Treatment of Non Alcoholic Fatty Liver Disease With n-3 Fatty Acids: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Treatment of Non Alcoholic Fatty Liver Disease With n-3 Fatty Acids (NCT00760513), a randomized phase 4 study. The primary outcome is Percentage of Liver Fat.

2. Clinical Question

The registry summary also describes interest in serum fibrosis markers and cardiovascular and type 2 diabetes risk markers. However, the posted primary result addressed percentage of liver fat. No secondary results are posted in the registry record, so the results cannot establish what happened to those other markers or risk factors.

3. Trial Design

This was a randomized, single-masked, parallel-group phase 4 trial. Randomization means assignment to the trial groups was intended to use a chance-based process; the registry record does not report details of the sequence generation or allocation concealment. Single masking is recorded, but which people were masked is not reported in the registry record. The parallel design means participants were assigned to one group rather than crossing between the treatments.

The registry lists an enrollment of 103. For the primary outcome summaries, the omega-3 fatty acid group has 46 participants and the dummy-pill group has 45. These are the group counts associated with the posted outcome summaries; the registry record does not explain how they relate to the enrollment figure. The adverse-event records give different at-risk counts, which are described separately below.

The intervention was OMACOR, an omega-3 fatty acid (fish oil) capsule, at 4 grammes daily. The comparator was an olive-oil dummy capsule at 4 grammes daily. The trial summary describes treatment for 18 months. The primary measure was taken at baseline and at 18 months, and the outcome was the change in liver fat percentage over that interval.

The trial is marked completed. Its primary completion date is recorded as 2013-11-01, and its start date as 2009-11-01. The sponsor was University Hospital Southampton NHS Foundation Trust. The registry record does not report the original sample-size justification, detailed eligibility criteria, or the identity of the masked party. These details matter for understanding how the trial was planned and conducted, but cannot be inferred from the group summaries.

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:

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 Percentage of Liver Fat, measured over Baseline and 18 months.

The primary endpoint was change in percentage of liver fat from baseline to 18 months. Liver fat percentage was measured using magnetic resonance spectroscopy, and the registry describes the scale as running from 0 to 100%. The change was defined as the end-of-study value minus the baseline value. Under that definition, a negative change means the measured liver fat percentage fell, while a positive change means it rose; the registry description calls a negative change a response to therapy.

This measure gives a continuous numerical outcome rather than a simple yes-or-no classification. A continuous measure can preserve information about the amount and direction of change across participants. The group mean describes the average change, while the standard deviation describes how spread out the individual changes were around that mean. Those summaries help distinguish the average group pattern from the variability among participants.

The endpoint was used to test the investigators’ stated hypothesis that long-chain n-3 fatty acid supplementation would favourably influence biomarkers for NAFLD. The comparison between groups is more informative about the treatment contrast than considering either group’s change alone: changes can occur in both groups, and the placebo group provides the trial’s comparator. The registry record does not report a threshold for a clinically important difference in liver fat percentage, so the size of a numerical difference cannot be classified as clinically important from this record alone.

7. Results Posted in the Registry

• Dummy Pill: mean -4.60 versus -7.90 on control; difference 3.30 (95% CI -2.40 to 9.00), standardized effect d = 0.24; z-test p = 0.257.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is a continuous measure, and the registry reports means and standard deviations for change in liver fat percentage. A mean summarizes the average change across the participants included in that group’s outcome summary. A standard deviation describes the spread of observed changes around the group mean. It is not the uncertainty around the mean itself: uncertainty in a group mean is commonly represented by a standard error or confidence interval.

What does the unadjusted comparison estimate?

The recalculation uses the posted group means and standard deviations to form a simple, unadjusted comparison. Its stated contrast is the mean in the dummy-pill group minus the mean in the omega-3 fatty acid group, producing a mean difference of 3.3. This is a difference between group averages, not a comparison of each participant’s individual change against their own counterfactual outcome. The calculation does not adjust for other variables or use the sponsor’s regression model.

The estimate must be read alongside its uncertainty. The 95% confidence interval runs from -2.402 to 9.002, so values on both sides of zero are compatible with the recalculated comparison under its assumptions. The unadjusted p-value is 0.257. A p-value describes how unusual data at least this inconsistent with a zero difference would be if the zero-difference model and the statistical assumptions held; it is not the probability that the treatment has no effect. Nor does it measure the probability that the result occurred by chance.

What does the sponsor’s regression analysis add?

The registry reports a linear-regression analysis with a net mean difference of -1.7, a 95% confidence interval from -6.3 to 3.0, and p = 0.48. Regression can estimate a group contrast while accounting for variables included in the model. However, the registry record does not report which covariates were included, whether baseline liver fat was included, or other model details. It also does not provide enough information to determine why the reported estimate differs in direction and value from the simple recalculation. The sponsor’s analysis and the unadjusted recalculation therefore need to remain distinct in interpretation.

