Ketogenic Diet (KD) in Alcoholism: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Ketogenic Diet (KD) in Alcoholism (NCT03255031), a randomized na study. The primary outcome is Withdrawal Symptoms Measured Using the Clinical Institute Withdrawal Assessment for Alcohol-Revised (CIWA-Ar).

2. Clinical Question

The trial addresses a specific question about dietary assignment during inpatient alcohol treatment, not a general comparison of diets in all people with alcohol use disorder. Its stated objective was to test the effects of a ketogenic diet on withdrawal symptoms. The posted primary outcome is a continuous score, with lower values representing fewer symptoms on the described scale. The record does not state that the primary question was about long-term alcohol use or outcomes after the inpatient period.

3. Trial Design

The registry classifies the study as randomized, double-masked, and parallel, with no applicable phase listed. The trial enrolled 53 participants. It compared two diet assignments: a ketogenic diet and a Standard American diet. The record identifies the National Institute on Alcohol Abuse and Alcoholism (NIAAA) as sponsor.

Eligibility was limited to adults aged 18 years or older who were moderate or severe alcohol drinkers, seeking treatment for alcohol use, and in the NIAAA inpatient alcohol treatment program. The study description says screening occurred under another protocol. Screening and study procedures included medical and psychiatric history, physical examination, blood and urine tests, and a breath test for alcohol. The description also lists MRI scans, thinking, memory, and attention tests, and measurement of sleep and waking. These are described as study procedures, not as the primary outcome.

The brief study description refers to a three-week clinic stay, while the diet-arm descriptions say the assigned diets were given for up to four weeks while inpatient. The registry record does not explain this difference. The primary outcome analysis population is described as participants who completed the dietary intervention. The arm summaries include 19 participants assigned to the ketogenic diet and 14 assigned to the Standard American diet. The record does not report the reasons participants did not contribute to these summaries or give a complete account of participant flow.

The primary outcome was measured in week one. The registry lists three secondary outcome topics: mood, sleep, and alcohol craving. It also records ten outcome measures overall. The precise timing and analysis details for all the secondary measures are 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

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: The analyses included participants who completed the dietary intervention.

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 Withdrawal Symptoms Measured Using the Clinical Institute Withdrawal Assessment for Alcohol-Revised (CIWA-Ar), measured over Week 1.

The primary endpoint was the mean CIWA-Ar score in week one. CIWA-Ar is the Clinical Institute Withdrawal Assessment for Alcohol-Revised, a 10-item scale used in the assessment and management of alcohol withdrawal. The registry describes item scoring from 0-7, except for the orientation category, which is scored from 0-4. The total score ranges from 0 - 67.

The registry defines mild withdrawal as a score less than or equal to 10, moderate withdrawal as scores 11 to 15, and severe withdrawal as a score equal to or greater than 16. These bands give clinical context to the scale, while the posted primary analysis compares group means rather than reporting the proportions in each severity band. The arm summaries do not show how many participants fell into each band.

As a continuous measure, the mean summarizes the average score in each analyzed group, and the standard deviation describes variation among scores within that group. General: a withdrawal assessment can provide a structured way to quantify symptoms during the period of interest. A mean comparison is useful for describing group-level differences, but it does not by itself describe every participant's experience or the distribution of scores. The registry specifies week one as the timeframe and says the analysis was an ANOVA between groups. It does not report further details of the endpoint's scoring schedule within that week.

7. Results Posted in the Registry

• Ketogenic Diet (KD): mean 4.16 versus 6.57 on control; difference -2.41 (95% CI -5.73 to 0.91), standardized effect d = -0.52; z-test p = 0.155.

8. Statistical Interpretation

9. Statistical Methods Explained

What kind of outcome is being compared?

The primary outcome is a continuous score, and the posted group summaries use means and standard deviations. A mean is the arithmetic average of the observed scores. A standard deviation describes how dispersed individual scores are around their group mean. These quantities answer different questions: the mean describes the group's location, while the standard deviation describes variability among participants.

