Fish Oil and Nonalcoholic Fatty Liver Disease (NAFLD) Study: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Fish Oil and Nonalcoholic Fatty Liver Disease (NAFLD) Study (NCT01285362), a randomized na study. The primary outcome is Participants With Normalized Liver Enzyme Levels.

2. Clinical Question

The registry background describes the study hypothesis as testing whether fish oil could normalize elevated liver enzymes and also improve plasma lipid levels and insulin resistance. Those latter outcomes were listed as secondary outcomes, but their numerical results are not reported in the registry record. The clinical question is therefore narrower than the full set of hoped-for effects: the primary endpoint concerns a binary classification of liver enzyme normalization, not the size or pattern of changes in individual enzyme measurements. The age wording discrepancy also limits certainty about exactly which age group the result applies to.

3. Trial Design

The registry describes a randomized, quadruple-masked, parallel-group trial. Participants were assigned to fish oil supplementation or placebo supplementation. The posted results include 4 participants in the fish oil group and 4 in the placebo group, for an enrollment of 8. Those are the arm counts used for the reported primary endpoint. The registry record does not report the randomization sequence, allocation concealment procedures, or whether assignment was planned in a particular ratio.

The fish oil group received capsules containing n-3 fatty acids at 4g/day. Each 1g capsule contained 465mg of EPA and 375 mg of DHA. The placebo group received corn oil capsules at the same dose, described as identical in size and color. The record labels the masking as quadruple but does not identify which roles were masked or describe how masking was maintained and assessed.

The study status is completed. The recorded start was 2013-03, and primary completion was 2014-09. The primary outcome was the number of participants with normalized liver enzyme levels, defined as having levels within a normal laboratory range, with a timeframe of up to 12 months from entry into the study. The registry also lists two secondary outcomes: normalization of plasma lipid levels and attenuation of insulin resistance.

The registry record does not report a protocol-level statistical analysis plan, a sample-size justification, a planned recruitment target beyond the recorded enrollment, or details of follow-up by participant. It also does not explain the difference between the official title’s reference to children and the primary outcome description’s reference to young adults. These omissions matter when judging how closely the posted results can be matched to the original intended population and analysis.

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 Participants With Normalized Liver Enzyme Levels, measured over Up to 12 months from entry into the study.

The primary endpoint counts participants whose liver enzyme levels were within a normal laboratory range. It converts a laboratory outcome into a binary status: each participant either met the stated normalization definition or did not. The record describes the outcome as a count of participants and defines normalization using the laboratory’s normal range. It does not identify which liver enzymes were assessed, give the numerical reference limits, or specify whether all measured enzymes had to fall within range.

A binary normalization endpoint can be useful when the clinical question concerns whether a participant crossed a predefined threshold rather than the amount of change in a laboratory measurement. It is also relatively straightforward to interpret as a participant count. However, it does not preserve the magnitude of each person’s measurement or change. Two participants with very different enzyme levels could receive the same binary classification if both were outside the normal range, while small changes near a threshold could alter the classification.

In this trial, the timeframe was up to 12 months from study entry. The registry does not report a more specific assessment schedule or say how measurements from different visits were handled. The posted results report 0 participants meeting the endpoint in each arm. The record does not give individual measurements, change-from-baseline results, or a definition for handling missing or unavailable enzyme tests. Consequently, the endpoint counts alone do not show the trajectory of liver enzyme values over time.

7. Why No Re-analysis Is Shown

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary at the participant level: a participant is counted if liver enzyme levels fall within a normal laboratory range, and otherwise is not counted as meeting the endpoint. The posted outcome is therefore a count, with the arm sizes giving the number of participants represented. This format is different from reporting a mean enzyme level or an average change from baseline. The registry record does not provide those continuous measurements.

What does a two-group comparison estimate?

In general, a comparison of two binary outcomes can focus on the difference in the proportions meeting the endpoint, a ratio of those proportions, or an odds-based measure. These statistics answer related but not identical questions. A difference describes an absolute contrast, while ratios describe a relative contrast. Each requires an analysis choice and an estimate of uncertainty. No such comparative estimate is reported for this outcome, and no recalculated comparison is presented. The registry record explicitly indicates that values were missing or not estimable for a two-arm comparison of this binary endpoint.

Why is uncertainty important?

In general, an observed count is only one realization from the process that could produce outcomes in a larger population. A confidence interval gives a range of values compatible with the observed data under a specified method and assumptions. With small groups, binary data can be especially coarse: a single participant’s classification can materially alter the observed count pattern. Here, the reported arm counts are 0 of 4 in each group, but no confidence interval or other uncertainty measure is reported. The counts should therefore be read as a description of the enrolled participants, not as a precise estimate for all people with NAFLD.