In general, adjustment can change an estimated contrast because it conditions the comparison on additional information, and because the model may define the contrast differently. That is a general statistical explanation, not a claim about the specific reason for the difference in these posted estimates. The registry record does not explain the difference, so it should not be attributed to a particular adjustment or coding choice.

Why does the spread of the outcome matter?

The standard deviations are 17.4 in the omega-3 fatty acid group and 9.2 in the dummy-pill group. The unequal spread suggests that a common-variance assumption may be consequential for a simple comparison. The recalculation uses a pooled standard deviation of 13.96, as recorded in the posted calculation. In general, pooling assumes that the groups can be represented by a shared variance; when variability differs, that assumption may affect standard errors and confidence intervals. The registry does not report a variance diagnostic or a sensitivity analysis, so the appropriateness of that assumption cannot be assessed from the record alone.

Over-dispersion is a general concern when observed variability is greater than a model expects. For a continuous endpoint, greater spread can make estimates less precise; for count outcomes, over-dispersion means that counts vary more than a basic model assumes. The primary endpoint is continuous, and no separate over-dispersion analysis is reported. The wide variation in the group summaries is relevant to precision, but it is not by itself proof that a particular model assumption failed.

What can and cannot be inferred from the analyses?

The registry labels the sponsor’s analysis as a superiority analysis. A superiority analysis tests whether the groups differ in a specified direction or by a nonzero contrast, depending on its model and coding. The registry gives a p-value and confidence interval but does not report a prespecified clinically important difference or the detailed analysis plan. General statistical convention treats a confidence interval that includes zero as not excluding a zero contrast at the corresponding confidence level. It does not prove that the true contrast is zero.

The calculations are based on the outcome summaries and do not provide information on individual participant trajectories, the handling of missing outcome values, or possible departures from model assumptions. Those details can affect interpretation. The registry record does not report an analysis population definition or a missing-data method. Consequently, the posted results support a cautious description of the recorded group summaries and model estimate, rather than a broader claim about the treatment effect in all people with NAFLD.

10. Confidence Intervals and Precision

A confidence interval expresses the range of estimates reasonably compatible with the data and the statistical model used to construct it. It is not a range containing a fixed proportion of individual participants’ outcomes, and it is not a probability statement about the true effect after the interval has been calculated. In repeated use of the same method under its assumptions, intervals at a stated confidence level would cover the true parameter at that rate.

For the unadjusted comparison of dummy pill with omega-3 fatty acid, the estimated mean difference is 3.3 and the 95% confidence interval is -2.402 to 9.002. The range includes zero and extends to values on either side. This indicates that the data do not pin down the direction or exact size of the between-group contrast with high precision. The interval is also consistent with some potentially meaningful differences, but the registry record does not define a threshold for clinical importance.

The sponsor’s regression estimate is -1.7, with a 95% confidence interval from -6.3 to 3.0. This interval also includes zero, and its reported p-value is 0.48. Because the sponsor analysis and recalculation use different reported approaches and the model details are not described, their intervals should be interpreted separately rather than combined or treated as two measurements of one fully specified model.

Precision depends on both the amount of information and the variability in the outcome. The group standard deviations, 17.4 and 9.2, indicate variation in the observed changes. The registry record does not provide participant-level data, details of missing outcome handling, or a clinical threshold that would allow a more specific assessment of whether the intervals are narrow enough for a decision. The uncertainty in the estimates should therefore remain central to interpretation.

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. They are illustrative calculations based on the observed effect, not the trial’s original design calculation. The registry record does not report the trial’s original sample-size assumptions or justification.

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 to detect is set at the stated fraction of the observed effect. For planning for 100% of the observed effect, the figures are 281 participants per arm for 80% power and 377 participants per arm for 90% power. For planning for 75% of the observed effect, they are 500 participants per arm for 80% power and 669 participants per arm for 90% power. For planning for 50% of the observed effect, they are 1,124 participants per arm for 80% power and 1,505 participants per arm for 90% power.

In plain language, 80% power is the chance, under the specified assumptions and effect size, that a study would detect an effect using its stated statistical test if that effect were present. The 90% column applies the higher target probability and therefore calls for more participants under these assumptions. Smaller effects require more participants to detect than larger effects, which is why the figures rise as the assumed fraction of the observed effect falls.

These are planning illustrations, not observed power. They do not describe the probability that the completed trial’s result is correct, and they are not a retrospective measure of the strength of its findings. Their relevance depends on whether the assumed effect, variance, allocation and analysis approach are suitable for a future study.