The registry says the primary analysis was an ANOVA between groups. General: analysis of variance compares group means while accounting for variation in the outcome. In a comparison of two groups, the substantive target is the difference between their average scores. The registry does not provide the ANOVA statistic, degrees of freedom, model specification, or adjusted group estimates. Those details are not reported in the registry record.

What does the recalculation represent?

The recalculated mean difference is -2.41, with the ketogenic diet mean compared against the Standard American diet mean. This is a simple unadjusted contrast based on the posted summary statistics for the completer groups. It is not a reproduction of every feature of the trial's sponsor analysis. In particular, it does not incorporate a mixed-model specification because the necessary model details and participant-level data are not reported.

The recalculated p-value is 0.155. General: a p-value measures how surprising data at least as incompatible with a specified null hypothesis would be under that hypothesis and the assumptions of the analysis. It is not the probability that the null hypothesis is true, nor does it measure the probability that the result occurred by chance. A p-value also does not express the size or clinical importance of an effect. The recalculated value belongs to the unadjusted summary-statistic comparison, not the registry's mixed-model analysis.

Why do the standard deviations matter?

Group means alone do not show how much scores varied. The posted standard deviations are 3.962 for the ketogenic diet group and 5.345 for the Standard American diet group. General: greater within-group variability tends to make a group difference less precisely estimated when sample sizes are otherwise similar. Precision also depends on the amount of information in the groups. Here, the group sizes used in the primary summaries are 19 and 14, and the standard deviations are substantial relative to the observed difference.

General: an unadjusted standard error for a mean difference reflects uncertainty in both group means. A confidence interval combines the estimate with its standard error and a chosen confidence level. The registry posts the recalculated interval, but does not give a confidence level in the outcome record. No separate adjustment for other variables is included in this simple recalculation.

How should the sponsor analysis be distinguished?

The reported analysis is named “Mixed Models Analysis” and has p = 0.067. The registry does not provide a model formula, covariates, repeated-measure structure, model estimates, standard errors, or confidence limits for that result. The primary outcome description separately states that analysis was performed as ANOVA between groups. The registry does not explain the relationship between that statement and the reported mixed-model result, so the precise analysis pathway is not reported in the registry record.

General: mixed models can account for correlated observations, such as repeated measurements from the same participant, when those data and model assumptions are appropriate. Their estimates can differ from a simple comparison of group means because they may use a different structure or information. That general possibility does not establish which features were used in this trial. The posted record does not give enough detail to infer them.

Why can over-dispersion matter?

General: over-dispersion arises when variability is greater than a statistical model assumes. If a model understates variability, its standard errors can be too small and its intervals too narrow. The primary outcome is a bounded score, and its observed spread is reported, but the registry does not report an over-dispersion assessment or a diagnostic for the model. It would therefore be inappropriate to assert that over-dispersion occurred or was addressed.

What does randomization contribute?

General: random assignment can reduce systematic differences between groups at the point of assignment, on average, but it does not guarantee that every characteristic is balanced in a small trial. It also does not eliminate uncertainty, missing outcome data, or limitations in the analysis population. The record identifies the trial as randomized and parallel, but does not report the allocation sequence method or any stratification factors. Those details are not reported in the registry record.

The trial is also classified as double-masked. The record does not specify which people were masked, how masking was maintained, or whether diet assignments could be distinguished in practice. No inference about the success of masking can be made from the classification alone.

10. Confidence Intervals and Precision

The recalculated mean difference is -2.41 points on the CIWA-Ar scale. Its confidence interval has a lower bound of -5.729 and an upper bound above zero. Since zero lies within the interval, the data do not precisely distinguish a negative mean difference from no difference or a positive difference under this unadjusted analysis. The interval includes a range of potentially different effect sizes, so the point estimate should not be read as a precise estimate of the underlying group difference.

