Dietary Ketosis: Fatty Acids Activate AMPK Energy Circuits Modulating Global Methylation: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Dietary Ketosis: Fatty Acids Activate AMPK Energy Circuits Modulating Global Methylation (NCT03319173), a randomized na study. The primary outcome is MoCA (Montreal Cognitive Assessment).

2. Clinical Question

The registry record describes a randomized comparison of dietary approaches and a primary cognitive outcome. The experimental group’s dietary intervention was designed to facilitate prolonged benign dietary ketosis, while the control group was assigned to continue its current dietary protocol, described as the Standard American Diet. The primary question is whether the groups’ Montreal Cognitive Assessment (MoCA) scores differ at the recorded 12-week assessment.

3. Trial Design

This was a randomized, parallel-group study with no masking. The registry lists the study phase as not applicable and describes the intervention as behavioral. Enrollment was 98. The study is recorded as completed, with a start date of 2017-10-15 and a primary completion date of 2018-09-30. These record details describe the design and status, not whether the intervention was followed as intended by participants.

The experimental group was assigned a dietary intervention involving clinically regulated meal plans designed to facilitate prolonged benign dietary ketosis. The control group was assigned its current dietary protocol, identified as the Standard American Diet. The control description includes 4-6 small meals per day and an approximate macronutrient breakdown per meal of 50% carbohydrate, 35% protein, and 15% fat. The available description of the experimental group’s plan is incomplete, so further specifics about foods, duration, adherence targets, or implementation are not reported in the registry record.

The primary outcome was MoCA score at 12 weeks. The registry describes it as a continuous score and reports group least-squares means with standard errors. The listed conditions are mild cognitive impairment and metabolic syndrome. The exact eligibility criteria, recruitment setting, randomization procedure, allocation concealment, and analysis populations are not reported in the registry record. The record also does not explain the rationale for the enrollment target or the assumptions used for the trial’s original sample-size planning.

Randomization is intended to make group comparisons less vulnerable to systematic differences in how participants are assigned. However, knowing that a study was randomized does not establish that groups were similar on every characteristic or that all later analysis decisions were unbiased. With no masking, participants and study personnel were not masked according to the registry entry. The record does not state whether outcome assessors were masked separately. These design details matter when interpreting a dietary intervention, because expectations and study procedures can influence behavior and measurement.

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 MoCA (Montreal Cognitive Assessment), measured over 12 weeks.

The primary endpoint is the Montreal Cognitive Assessment (MoCA), reported as a score on a scale at 12 weeks. The registry describes the measure as assessing changes in cognitive function over time. Its stated range is 0 points at the minimum and 30 points at the maximum. The registry labels scores >25 as normal cognitive function, scores 17-25 as mild cognitive impairment, and scores <17 as indicating increased likelihood of Alzheimer’s disease or dementia. These are the registry’s descriptions of score ranges; a score category is not, by itself, a clinical diagnosis.

A cognitive assessment is used because the study question concerns memory complaints and cognitive function. For a continuous endpoint, the group mean summarizes the average score in each group, while the between-group mean difference expresses the estimated separation in score units. The posted primary results give least-squares means for the groups and a mean difference at the stated assessment time. That makes the result interpretable in MoCA scale points, rather than only as a test of whether the groups differ.

The registry does not report enough detail to determine how the 12-week score was handled for participants without a recorded assessment or how the primary measure was collected. Nor does the endpoint alone establish whether a score change reflects a lasting change in cognition. It is one measured outcome at the recorded time point.

7. Results Posted in the Registry

• Experimental Group: mean 28.38 versus 20.22 on control; difference 8.16 (95% CI 7.55 to 8.77), standardized effect d = 5.30; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry reports least-squares means and standard errors for the primary continuous outcome, and a linear regression analysis of final values. A separate unadjusted recalculation uses the posted group summaries. These methods answer related but not identical questions: a direct comparison of group summaries is unadjusted, whereas a regression estimate can depend on the variables and modeling choices included in the regression. The registry does not report the regression specification beyond identifying it as linear regression.

What does a least-squares mean represent?

General statistical explanation: a least-squares mean is a model-based estimate of a group’s average outcome. In a simple model, it may be close to the ordinary group mean; in a model that includes other terms, it can reflect an adjusted estimate. Its interpretation therefore depends on the model used. The registry lists least-squares means of 28.38 for the experimental group and 20.22 for the control group, each with a standard error of 0.22. Because the model details are not reported, the precise adjustment represented by the least-squares means is not reported in the registry record.

What does the mean difference express?

General statistical explanation: subtracting one group’s estimated mean from another gives a difference in the outcome’s original units. Here, the outcome is a MoCA score, so the reported mean differences are in score points. The unadjusted recalculation gives 8.16, while the reported linear regression analysis gives 8.24. These are distinct estimates from distinct analyses. A difference in average scores does not describe every participant’s score or show the amount of within-group variation.

