting the study’s motivating hypothesis: evidence about individual arm contrasts is not automatically a formal test of the proposed matching effect.
3. Trial Design
This was a randomized, single-masked, parallel-group study. The registry lists the study as completed, with enrollment of 145. The recorded start date is 2020-02-27 and the primary completion date is 2021-12-21. The registry lists phase as NA and names Pennington Biomedical Research Center as the sponsor. Further details about the masking procedure, randomization implementation, allocation concealment, and study sites are not reported in the registry record.
The interventions were behavioral dietary assignments: a high-fat diet and a high-carbohydrate diet. The four arm descriptions cross the two diets with the Fat Responder and Carbohydrate Responder categories. Fat Responders (1) and Carbohydrate Responders (1) received the high-fat diet; Fat Responders (2) and Carbohydrate Responders (2) received the high-carbohydrate diet. The record does not explain how the responder categories were determined, whether participants were assigned within responder strata, or how the category labels were defined.
Weight Change was the primary outcome, measured from baseline to 12 weeks as weight at 12 weeks minus weight at baseline. The posted analysis summarizes the mean and standard deviation for each arm and gives mean differences against Fat Responders (1). It also lists six secondary outcome names, while numerical results are posted for three of them. The planned sample size, original sample-size assumptions, detailed statistical analysis plan, analysis populations, and handling of missing measurements are not reported in the registry record.
Enrollment is not the same as the number with a posted primary outcome: the arm-level primary outcome counts are 44.0, 21.0, 41.0, and 16.0. The registry does not explain the relationship between enrollment and these outcome counts. These counts describe the posted arm summaries and should not be treated as proof of a particular analysis population or missing-data procedure.
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
| Stage | Fat Responders (1) | Carbohydrate Responders (1) | Fat Responders (2) | Carbohydrate Responders (2) |
|---|---|---|---|---|
| STARTED | 50 | 23 | 49 | 23 |
| COMPLETED | 46 | 22 | 43 | 18 |
| NOT COMPLETED | 4 | 1 | 6 | 5 |
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: Includes participants that completed the study and were included in the analysis. Of the 129 participants that completed the study, 7 participants were incorrectly genotyped and were not included in the final analysis.
| Characteristic | Unit | Fat Responders (1) | Carbohydrate Responders (1) | Fat Responders (2) | Carbohydrate Responders (2) | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 44 | 21 | 41 | 16 | 122 | |
| Age, Continuous | years | 57.4 (SD 11.5) | 49.8 (SD 14.1) | 54.4 (SD 14.2) | 52.4 (SD 13.0) | 54.4 (SD 13.2) |
| Sex: Female, Male: Female | Participants | 37 | 17 | 35 | 13 | 102 |
| Sex: Female, Male: Male | Participants | 7 | 4 | 6 | 3 | 20 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Asian | Participants | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 12 | 9 | 10 | 5 | 36 |
| Race (NIH/OMB): White | Participants | 30 | 12 | 31 | 10 | 83 |
| Race (NIH/OMB): More than one race | Participants | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 2 | 0 | 0 | 1 | 3 |
| Weight | kg | 94.2 (SD 14.0) | 95.2 (SD 17.6) | 93.5 (SD 14.4) | 95.6 (SD 18.1) | 94.3 (SD 15.2) |
6. Primary Endpoint
The registry lists the primary outcome as Weight Change, measured over Baseline to 12 weeks.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | kg |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is Weight Change, expressed in kg, from baseline to 12 weeks. It is defined as weight at 12 weeks minus weight at baseline. A negative value therefore denotes a lower measured weight at the 12-week assessment than at baseline; a positive value would denote a higher measured weight. The registry reports the endpoint as a mean with a standard deviation for each arm.
Weight change is used to quantify the change in body weight over the stated follow-up interval and to compare average changes between groups. The arm summaries give the mean change and its spread among participants included in each posted summary. The mean difference contrasts each listed arm with Fat Responders (1). It describes the difference between those group means, not the change for an individual participant and not a direct measure of how consistently individuals changed.