General: a confidence interval describes a range of values compatible with the observed data under the analysis assumptions and the stated confidence procedure. It is not a range containing a fixed proportion of individual participant scores, and it does not assign a probability to a particular effect after the data have been observed. The registry outcome entry does not state the confidence level for the recalculated interval, so a confidence percentage should not be inferred from that entry.

The relatively small completer groups, with 19 participants in the ketogenic diet arm and 14 in the Standard American diet arm, are relevant to precision. The within-group standard deviations are 3.962 and 5.345, respectively. General: when outcome variability is appreciable compared with the group difference, and the groups contain limited information, estimated differences can remain uncertain. These considerations are reflected in the broad interval, but they do not explain the full analysis because the sponsor model details are not reported.

The sponsor's mixed-model p-value is 0.067, but the registry does not provide its effect estimate or confidence interval. Its precision therefore cannot be assessed from the reported p-value alone. The recalculated interval pertains only to the unadjusted comparison and should not be presented as the interval for the sponsor model.

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 display expresses sample size as participants per arm, not total events. Its calculations use the observed mean difference as a reference and show planning illustrations for detecting 100%, 75%, or 50% of that observed effect. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The trial's own original design assumptions and sample-size justification are not reported in the registry record.

For planning at 100% of the observed effect, the display gives 58 participants per arm for 80% power and 77 participants per arm for 90% power. For planning at 75% of the observed effect, it gives 102 participants per arm for 80% power and 136 participants per arm for 90% power. For planning at 50% of the observed effect, it gives 229 participants per arm for 80% power and 306 participants per arm for 90% power.

In plain language, the 80% power column gives the planned number of participants in each arm under the stated assumptions for a design with an 80% chance of detecting the specified effect if that effect is present. The 90% power column expresses the corresponding planning target for a 90% chance. These are design calculations, not claims about the probability that the trial's result is correct. The curve represents the same relationship between the assumed effect size and required sample size. Smaller effects need more participants to detect reliably; increasing the desired power also requires a larger planned sample.

These figures are planning illustrations based on the observed effect, not observed power. They should not be read as a retrospective measure of whether this completed trial was adequately powered, and they do not establish what assumptions informed its original design.

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 = -2.410; pooled standard deviation σ = 4.593.
2. n = 2 × (1.96 + 0.842)² × 4.593² / -2.410² = 57.0, rounded up to 58 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 <- -2.41                      # observed difference in means
sigma <- 4.59295153187942                     # 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(3255031)
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 = 58 (80% power), 77 (90% power)
 75% of observed effect: n per arm = 102 (80% power), 136 (90% power)
 50% of observed effect: n per arm = 229 (80% power), 306 (90% power)
power.t.test: 58 
Simulated power at n = 58 per arm: 0.802 (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 primary comparison as a mixed-model analysis with p = 0.067. It does not give an effect estimate, confidence interval, model specification, or sufficient detail to reproduce that analysis. The outcome description also identifies an ANOVA between-groups analysis, but the registry does not explain how that description relates to the reported mixed-model result.

The recalculated comparison is a simple unadjusted analysis of the posted group means and standard deviations. It gives a mean difference of -2.41 and p = 0.155. The difference between the two p-values does not by itself show that one analysis is erroneous: they are identified as different analytical approaches, and the record lacks the detail needed to reconcile them. The recalculation cannot replace the sponsor's analysis or recover information that is not reported.

The registry does not flag a discrepancy between the sponsor result and the recalculation. The sponsor result should therefore be read as the trial's reported analysis, while the recalculation is a supplementary, unadjusted comparison of the posted summaries. Neither p-value should be interpreted as a measure of clinical importance. Because the sponsor analysis has no posted effect estimate or interval, its estimated size and precision cannot be directly compared with the recalculated mean difference and confidence interval.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists ten outcome measures and three secondary outcome topics: mood, sleep, and alcohol craving. Multiple outcomes can create multiple opportunities for apparently notable results. General: when many hypotheses are tested, a prespecified multiplicity strategy may be used to control the chance of false-positive findings across a family of tests. The registry record does not report whether a multiplicity adjustment was planned or used, how outcome families were defined, or whether the primary endpoint had a special testing position in a hierarchy.