Why is a standard error reported?

General statistical explanation: a standard error describes the estimated sampling variability of a statistic under the analysis model. It is not the spread of individual scores. A standard error is used to quantify uncertainty around an estimated mean or difference and contributes to the calculation of an interval and a test statistic. The registry gives a standard error of 0.22 for each group’s least-squares mean. Those values should not be mistaken for standard deviations or for the range of individual MoCA scores.

How should the regression result be read?

The reported method is linear regression, and the parameter is the mean difference in final values. The estimate is 8.24, the 95% confidence interval is 7.79 to 8.7, and the reported p-value is < 0.001. General statistical explanation: linear regression estimates a relationship between an outcome and one or more explanatory terms under a specified model. The coefficient for a group contrast represents an estimated difference under that model. Without the model specification, readers cannot determine which terms were included, how missing values were handled, or whether the estimate was adjusted for baseline score or other characteristics. Those details are not reported in the registry record.

What is the recalculated standardized effect?

The unadjusted recalculation also reports a pooled standard deviation of 1.54, marked as approximate, and a standardized effect, d, of 5.298. General statistical explanation: a standardized effect expresses a mean difference relative to a measure of outcome variability, rather than in the outcome’s original units. This can assist comparisons across measures, but it depends on how the variability estimate is obtained. The approximation flag matters: the posted summary statistics do not provide the raw participant-level scores, and the recalculation uses an approximate pooled standard deviation. The standardized estimate should therefore be read as a summary-statistic-based calculation, not as an independently verified participant-level analysis.

What does a p-value tell the reader?

General statistical explanation: a p-value evaluates how compatible the observed data are with a specified null hypothesis under the model and its assumptions. A small p-value can indicate that the observed group contrast would be unusual under that null model. It does not quantify the probability that the null hypothesis is true, establish the probability of a causal explanation, or express clinical importance. The recalculated unadjusted p-value is <0.001; the regression analysis reports p < 0.001. These values arise from the respective analyses and are not interchangeable statements about all possible analysis choices.

Why can the two estimates differ?

General statistical explanation: estimates may differ when they come from different methods, populations, covariate adjustments, or handling of outcome data. The direct recalculation uses posted summary statistics and is unadjusted. The registry’s regression result is identified as a linear analysis of final values, but the model details are not reported. The numerical difference between the estimates cannot be attributed to a specific modeling decision from the registry record. The recalculation is useful as a check on the scale and broad direction of the comparison, while the reported regression analysis remains the analysis described in the registry.

10. Confidence Intervals and Precision

A confidence interval gives a range of values compatible with the data and the assumptions of the method used. General statistical explanation: narrower intervals indicate greater precision under those assumptions; wider intervals indicate more uncertainty about the estimated quantity. An interval is not a guarantee that the true value lies within its bounds, and it does not account for every possible source of bias or model misspecification.

The recalculated, unadjusted mean difference is 8.16, with bounds of 7.55 and 8.77. The registry’s regression analysis reports a 95% confidence interval from 7.79 to 8.7 around an estimate of 8.24. The registry explicitly identifies the regression interval as 95%. The recalculated interval is listed with its bounds, but its confidence level is not stated in the registry record, so it should not be assigned a confidence level based on assumption.

Both intervals indicate that the estimated difference is positive under the respective analyses. They are intervals for a group-level mean difference, not ranges of individual MoCA scores. They also do not capture uncertainty from unreported design and analysis decisions, such as how missing scores were handled or what variables were included in the regression. The record does not report those details.

The group means are reported with standard errors of 0.22. A standard error concerns precision of an estimated mean; it is not a description of the spread of participants’ scores. The recalculation’s pooled standard deviation is marked approximate, which adds a separate qualification to the standardized effect calculation. Precision should therefore be judged in relation to the particular statistic and method being described, rather than inferred from one uncertainty measure alone.

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 events. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect used in each scenario is the stated fraction of the observed effect. These are planning illustrations based on the observed result, not the assumptions used to design the original trial; the original design assumptions are not reported in the registry record.

The 80% power column gives the planned participants per arm under the stated assumptions to have an 80% chance of detecting the chosen effect if that effect and the model assumptions are correct. The 90% power column gives the corresponding per-arm planning figure for a 90% chance. Higher target power generally calls for at least as many participants under otherwise unchanged assumptions. The displayed values are very small: for planning at 100% of the observed effect, the figure is 1 participant per arm for 80% power and 1 participant per arm for 90% power. At 50% of the observed effect, the figure is 3 participants per arm for each power target.