Statistical tests also depend on assumptions and choices, including the test used, the analysis population, and how missing outcomes are handled. The registry record does not report the method for testing the primary comparison, a significance threshold, or an analysis plan. A p-value cannot be reconstructed from the information in the registry record and should not be inferred from the matching counts.

What is the role of the planning calculations?

In general, sample-size planning asks how many participants might be needed to detect a prespecified effect under stated assumptions. Such calculations are planning illustrations, not observed power, and they do not show whether an intervention has an effect. No numerical planning estimates are reported in the registry record for this outcome. The record also does not report the trial’s own sample-size justification, a target effect, or the assumptions used to choose its enrollment. The listed enrollment of 8 is the recorded study enrollment, not evidence that the study had adequate power for the primary comparison.

For a binary outcome, planning depends on assumptions about the event frequency in each group and the size of the difference worth detecting, as well as the chosen error rate, allocation, and calculation method. The registry record does not give the underlying event-frequency assumptions or a prespecified effect size. No additional planning values should be inferred from the observed endpoint counts.

Why can model choice matter?

In general, statistical methods for binary outcomes may use exact approaches, large-sample approximations, or regression models. The suitability of a method depends in part on the amount of data, the distribution of outcomes, and the question being asked. With sparse counts, some approximations can be unreliable or produce estimates that are not finite; exact methods can avoid some approximation issues but may still yield broad uncertainty. These are general considerations, not methods identified as used in this trial. The registry record does not report which method, if any, was used for a formal primary comparison.

Randomization supports a causal comparison when assignment, follow-up, and analysis are handled appropriately, but randomization alone does not remove uncertainty or correct incomplete outcome data. The record describes the design as randomized and parallel-group but does not report allocation procedures, participant flow, deviations from assignment, or a prespecified analysis population. It is therefore not possible to assess these aspects from the registry entry.

The endpoint’s laboratory threshold also has methodological implications. A binary definition may be easier to communicate, but results can depend on the chosen reference ranges, measurement timing, and rules for multiple enzymes or repeated assessments. The record defines normalization as within a normal laboratory range but does not report threshold values or the precise assessment rules. That limits reproducibility and makes it difficult to tell how borderline or inconsistent measurements were classified.

10. Exact Estimates for Each Arm

No two-arm comparison is shown for this trial, but each arm's result can still be summarized with exact interval estimates computed from the posted counts. The Clopper-Pearson interval is exact and conservative; the Wilson interval is a common closer-to-nominal alternative; the Bayesian credible interval uses a uniform Beta(1, 1) prior. For small groups the three can differ noticeably.

R code and output

arm    <- c("Fish Oil Supplementation (Group A)", "Placebo Supplementation (Group B)")
n      <- c(4, 4)
events <- c(0, 0)
for (i in seq_along(n)) {
  ci <- binom.test(events[i], n[i])$conf.int          # Clopper-Pearson exact interval
  cr <- qbeta(c(0.025, 0.975), 1 + events[i], 1 + n[i] - events[i])   # Bayesian, uniform Beta(1,1) prior
  wi <- (function(x, n) { p <- x / n; z <- qnorm(0.975); d <- 1 + z^2 / n
    c((p + z^2 / (2 * n) - z * sqrt(p * (1 - p) / n + z^2 / (4 * n^2))) / d, (p + z^2 / (2 * n) + z * sqrt(p * (1 - p) / n + z^2 / (4 * n^2))) / d) })(events[i], n[i])
  cat(sprintf("ARM|%s|%d|%d|%.1f|%.1f|%.1f|%.1f|%.1f|%.1f|%.1f\n", arm[i], n[i], events[i], 100 * events[i] / n[i],
              100 * ci[1], 100 * ci[2], 100 * wi[1], 100 * wi[2], 100 * cr[1], 100 * cr[2]))
}

ARM  Fish Oil Supplementation (Group A)  4  0  0.0  0.0  60.2  0.0  49.0  0.5  52.2
ARM  Placebo Supplementation (Group B)  4  0  0.0  0.0  60.2  0.0  49.0  0.5  52.2

11. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary outcome, the number of participants with normalized liver enzyme levels, and two secondary outcomes: the number with normalized plasma lipid levels and the number with insulin resistance attenuated. Numerical results for the two secondary outcomes are not reported in the registry record. A plan for interpreting multiple outcomes, including whether any adjustment or hierarchy was intended, is also not reported in the registry record.