The record identifies a primary endpoint and reports a sponsor p-value for its comparison. It does not report an analysis plan, a prespecified testing sequence, or whether the secondary outcomes were treated as exploratory. Without those details, the implications of testing several outcomes cannot be fully assessed. The existence of multiple listed outcomes does not establish that a particular adjustment was required or that one was omitted; the approach is not reported in the registry record.

The primary analysis population is described as participants who completed the dietary intervention. The posted arm summaries include 19 participants assigned to the ketogenic diet and 14 assigned to the Standard American diet, whereas enrollment was 53. The registry does not provide a complete participant-flow account, reasons for noncompletion, or the number with missing primary outcome measurements at each assessment. It also does not describe imputation, other missing-data procedures, or sensitivity analyses. These details are not reported in the registry record.

The record does not state whether the primary analysis was intention-to-treat, per-protocol, or another defined analysis population. The completer description indicates who was included in the stated analysis, but does not establish how all randomized participants were handled. Consequently, the extent to which missing outcomes or intervention completion may affect the results cannot be evaluated from the posted information.

The trial is described as randomized and double-masked, but the registry does not provide the allocation concealment method, masking procedures, or a statistical analysis plan. Nor does it report whether interim analyses were planned or conducted. These omissions limit assessment of prespecification and analytic flexibility; they are not evidence that any particular procedure occurred.

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.

Most frequent non-serious adverse event terms

The registry lists serious adverse events for 33 participants at risk in the ketogenic diet group and 20 at risk in the Standard American diet group. It reports zero participants affected by serious adverse events in each group. Deaths are also recorded as zero in both groups. These figures describe the registry's serious-event reporting for the listed at-risk groups.

The record separately reports other adverse events among 33 participants at risk in the ketogenic diet group and 20 at risk in the Standard American diet group. Five participants in the ketogenic diet group and two in the Standard American diet group were affected. The registry does not provide serious adverse event terms because none are listed in the serious-event category.

These counts should be read as event-reporting summaries, not as a complete description of the nature, timing, severity, or duration of all events. The record does not provide event-level descriptions for the other adverse events in this summary, or explain how adverse events were collected. The at-risk groups differ from the completer groups used in the primary outcome summaries, so the safety and efficacy populations should not be assumed to be the same.

General: zero reported serious events in a study does not establish that an event is impossible or rule out uncommon harms. The registry figures describe what was recorded during this trial; they do not, by themselves, support broader conclusions about safety.

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

The posted primary outcome summaries show lower average week-one CIWA-Ar scores in the ketogenic diet group than in the Standard American diet group among participants who completed the dietary intervention. The unadjusted mean difference was -2.41 points. However, the recalculated confidence interval extends across zero, and the unadjusted p-value is 0.155. The sponsor's mixed-model analysis reports p = 0.067 but does not include an effect estimate or interval in the registry record.

These results do not establish that one diet caused lower withdrawal symptoms. The registry analysis population consists of intervention completers, and details on noncompletion and missing outcome data are not reported. The limited information on the sponsor model also means its estimate and precision cannot be examined alongside the simple recalculation. The difference in reported p-values should be understood in light of the different named methods and incomplete model details, rather than as a direct contradiction.

The score ranges from 0 - 67, and the record gives bands for mild, moderate, and severe symptoms. The group means alone do not show how many participants were in each severity category, how scores changed within individuals, or how symptoms varied over time in week one. The reported outcome is not a measure of longer-term alcohol use or recovery. Although mood, sleep, and alcohol craving are listed as secondary outcome topics, detailed results for those topics are not contained in this primary-outcome record.