Smaller effects are harder to distinguish from random variation and therefore require more participants under otherwise comparable assumptions. The calculations are sensitive to the observed effect used as their starting point. A planning calculation based on an unusually large observed estimate can yield very small figures and should not be treated as evidence that a future study of that size would reliably reproduce the result. This is not observed power: it is a prospective illustration calculated from the observed effect, not a measure of the trial’s achieved probability of detecting an effect.

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 = 8.160; pooled standard deviation σ = 1.540.
2. n = 2 × (1.96 + 0.842)² × 1.540² / 8.160² = 0.6, rounded up to 1 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 <- 8.16                      # observed difference in means
sigma <- 1.54032734616163                     # 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(3319173)
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 = 1 (80% power), 1 (90% power)
 75% of observed effect: n per arm = 1 (80% power), 2 (90% power)
 50% of observed effect: n per arm = 3 (80% power), 3 (90% power)
power.t.test: 2.1 
Simulated power at n = 1 per arm: NA (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. Analyses Reported by the Sponsor

The registry reports the sponsor’s linear regression analysis of final values as a mean difference of 8.24, with a 95% confidence interval from 7.79 to 8.7 and p < 0.001. The summary-statistic recalculation is unadjusted and gives a mean difference of 8.16, with an interval from 7.55 to 8.77 and an unadjusted p-value of <0.001. The estimates are close, but they are not identical.

The recalculation is a simple check using the posted group summaries; it is not a reconstruction of the regression model. The registry identifies the reported method as linear regression but does not describe the model terms or other analysis details. The record therefore does not explain why the estimates differ. Their different reported p-value formats should also be retained as stated rather than interpreted as evidence that the estimates answer exactly the same question.

The posted results do not flag a discrepancy between the recalculation and the reported analysis. The regression result remains the sponsor-reported analysis, while the recalculation offers an unadjusted comparison based on summary statistics. Neither estimate alone resolves questions about missing data, analysis populations, or unreported modeling choices.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 16 outcome measures and 16 analyses, with 15 secondary outcomes posted. The secondary outcomes include small LDL-P, the LP-IR score, fasting triglycerides, the triglyceride/HDL ratio, fasting insulin, fasting glucose, HOMA-IR, and HgA1c. A count of outcomes or analyses does not reveal which comparisons were considered confirmatory, how they were ordered, or whether adjustments were made for testing multiple outcomes.

Multiplicity matters because conducting many statistical tests can increase the chance that at least one result appears unusual even when no underlying effect exists. General statistical explanation: methods that control a family-wise error rate or a false-discovery rate can address different multiplicity goals, but the appropriate method depends on the study’s aims and analysis plan. Any multiplicity adjustment or testing hierarchy is not reported in the registry record. The posted primary p-value should therefore be read as the value for its stated analysis, without assuming that it was adjusted for other outcomes.

The registry does not report how missing MoCA assessments or missing secondary measurements were handled. It also does not identify an intention-to-treat, per-protocol, or other analysis population for the primary comparison. These omissions make it difficult to assess whether the reported groups represent all randomized participants or only those with available outcome measurements, and whether exclusions could have affected the result.

The registry record does not report an interim analysis plan, stopping rules, or the trial’s full statistical analysis plan. It also does not report the original sample-size justification. These details are relevant to understanding which analyses were planned in advance and how the final results were selected and interpreted. Their absence from the registry record does not establish that such procedures were absent; it means their details cannot be evaluated from the record.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

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

The registry lists 0 serious adverse events among 48 participants at risk in the experimental group and 0 among 50 participants at risk in the control group. Deaths are listed as 0 in each group. Other adverse events are also listed as 0 among 48 participants at risk in the experimental group and 0 among 50 participants at risk in the control group.

These entries describe the adverse-event figures recorded in the registry; they do not establish that no symptoms or events occurred outside the registry’s reporting definitions, observation period, or collection process. The record does not provide details about how adverse events were solicited, defined, assessed, or followed over time. It also does not list serious adverse-event terms. Therefore, the zeros should be read as the posted counts, with the available reporting detail in mind, rather than as proof that the intervention had no risks.

The at-risk figures are group-specific. They should not be interpreted as evidence about event rates over a specified duration, because the registry record does not give an adverse-event observation timeframe. The posted counts also do not compare severity beyond the serious and other adverse-event categories shown.

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

The result describes a difference in average MoCA scores between the randomized groups at the stated 12-week assessment. The experimental group’s posted mean is 28.38, compared with 20.22 in the control group. The unadjusted recalculation estimates a mean difference of 8.16 points, and the sponsor-reported regression analysis estimates 8.24 points. Both estimates are in the direction of a higher average score in the experimental group.

That comparison does not establish that the dietary intervention caused the entire difference. Randomization is an important design feature, but the registry record does not report enough information about implementation, participant follow-up, missing values, analysis populations, or the regression model to assess all possible sources of bias. The record also does not provide baseline MoCA values or individual-level changes, so the posted final-value comparison cannot show how each participant’s score changed over time.