The registry’s description makes weight change the primary measure for testing the study’s dietary hypotheses. That choice identifies what the primary outcome represents, but it does not establish what clinically meaningful difference was prespecified. A threshold for meaningful change, the method for measuring weight, and details about visits or adherence are not reported in the registry record. The 12-week timeframe also defines the period represented by these results; it does not provide evidence about outcomes beyond that assessment.
7. Results Posted in the Registry
- Carbohydrate Responders (1): mean -4.10 versus -5.50 on control; difference 1.40 (95% CI 0.59 to 2.21), standardized effect d = 1.02; z-test p = <0.001.
- Fat Responders (2): mean -5.30 versus -5.50 on control; difference 0.20 (95% CI -0.33 to 0.73), standardized effect d = 0.16; z-test p = 0.462.
- Carbohydrate Responders (2): mean -5.10 versus -5.50 on control; difference 0.40 (95% CI -0.46 to 1.26), standardized effect d = 0.30; z-test p = 0.362.
Mean difference: Carbohydrate Responders (1)
95% CI: 0.59 to 2.21
Recalculated from the posted summary statistics
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.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Change in Waist Circumference | Continuous Endpoint | Mean difference | 0.80 (-0.27 to 1.87) | 75 per arm |
| Change in Food Cravings | Continuous Endpoint | Mean difference | -0.20 (-0.31 to -0.09) | 16 per arm |
| Change in Fat Preference Index | Continuous Endpoint | Mean difference | 0.00 (-0.24 to 0.24) | n/a |
Change in Waist Circumference
- 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 deviations.
- Result:
- Carbohydrate Responders (1): mean -4.20 versus -5.00 on control; difference 0.80 (95% CI -0.27 to 1.87), standardized effect d = 0.46; z-test p = 0.142.
- Fat Responders (2): mean -4.40 versus -5.00 on control; difference 0.60 (95% CI -0.02 to 1.22), standardized effect d = 0.41; z-test p = 0.057.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Carbohydrate Responders (1) and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Fat Responders (2) and the control. The interval gives the range of effects that remain compatible with the data.
Change in Food Cravings
- 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 deviations.
- Result:
- Carbohydrate Responders (1): mean -0.50 versus -0.30 on control; difference -0.20 (95% CI -0.31 to -0.09), standardized effect d = -1.00; z-test p = <0.001.
- Fat Responders (2): mean -0.30 versus -0.30 on control; difference 0.00 (95% CI -0.09 to 0.09), standardized effect d = 0.00; z-test p = 1.000.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Carbohydrate Responders (1) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Fat Responders (2) and the control. The interval gives the range of effects that remain compatible with the data.
Change in Fat Preference Index
- 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 deviations.
- Result:
- Carbohydrate Responders (1): mean 0.00 versus 0.00 on control; difference 0.00 (95% CI -0.24 to 0.24), standardized effect d = 0.00; z-test p = 1.000.
- Fat Responders (2): mean 0.00 versus 0.00 on control; difference 0.00 (95% CI -0.19 to 0.19), standardized effect d = 0.00; z-test p = 1.000.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Carbohydrate Responders (1) and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Fat Responders (2) and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes broaden the description beyond weight change to include waist circumference, food cravings, fat preference, disinhibition, hunger, and cognitive restraint. Numerical results are posted for waist circumference, food cravings, and fat preference; the other named outcomes do not have numerical results in the registry record. The available secondary measures therefore give an incomplete view of the wider set of outcomes named for the study.
Overall, the secondary summaries do not give a single consistent pattern that independently establishes the study’s genetic responder-by-diet hypothesis. They include contrasts that differ in magnitude and direction, and some reported intervals include zero while others do not. These outcomes are related to the study’s broader dietary and behavioral context, but they are not substitutes for the primary weight-change outcome. Their interpretation also depends on the exact arm comparisons, which use Fat Responders (1) as the reference.
Secondary results can help describe what else changed during the study period, but they should generally carry less confirmatory weight than a prespecified primary analysis. The registry does not report which secondary analyses were prespecified, how many were planned, or whether any adjustment for multiple testing was applied. When several outcomes and comparisons are examined, some results may appear more unusual by chance alone. The posted unadjusted results do not address that issue.