General: statistical uncertainty concerns the range of effects compatible with the data under an analysis; clinical importance requires context beyond a point estimate or p-value. The registry does not define a clinically important difference for the CIWA-Ar outcome. The results therefore describe the observed group summaries and the uncertainty around an unadjusted contrast, without establishing whether the difference would be clinically meaningful.

17. Why This Trial Matters Statistically

This trial is statistically informative because it puts a randomized dietary comparison alongside a continuous clinical score and reports both group summaries and a sponsor analysis. The arm means and standard deviations make the scale of observed variation visible, while the recalculated difference and confidence interval show why a point estimate should not be read on its own. The observed mean was lower in the ketogenic diet group, but the interval includes zero and spans a range of possible effects.

The record also illustrates why analysis methods matter. The simple unadjusted comparison yields p = 0.155, whereas the sponsor's mixed-model analysis reports p = 0.067. The registry does not supply enough model detail or an effect estimate for the sponsor analysis to explain the difference. Reporting the method name without its model specification limits reproducibility and makes it harder to assess how the reported analysis relates to the stated ANOVA description.

The analysis population is another important statistical feature. The primary results concern intervention completers, with 19 participants in one arm and 14 in the other, while enrollment was 53. The registry does not describe participant flow or missing-data handling. That gap prevents readers from judging how selection into the analyzed groups may affect interpretation.

Finally, planning calculations based on the observed effect show how sample-size requirements depend on the effect a future study aims to detect. They are not evidence about the original design rationale or a retrospective verdict on this trial. Clear distinctions among observed summaries, sponsor-model results, and planning illustrations help prevent those different statistical quantities from being mistaken for one another.

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 gives limited detail about how the trial was conducted and analyzed. Although the study is classified as randomized and double-masked, it does not describe the allocation sequence, concealment procedures, who was masked, or how masking was maintained. It also does not provide the statistical analysis plan, model specification, or an explanation of the relationship between the stated ANOVA and reported mixed-model analysis.

The primary results are reported for participants who completed the dietary intervention. The record does not explain why other enrolled participants are absent from the arm summaries, provide a full flow of participants, or describe how missing outcome values were handled. It is therefore not possible to assess from the record whether the completer results may differ from results for all randomized participants.

The study description refers to a three-week clinic stay, while the arm descriptions refer to diets for up to four weeks. The registry record does not explain the difference. The primary endpoint timeframe is week one, but the exact measurement schedule within that timeframe is not described. The outcome record gives no sponsor-model effect estimate or confidence interval, limiting assessment of that analysis's size and precision.

The registry lists ten outcome measures but does not report a multiplicity strategy, a hierarchy for testing outcomes, or detailed analysis plans for the secondary measures. Detailed results for mood, sleep, and alcohol craving are not included in this primary-outcome entry. A clinically important difference for the CIWA-Ar score is also not specified.

The dietary comparison is described within an inpatient treatment program, and the record does not report results beyond the stated primary timeframe. These features restrict interpretation to the setting and outcome described; they do not establish how findings would apply in other populations or settings. No original sample-size justification, interim analysis plan, or assessment of over-dispersion is reported in the registry record.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Ketogenic Diet (KD) in Alcoholism — NCT03255031.
• Registry record last updated 2024-07-17; status last verified 2024-01-25.
• Results first posted 2024-07-17.
• 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

The registry describes a completed, randomized, double-masked, parallel trial of a ketogenic diet versus a Standard American diet among inpatients with alcohol use disorder. Enrollment was 53. The primary endpoint was week-one CIWA-Ar score, analyzed among participants who completed the dietary intervention.

The posted means were 4.16 for the ketogenic diet group and 6.57 for the Standard American diet group. The unadjusted recalculated mean difference was -2.41, with a confidence interval that includes zero; its p-value was 0.155. The registry reports a mixed-model p-value of 0.067 but does not report that analysis's effect estimate or confidence interval. Missing-data procedures, detailed model specifications, and the trial's original sample-size assumptions are not reported in the registry record.