The score ranges described in the registry can provide context for MoCA results, but group means do not show how many participants were within each score band. The record does not provide the score distribution or the number of participants whose scores changed categories. A mean difference is not equivalent to a diagnosis, and it does not demonstrate a durable change beyond the recorded time point.

The study’s summary proposes links among metabolic flexibility, energy pathways, and global DNA methylation. The primary result is a cognitive score comparison; it does not itself establish those biological mechanisms. The listed secondary measures concern metabolic markers, but a joint analysis linking them to the cognitive result is not described in the registry record.

Accordingly, the posted data support a precise description of the reported group-level score contrast under the analyses shown. They do not establish the effect of the intervention in other populations or settings, prove the proposed mechanism, or resolve the unreported analysis and follow-up details. The registry result is evidence about this recorded comparison, not a basis for medical advice.

17. Why This Trial Matters Statistically

This trial raises several statistical issues that are especially relevant to behavioral interventions and clinical outcomes. Random allocation can help balance measured and unmeasured characteristics on average, but the registry record does not describe the sequence generation or allocation concealment. No masking is listed, and the available record does not state whether outcome assessors were masked. For a dietary study with a cognitive outcome, awareness of group assignment can affect behavior, expectations, and potentially the measurement process.

The primary result is a continuous-score comparison, which preserves information about the magnitude of the MoCA difference rather than reducing the outcome to a category. At the same time, a difference in means can conceal variation in participant scores and changes in score categories. The registry gives group means and uncertainty estimates, but not the score distributions or individual-level results needed to describe that variation.

The close but nonidentical estimates from the unadjusted recalculation and reported regression analysis illustrate why analysis specifications matter. The record does not identify the regression covariates or explain how missing values were handled. It also lists multiple outcomes and analyses without reporting a multiplicity plan. Those omissions limit a reader’s ability to distinguish a prespecified confirmatory result from other analyses or to evaluate sensitivity to analytic choices.

The planning illustration is another useful caution. Its very small per-arm figures are calculated from the observed effect and are not the original trial’s design rationale. A sample-size calculation can be highly dependent on the effect assumed, and an observed estimate may not be a reliable basis for planning without external justification. Keeping planning calculations separate from observed results prevents them from being mistaken for evidence about the trial’s achieved power or for a validation of the original design.

18. Limitations

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

The registry record leaves several trial-specific details unresolved. It lists randomized allocation and no masking, but does not describe the randomization process, concealment of assignments, recruitment setting, eligibility criteria, or participant characteristics. The listed conditions are mild cognitive impairment and metabolic syndrome, but the record does not establish whether every participant had both conditions or how these diagnoses were determined.

The dietary descriptions are incomplete. The experimental arm text describes meal plans intended to facilitate prolonged benign dietary ketosis but ends before giving a full account. The control description identifies the Standard American Diet and approximate meal composition, but its full text is also incomplete. The record does not report adherence, dietary intake measurement, intervention fidelity, or the extent to which participants changed their diets.

For the primary MoCA result, the record does not provide baseline scores, participant-level distributions, missing-data handling, or a clearly named analysis population. The regression analysis is identified as linear regression of final values, but its model terms are not reported. Consequently, the difference between that estimate and the unadjusted recalculation cannot be explained from the registry record, and robustness to alternative assumptions cannot be assessed.

The registry does not report the original sample-size justification, a multiplicity plan, or interim-analysis procedures. It also does not provide the details needed to interpret the adverse-event collection process or its observation period. These limitations concern what can be evaluated from the registry record; they do not establish that the study failed to conduct procedures that are not described there.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Dietary Ketosis: Fatty Acids Activate AMPK Energy Circuits Modulating Global Methylation — NCT03319173.
• Registry record last updated 2019-11-12; status last verified 2019-11.
• Results first posted 2019-11-12.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT03319173 is recorded as a completed, randomized, parallel-group behavioral dietary study with no masking and enrollment of 98. It lists mild cognitive impairment and metabolic syndrome as conditions. The experimental intervention was designed to facilitate prolonged benign dietary ketosis; the control group followed its current dietary protocol, identified as the Standard American Diet.

The primary outcome was MoCA score at 12 weeks. The posted group means were 28.38 for the experimental group and 20.22 for the control group. The unadjusted recalculation gives a mean difference of 8.16, while the registry-reported linear regression analysis gives 8.24, with its reported 95% confidence interval and p-value.

Important details—including eligibility, missing-data handling, analysis populations, regression specification, multiplicity procedures, and original sample-size assumptions—are not reported in the registry record. The adverse-event entries list 0 serious adverse events, 0 other adverse events, and 0 deaths in each group.