The primary findings and secondary summaries should therefore be considered together without treating one secondary contrast as decisive evidence for the main hypothesis. The registry record does not report a combined analysis across outcomes, a hierarchy for interpreting them, or a formal synthesis. Numerical findings should be read as outcome-specific descriptions over baseline to 12 weeks, with the limitations of the posted comparisons and uncertainty kept in view.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Change in Waist Circumference
- Change in Food Cravings
- Change in Fat Preference Index
- Change in Disinhibition
- Change in Hunger
- Change in Cognitive Restraint
9. Statistical Interpretation
The posted primary arm means are negative in all four groups: Fat Responders (1) had a mean change of -5.5 kg, Carbohydrate Responders (1) -4.1 kg, Fat Responders (2) -5.3 kg, and Carbohydrate Responders (2) -5.1 kg. These are group averages over baseline to 12 weeks. They do not describe every participant’s change or the distribution of individual outcomes.
Against Fat Responders (1), the mean difference for Carbohydrate Responders (1) is 1.4 kg, with a 95% confidence interval from 0.591 to 2.209 and an unadjusted p-value of <0.001. The mean difference for Fat Responders (2) is 0.2 kg, with a 95% confidence interval from -0.333 to 0.733 and an unadjusted p-value of 0.462. For Carbohydrate Responders (2), the mean difference is 0.4 kg, with a 95% confidence interval from -0.460 to 1.26 and an unadjusted p-value of 0.362. The interval for the latter two comparisons includes zero, so the posted estimates are compatible with no mean difference as well as with differences in either direction within the respective intervals.
The first contrast is between two responder categories assigned to the same high-fat diet. The other contrasts compare the high-carbohydrate arms with the high-fat Fat Responders (1) arm. Thus, these three comparisons are not a single direct test of whether a diet’s effect depends on responder category. The registry does not report a formal interaction test, a direct within-responder comparison between diets, or a prespecified contrast matching each responder category to the hypothesized diet. The posted comparisons should be read according to their actual arm pairings.
The p-values are unadjusted. They describe each contrast without accounting for the fact that several comparisons and outcomes are reported. They do not measure the size or importance of an effect, and they do not establish the probability that a hypothesis is true. The confidence intervals are useful alongside the p-values because they show ranges of estimates compatible with the observed data under the analysis assumptions.
The registry reports no sponsor analysis results in its analysis list, and no detailed primary analysis method is reported in the registry record. These comparisons are therefore best understood as the posted arm summaries and unadjusted contrasts, rather than as evidence that the study’s full planned analysis has been reproduced. The results describe measured group differences over 12 weeks; they do not, on their own, establish a causal genetic matching effect or a conclusion about longer-term outcomes.
10. Statistical Methods Explained
The primary measure is continuous: weight change in kg. The record reports a mean and standard deviation for each arm. A mean gives the average observed change among participants included in that arm’s summary. The standard deviation describes how spread out individual observations are around that average. It is not a confidence interval for the mean and does not show the range containing every participant’s result.
What does a mean difference represent?
Each posted mean difference compares one arm’s mean with the mean for Fat Responders (1). The estimated contrast is the second arm’s mean minus the reference arm’s mean. Because all arm means are negative, a positive contrast means the second arm’s mean change is less negative than the reference mean change; it does not mean that the second arm had a positive mean change. The contrast is an unadjusted difference between group averages, not a participant-level change and not an adjusted estimate accounting for other characteristics.
The comparison groups matter. Carbohydrate Responders (1) and Fat Responders (1) both received the high-fat diet, whereas Fat Responders (2) and Carbohydrate Responders (2) received the high-carbohydrate diet. A comparison of two arms on the same diet addresses a different question from a comparison across diets. A model that directly tests whether the difference between diets varies by responder category would address an interaction question. Such a test is not reported in the registry record.
How should a confidence interval be understood?
General explanation: a confidence interval represents uncertainty around an estimated quantity under a statistical procedure and its assumptions. For the posted mean differences, the intervals give a range of values compatible with the data under the calculation used. A narrower interval indicates greater precision than a wider interval, all else equal. An interval that includes zero does not prove that the groups are identical; it indicates that zero is among the values compatible with the interval. Nor does an interval that excludes zero show that an effect is clinically important. Clinical importance requires context and a meaningful-change criterion, which is not reported in the registry record.