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 = 3.300; pooled standard deviation σ = 13.962.
2. n = 2 × (1.96 + 0.842)² × 13.962² / 3.300² = 281.0, rounded up to 281 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 <- 3.3                      # observed difference in means
sigma <- 13.9615684383391                     # 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(760513)
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 = 281 (80% power), 377 (90% power)
 75% of observed effect: n per arm = 500 (80% power), 669 (90% power)
 50% of observed effect: n per arm = 1,124 (80% power), 1,505 (90% power)
power.t.test: 281.9 
Simulated power at n = 281 per arm: 0.800 (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 sponsor’s posted analysis uses linear regression and reports a net mean difference of -1.7, with a 95% confidence interval from -6.3 to 3.0 and p = 0.48. This is the registry’s reported trial analysis. Its confidence interval includes zero, so the displayed analysis does not rule out a zero contrast at the stated confidence level.

The simple unadjusted recalculation from the posted group summaries is expressed as dummy pill minus omega-3 fatty acid. It gives a mean difference of 3.3, a 95% confidence interval from -2.402 to 9.002 and p = 0.257. The registry record does not provide the sponsor model’s covariates, contrast coding or other details needed to reconcile the estimate with this recalculation. The different signs and values should not be explained by assuming a particular adjustment or coding choice.

Both results indicate uncertainty around the between-group contrast, but they are not interchangeable: one is the sponsor’s regression analysis and the other is an unadjusted recalculation from summary statistics. The registry record does not identify which model details account for their difference. The sponsor’s analysis should be read as the analysis reported for the trial, while the recalculation is a separate check based on the posted summaries.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists three outcome measures and three analyses, but no secondary results are posted in the registry record. The primary result available for interpretation is change in liver fat percentage. The registry summary describes additional interests in fibrosis markers and cardiovascular and type 2 diabetes risk factors, but results for those measures are not reported in the registry record.

When a study tests multiple outcomes or makes multiple comparisons, the chance of at least one apparently unusual result can increase. Statistical methods for handling multiplicity can control or account for that issue, but the registry record does not report a multiplicity adjustment, a hierarchy of outcomes, or the planned status of each analysis. It is therefore not possible to determine from this record whether multiplicity was addressed in the original analysis plan. This matters particularly when interpreting any secondary findings, which are not posted in any case.

The registry record does not report how missing primary outcome measurements were handled, whether the analysis used all randomized participants, or the definition of the analysis population. The primary outcome group summaries list 46 participants for omega-3 fatty acid and 45 for dummy pill, while the adverse-event records list at-risk counts of 51 and 52. These figures refer to different posted records and should not be treated as interchangeable denominators. The registry does not explain the difference.

Missing-data methods can affect estimates if outcome availability is related to treatment assignment or to the outcome itself. In general, complete-case analysis, imputation and model-based methods rely on different assumptions. The record does not identify which approach was used, so none should be attributed to this trial. The absence of these details limits assessment of possible bias and makes it difficult to judge how closely the posted estimates represent the randomized groups as originally assigned.

The registry also does not report protocol deviations, adherence information, or participant flow for the primary endpoint. These omissions do not show that a problem occurred; they mean the extent and handling of those issues cannot be assessed from the registry record.

15. Safety Results

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

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: anaemia and disorientation (2.0%), cellulitis on right lateral malleolus (2.0%), severe chest pain (2.0%), tonsillectomy (2.0%), seminoma (1.9%).

The adverse-event record lists serious events for an at-risk count of 51 in the omega-3 fatty acid group, with 4 affected, and an at-risk count of 52 in the dummy-pill group, with 8 affected. Other adverse events are listed for the same at-risk counts: 49 affected in the omega-3 fatty acid group and 44 in the dummy-pill group. These are separate registry counts and are not the same denominators as the primary outcome summaries.

The record lists several serious-event terms with percentages: “Anaemia and disorientation,” “cellulitis on right lateral malleolus,” “severe chest pain,” and “Tonsillectomy” are each recorded as 2.0%; “seminoma” and “Acute asthma attack” are each recorded as 1.9%. The registry record does not provide enough detail in these entries to determine the clinical circumstances or the relationship of each event to treatment. The list should not be read as a complete description of all clinical details.

Deaths are not reported in the registry record. Counts of events alone do not establish whether an event was caused by a treatment, and differences in the posted counts should be interpreted cautiously without further information about event definitions, follow-up, and ascertainment. These figures describe the safety entries in the registry; they are not a substitute for an assessment of individual events or a comprehensive safety report.

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

The posted data describe a randomized comparison of omega-3 fatty acid capsules and olive-oil placebo for change in liver fat percentage over 18 months. The group means were negative in both groups, and the unadjusted comparison produced a mean difference of 3.3 for dummy pill minus omega-3 fatty acid. The confidence interval for that recalculation includes zero. The sponsor’s regression estimate also has a confidence interval that includes zero.