The listed p-values are unadjusted. In general, a p-value assesses how incompatible the observed data are with a specified null model, assuming that model and the analysis conditions are appropriate. It is not the probability that the null hypothesis is true, and it does not describe effect magnitude. Because multiple arm contrasts and secondary outcomes appear in the record, unadjusted p-values do not account for the broader set of opportunities to identify apparently notable results.
Why does variation matter?
General explanation: statistical precision depends on both the amount of information and the variability of observations. Greater variability makes a group mean harder to estimate precisely when other factors are comparable. Standard deviations describe observed spread; standard errors describe uncertainty in an estimated quantity. The record includes standard errors for arm means within the comparison calculations, but it does not report the full statistical model, any covariate adjustment, or a detailed method for constructing the intervals and p-values. Those analytic details are not reported in the registry record.
The posted arm counts differ across groups, and the summaries are based on 44.0, 21.0, 41.0, and 16.0 participants, respectively. Unequal group sizes can affect precision, especially when combined with differing variability. The available summaries do not establish why the counts differ from one another or from the enrollment of 145. The analysis population and any procedures for missing data are not reported in the registry record.
What is the role of power planning?
The sample-size illustrations use the observed effect as a reference and show hypothetical participant counts per arm for specified fractions of that effect. They are planning illustrations based on the stated assumptions, not a record of the original trial design. General explanation: power is the probability that a study design will identify a specified effect under assumptions about the effect, variability, significance threshold, and analysis. The posted power columns therefore answer a planning question about future study sizes under those assumptions. They do not report the probability that the current study’s finding is correct.
For a continuous outcome, assumptions about effect size and variability shape how many participants are needed to distinguish a mean difference from random variation. Smaller target effects are harder to distinguish and generally require more participants. The original protocol’s sample-size justification and design assumptions are not reported in the registry record. The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, a normal approximation, and effect sizes defined as stated fractions of the observed effect.
What cannot be inferred from the posted summaries?
Arm means and standard deviations do not reveal how results were distributed, whether there were outliers, or whether assumptions for a particular analysis held. The record does not report diagnostic checks, covariate-adjusted results, subgroup methods, interim analyses, or a prespecified multiplicity strategy. It also does not report whether the comparisons were intended as primary contrasts or were calculated for descriptive presentation. Those omissions limit how specifically the analytical process can be reconstructed.
Random allocation is part of the design, but the posted contrasts do not alone show whether allocation was successfully implemented or whether every randomized participant contributed to each analysis. The registry does not report analysis by intention to treat, per-protocol analysis, adherence, or imputation. Accordingly, the results can be described as posted arm-level summaries and contrasts without asserting a particular analysis population or missing-data method.
11. Confidence Intervals and Precision
The precision of a mean difference is conveyed by its confidence interval as well as by the point estimate. For the comparison of Carbohydrate Responders (1) with Fat Responders (1), the estimated mean difference is 1.4 kg, and the 95% confidence interval runs from 0.591 to 2.209. The interval does not include zero, while still allowing a range of possible differences around the estimate. Its width reflects uncertainty in the contrast, not the range of individual participants’ weight changes.
For Fat Responders (2) compared with Fat Responders (1), the estimate is 0.2 kg, with a 95% confidence interval from -0.333 to 0.733. For Carbohydrate Responders (2), the estimate is 0.4 kg, with a 95% confidence interval from -0.460 to 1.26. Both intervals include zero and extend to values on either side of it. These intervals therefore do not isolate a direction of difference between the corresponding group means at the stated confidence level.
Confidence intervals are not guarantees that the true difference lies within a particular interval, and they do not account for sources of uncertainty omitted from the analysis. The record does not report adjustment for multiple comparisons, covariate modeling, or the detailed method used to derive the intervals. The posted intervals should therefore be interpreted as unadjusted estimates for the listed contrasts. A confidence interval also does not resolve whether an estimated difference is clinically meaningful; the registry does not report a threshold for that judgment.