These results do not establish a clear difference between the groups in the primary outcome. They also do not demonstrate equivalence: the intervals allow a range of possible differences, and no equivalence margin is reported. Without a threshold for a clinically important change, the clinical meaning of particular values within those intervals cannot be determined from the registry record.

The endpoint is a measurement of liver fat percentage, not a direct measure of every aspect of NAFLD or its long-term consequences. The registry summary refers to other biomarkers and risk factors, but secondary results are not posted in the registry record. The primary result therefore cannot answer whether there were changes in fibrosis markers, cardiovascular risk, type 2 diabetes risk, or later liver outcomes.

The posted summaries also do not resolve questions about missing data, analysis populations, adherence, or the sponsor model’s specifications. Such information could help assess how robustly the results reflect the randomized comparison. The result should be understood as an uncertain estimate of the treatment-group contrast for the measured endpoint in this trial, not as a definitive statement about all possible effects of omega-3 fatty acids in people with NAFLD.

More generally, a non-small p-value is not proof that no effect exists, just as a numerical difference in group means is not proof of a treatment effect. Interpretation requires the effect estimate, its precision, the outcome’s clinical relevance and the analysis context. Here, the intervals and absent clinical threshold limit conclusions about the magnitude and importance of any difference.

17. Why This Trial Matters Statistically

This trial illustrates why a comparison between randomized groups is more informative than interpreting a within-group change in isolation. The mean liver fat percentage change was negative in both arms, but the primary question concerns whether the groups differed, not whether either group’s mean moved downward from baseline. The unadjusted between-group estimate and the sponsor’s regression result both retain substantial uncertainty.

It also illustrates the role of variability in continuous outcomes. The standard deviations, 17.4 and 9.2, show that individual changes were spread around the group means. Such variation affects how precisely an average difference can be estimated. A mean can give a compact description of a group while masking a wide range of participant-level outcomes.

The registry includes both a sponsor analysis and a simple recalculation from summary statistics. Their estimates are not numerically identical, and the record does not contain enough methodological detail to reconcile them. This is a useful reminder that an estimate depends on the analysis specification and that the model, contrast and handling of data need to be reported for independent interpretation.

Finally, the planning illustrations show how design requirements depend on the effect size targeted: smaller effects need larger samples under the listed assumptions. Those calculations are not observed power and do not replace the trial’s original design rationale, which is not reported in the registry record. Taken together, the posted information highlights the importance of effect estimates, confidence intervals, analysis transparency and clear reporting of missingness and outcomes, rather than relying on a single p-value.

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 does not report the original sample-size justification or design assumptions. The planning illustrations are based on the observed effect and cannot be used to infer the trial’s original rationale. The record also does not report the detailed statistical analysis plan, covariates in the sponsor’s regression, or the contrast coding needed to reconcile the sponsor’s estimate with the unadjusted recalculation.

Missing outcome handling and the analysis population are not reported in the registry record. The outcome summary counts and adverse-event at-risk counts differ, and the record does not explain why. Participant flow, adherence, protocol deviations and the extent of missing measurements are also not described in the posted information. These omissions limit assessment of how representative the endpoint summaries are of the randomized groups.

The record lists three outcome measures and three analyses, but no secondary results are posted. It does not report whether multiplicity was addressed or how the primary outcome was prioritized in the analysis plan. A clinically important threshold for change in liver fat percentage is not reported, so the clinical importance of the estimated effects cannot be determined from the numerical results alone.

The trial is recorded as single-masked, but the identity of the masked party is not reported. Detailed eligibility criteria and the sponsor model’s assumptions are also not available in the registry record. Finally, the adverse-event listings give event counts and terms without sufficient clinical context to establish attribution or interpret each event’s circumstances. These are limits of the posted record, not evidence that the trial necessarily had deficiencies in conduct.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Treatment of Non Alcoholic Fatty Liver Disease With n-3 Fatty Acids — NCT00760513.
• Registry record last updated 2019-10-25; status last verified 2019-10.
• Results first posted 2019-10-25.
• 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 record describes a completed, randomized, single-masked, parallel-group phase 4 trial sponsored by University Hospital Southampton NHS Foundation Trust. It lists enrollment of 103 and a treatment period of 18 months. OMACOR, described as omega-3 fatty acid (fish oil), was compared with an olive-oil dummy pill; both were recorded as 4 grammes daily oral capsules.

The primary endpoint was change in liver fat percentage measured by magnetic resonance spectroscopy at baseline and 18 months. The posted group means were -7.9 for omega-3 fatty acid and -4.6 for dummy pill. The unadjusted recalculation and sponsor regression analysis both have confidence intervals that include zero, with different estimates and reported methods.

The registry lists three outcome measures and three analyses, but no secondary results are posted. The record does not report the original sample-size rationale, missing-data approach, analysis population, detailed regression specification, or deaths. Interpretation is therefore limited to the posted primary outcome summaries, the reported sponsor analysis and the safety entries.