Arm sizes are unequal, with primary outcome summaries based on 44.0, 21.0, 41.0, and 16.0 participants. General explanation: smaller samples typically provide less precise estimates when other conditions are comparable, while observed variability also affects precision. The corresponding standard deviations differ across arms. These features help explain why estimates should be read with their intervals rather than as exact values. They do not identify why the numbers with outcome data differ, which is not reported in the registry record.
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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 16 | 21 |
| 75% of the observed effect | 28 | 37 |
| 50% of the observed effect | 61 | 82 |
The displayed planning figures are participants per arm, not total participants across a trial. The listed assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each planning scenario uses the stated fraction of the observed effect as the effect to detect. The registry record does not report the original trial’s sample-size justification or design assumptions, so these figures should not be mistaken for the study’s original recruitment target.
The 80% power column gives the estimated participants per arm for a hypothetical study with an 80% chance of detecting the selected effect under the planning assumptions, if that effect and assumptions are correct. The 90% power column gives the corresponding per-arm count for a 90% chance. These are conventional design probabilities, not guarantees of a result. They also do not describe the probability that a treatment effect exists or that an observed result is true.
Rows using 100%, 75%, and 50% of the observed effect represent progressively smaller target differences relative to the observed contrast. Smaller effects are generally more difficult to distinguish from random variation and therefore require more participants. The values can change substantially across contrasts because the estimated effects differ. The planning exercise is based on observed summaries and its assumptions; it is not observed power.
Read each figure as a hypothetical design requirement for each arm under its particular scenario, rather than as a count of participants enrolled in the completed study. The 80% and 90% columns are alternative design targets, not analyses of what the current trial achieved. If the underlying effect, variability, allocation, or analysis differs from the planning assumptions, the actual sample size needed could differ as well. No claim about the study’s original planning can be inferred from these illustrative values.
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 z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = 1.400; pooled standard deviation σ = 1.379.
- n = 2 × (1.96 + 0.842)2 × 1.3792 / 1.4002 = 15.2, rounded up to 16 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 <- 1.4 # observed difference in means
sigma <- 1.37852002535961 # 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(4145466)
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 = 16 (80% power), 21 (90% power)
75% of observed effect: n per arm = 28 (80% power), 37 (90% power)
50% of observed effect: n per arm = 61 (80% power), 82 (90% power)
power.t.test: 16.2
Simulated power at n = 16 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.
14. Multiplicity, Missing Data and Analysis Populations
Several arm comparisons and multiple outcomes are listed. The primary result includes three contrasts against Fat Responders (1), and the secondary outcome list names six measures. Numerical secondary results are available for only some of those outcomes. The p-values reported for the comparisons are unadjusted. Whether the original analysis plan specified a hierarchy, a limited set of confirmatory tests, or a multiplicity adjustment is not reported in the registry record.
General explanation: when many hypotheses are tested, the chance of at least one apparently notable result can increase even if all null hypotheses are true. Multiplicity procedures can control or otherwise address that concern, but they may change the interpretation of individual p-values and confidence intervals. Without a reported plan or adjustment, the unadjusted values should be treated as individual comparisons rather than as a controlled family of confirmatory tests.
Missing-data handling is also not reported in the registry record. The primary outcome counts are 44.0, 21.0, 41.0, and 16.0 across the four arms, while total enrollment is 145. The registry does not explain the difference between these figures, whether the outcome counts reflect all randomized participants with measurements, or whether participants were excluded for particular reasons. It does not report imputation, sensitivity analyses, or assumptions about missing outcomes.
The analysis population is not reported in the registry record. In particular, it is not stated whether the primary results use all randomized participants, participants with observed outcomes, or another defined population. The record also does not state whether analyses followed intention-to-treat principles or whether adherence-based analyses were conducted. These details matter because analysis populations and missing-data assumptions can affect estimates, uncertainty, and the interpretation of randomized comparisons. No specific method should be inferred from the arm summaries alone.
15. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Fat Responders (1) | 1 | 46 | 2.2% |
| Carbohydrate Responders (1) | 0 | 22 | 0.0% |
| Fat Responders (2) | 1 | 43 | 2.3% |
| Carbohydrate Responders (2) | 0 | 18 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Fat Responders (1) | 0 of 46 |
| Carbohydrate Responders (1) | 0 of 22 |
| Fat Responders (2) | 0 of 43 |
| Carbohydrate Responders (2) | 0 of 18 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Fat Responders (1) | 0 of 46 |
| Carbohydrate Responders (1) | 0 of 22 |
| Fat Responders (2) | 2 of 43 |
| Carbohydrate Responders (2) | 0 of 18 |
Most frequent serious adverse event terms
| Event term | Organ system | Fat Responders (1) | Carbohydrate Responders (1) | Fat Responders (2) | Carbohydrate Responders (2) |
|---|---|---|---|---|---|
| Hospitalized | Gastrointestinal disorders | 1 of 46 | 0 of 22 | 0 of 43 | 0 of 18 |
| Hospitalization | Respiratory, thoracic and mediastinal disorders | 0 of 46 | 0 of 22 | 1 of 43 | 0 of 18 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Fat Responders (1) | Carbohydrate Responders (1) | Fat Responders (2) | Carbohydrate Responders (2) |
|---|---|---|---|---|---|
| Lymphodema | Blood and lymphatic system disorders | 0 of 46 | 0 of 22 | 1 of 43 | 0 of 18 |
| Lipedema | Cardiac disorders | 0 of 46 | 0 of 22 | 1 of 43 | 0 of 18 |
Serious events with the highest arm-level rate: hospitalization (2.3%), hospitalized (2.2%).
The registry lists serious adverse events for each arm using the number at risk and the number affected. Fat Responders (1) had 1 serious event among 46 at risk; Carbohydrate Responders (1) had 0 among 22; Fat Responders (2) had 1 among 43; and Carbohydrate Responders (2) had 0 among 18. Deaths are listed as 0 in all four groups. These are event counts as recorded, not estimates of comparative risk.
For other adverse events, the record lists 0 among 46 for Fat Responders (1), 0 among 22 for Carbohydrate Responders (1), 2 among 43 for Fat Responders (2), and 0 among 18 for Carbohydrate Responders (2). The listed serious-event terms include “Hospitalization” at 2.3% and “Hospitalized” at 2.2%. The record does not explain whether these terms refer to distinct events, overlapping descriptions, or how the percentages were calculated. They should be read as registry terminology rather than treated as separate comparative measures.
These figures are descriptive. The record does not provide a statistical comparison of adverse events, information about event timing or relatedness, or a detailed safety analysis plan. Counts alone do not establish that a difference between arms is meaningful, and the absence of a recorded event in an arm does not establish absence of all possible safety concerns.
16. What the Result Does, and Does Not, Mean
The results describe average weight changes in four randomized arms over baseline to 12 weeks and unadjusted mean differences relative to Fat Responders (1). All four posted arm means are negative. The contrast for Carbohydrate Responders (1) has an interval that excludes zero, while the intervals for Fat Responders (2) and Carbohydrate Responders (2) include zero. These observations are specific to the posted group summaries and the comparisons defined in the registry.
They do not establish that genetic responder status predicts which diet will produce greater weight loss. The reported contrasts do not directly test a responder-by-diet interaction or show a within-category comparison of the two diets. The primary question motivating the study is broader than the three contrasts against a single reference group. A direct analysis of that question is not reported in the registry record.
The estimates also do not show how every participant responded. A group mean can conceal variation among individuals, and the standard deviations describe spread rather than a treatment effect for a particular person. The registry does not report adherence, the method used to determine responder status, or an analysis connecting individual genetic classification to individual dietary response. Therefore, the posted group-level summaries should not be used to infer an individual outcome.
The study’s 12-week timeframe does not establish what happened after that period. No longer-term weight outcome is included in the posted primary endpoint. Nor does the record report a threshold for clinical importance, so statistical uncertainty and clinical importance cannot be equated. Unadjusted secondary results add descriptive context but do not independently confirm the primary hypothesis, particularly because the multiplicity strategy is not reported.
Overall, the record supports a cautious description of short-term group averages and their uncertainty. It does not provide enough detail to reconstruct the full analysis plan, assess missing-data assumptions, or draw conclusions beyond the specific measures and comparisons posted. The results should not be interpreted as personalized guidance or as proof that one dietary assignment is superior for an individual.
17. Why This Trial Matters Statistically
This trial is statistically interesting because its central hypothesis concerns whether a participant characteristic modifies the relationship between diet assignment and weight change. That is an interaction question: the comparison between diets would need to be assessed across responder categories, rather than inferred from one or more isolated arm contrasts. The registry’s posted comparisons instead use Fat Responders (1) as a common reference. Recognizing that distinction prevents a descriptive contrast from being mistaken for a direct test of the motivating hypothesis.
The design also illustrates why endpoint, comparator, and analysis plan need to be read together. All four arm means are negative, but the interpretation of their differences depends on which arms are compared, how the categories were formed, and whether the planned contrasts match the scientific question. The registry provides the arm descriptions and summary results, but the methods needed to establish that connection are not reported in the registry record.
Precision is another important part of the statistical reading. The confidence intervals range from estimates that exclude zero to intervals that include it, and the arm sizes are unequal. Looking only at point estimates or p-values would omit information about the uncertainty of each contrast. The illustrative sample-size figures further show how planning requirements depend on the target effect and assumptions, while remaining separate from the trial’s original design justification.
Finally, the record lists multiple outcomes and unadjusted comparisons, but does not report a multiplicity strategy or details of missing-data handling. These are not minor technicalities: they affect how strongly individual findings can be treated as confirmatory. The study therefore offers a useful example of how to separate observed group summaries, specific pairwise comparisons, a broader interaction hypothesis, and the design assumptions needed for a fuller interpretation.
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 trial-specific limitations of interpretation arise from what the registry record does not report. It does not describe how Fat Responder and Carbohydrate Responder status was defined or measured, nor how those categories were incorporated into randomization. Without those details, it is difficult to evaluate how well the four arm structure corresponds to the proposed genetic matching hypothesis. The record also does not report a direct test of the responder-by-diet interaction.
The posted primary comparisons all use Fat Responders (1) as the reference, even though this means some contrasts compare responder categories within the high-fat diet and others compare diets and categories at the same time. The resulting estimates do not isolate every component of the study question. A prespecified contrast plan is not reported in the registry record.
Primary outcome counts vary across arms and are smaller than total enrollment, but the reasons are not given. The record does not report participant flow, missing weight measurements, adherence, or an analysis population. Without those details, it is not possible to determine from the posted summaries whether the comparisons represent all randomized participants or a subset defined by outcome availability or other criteria.
The record also lacks numerical results for some named secondary measures and does not report a multiplicity plan. It does not describe methods for handling baseline values, covariates, protocol deviations, or any potential departures from the planned analysis. The study period for the primary endpoint ends at 12 weeks; the posted primary outcome does not characterize longer-term change. These limitations constrain interpretation of the registry results and are not resolved by the precision of the reported arm summaries.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: The Personalized Nutrition Study — NCT04145466.
- Registry record last updated 2025-01-30; status last verified 2024-12.
- Results first posted 2025-01-30.
- 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.
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22. Record Summary
The Personalized Nutrition Study is listed as a completed, randomized, single-masked, parallel-group study with enrollment of 145 and a primary completion date of 2021-12-21. It compared high-fat and high-carbohydrate dietary assignments across Fat Responder and Carbohydrate Responder categories. The primary outcome was mean weight change in kg from baseline to 12 weeks.
All four posted primary arm means were negative. The registry reports three unadjusted mean differences against Fat Responders (1), with confidence intervals and p-values. Numerical secondary results are posted for waist circumference, food cravings, and fat preference; the registry names additional secondary outcomes without numerical results in the record. Serious and other adverse event counts are also listed by arm.
The posted contrasts do not report a direct interaction test of responder category and diet. The original sample-size justification, detailed statistical plan, multiplicity strategy, analysis populations, and missing-data procedures are not reported in the registry record. The results are best read as short-term arm summaries and unadjusted comparisons, with those reporting limits in mind.