In general, testing several outcomes can increase the chance of finding an apparently notable result by chance if each is examined independently. A prespecified outcome hierarchy or a multiplicity adjustment can address aspects of this issue, but the appropriate approach depends on the study’s aims. No such plan should be assumed for this trial. The posted primary outcome counts alone do not resolve the secondary questions.

The registry record does not report the number of participants with missing primary outcome measurements, the reasons for missingness, or how missing values were handled. It also does not state whether the analysis included all randomized participants, only participants with observed outcomes, or another defined group. The arm counts in the posted endpoint results are 4 per group, but the record does not supply a participant-flow account that would clarify whether any data were unavailable or excluded.

In general, missing outcome data can affect an estimate when the probability of missingness is related to the outcome or differs between groups. Approaches may include defined assumptions, sensitivity analyses, or other prespecified procedures; none is reported in the registry record. Consequently, the endpoint counts cannot be evaluated for robustness to missing-data assumptions.

12. 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 posted safety figures report 0 serious adverse events among 4 participants at risk in the fish oil group and 0 among 4 participants at risk in the placebo group. The figures also report 0 other adverse events among 4 participants at risk in each group, and 0 deaths in either group. No serious adverse-event terms are listed.

These are event counts for the participants represented in the registry record. They do not establish that no adverse events could occur, nor do they quantify risk beyond the observed study experience. In general, the absence of a recorded event in a small group leaves substantial uncertainty about event frequencies in a wider population. The registry record does not report detailed event definitions, severity classifications beyond the serious/other categories, exposure-adjusted rates, or follow-up completeness for safety assessment.

The safety counts should be read separately from the primary liver enzyme endpoint. A zero count of serious adverse events does not establish a favorable or unfavorable effect on liver enzymes, and the primary endpoint counts do not determine safety. The available record supports only the descriptive statement that no serious adverse events, other adverse events, or deaths were recorded in these groups.

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

The registry results document a small randomized comparison of fish oil and placebo supplementation, with 4 participants in each group. For the primary endpoint, 0 participants in either group were recorded as having normalized liver enzyme levels during the stated timeframe of up to 12 months from entry. This is the direct descriptive result. It does not quantify a treatment effect, establish equivalence, or determine what would happen in a larger or different population.

The endpoint is a threshold-based measure, not a complete account of liver enzyme response. It does not indicate whether participants’ values improved without reaching the normal range, worsened, or remained similar. No individual measurements or continuous changes are reported. The record also does not identify the enzyme thresholds or the rules used to combine measurements, limiting interpretation of what exactly counted as normalization.

The trial’s stated hypothesis included normalization of liver enzymes and possible changes in plasma lipid levels and insulin resistance. The registry names those secondary outcomes, but their numerical results are not reported in the registry record. The primary endpoint cannot be treated as a substitute for those results, and the background hypothesis should not be mistaken for evidence that an outcome occurred.

The record describes randomized assignment and quadruple masking, but does not give enough detail to assess allocation procedures, masking roles, analysis populations, missing data, or the statistical plan. These omissions, together with the small recorded enrollment and lack of a comparative estimate or uncertainty interval, constrain what can be concluded from the results. They do not show that the study was improperly conducted; they mean that those aspects cannot be evaluated from the registry record.

In general, clinical trial results are interpreted by considering the outcome definition, the estimated effect, its precision, and the design and analysis assumptions. Here, the posted primary outcome information is limited to counts. It supports a descriptive account of the recorded participants, while leaving the size and precision of any broader group difference unquantified.

14. Why This Trial Matters Statistically

This trial illustrates the difference between recording an outcome and estimating a treatment contrast. The registry reports a binary primary endpoint and the number of participants meeting it in each group, but does not report a comparative estimate or its uncertainty. A count can be transparent and easy to understand, yet it does not by itself show how precisely the result applies beyond the participants observed.

The small enrollment also makes precision especially important. In general, sparse binary outcomes can produce unstable estimates, and the outcome classification of one participant can noticeably change the observed pattern. A confidence interval and a clearly described method would help readers understand the uncertainty, but neither is reported for the primary comparison. The matching observed counts should not be confused with proof that the groups are alike.

The endpoint definition raises another statistical issue: threshold-based outcomes simplify interpretation but can discard information about measurement levels and changes. Reporting continuous laboratory results alongside a prespecified binary endpoint can help describe what happened across the full range of measurements. Such results are not reported in the registry record.

Finally, the record shows why complete reporting of analysis plans, participant flow, missing data, and secondary outcomes matters. Those details make it possible to assess whether results were analyzed as intended and how sensitive conclusions might be to analytical choices. Their absence means the available evidence is descriptive and limited, rather than a full account of the trial’s statistical findings.

15. 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 affect interpretation of the posted results. The recorded enrollment was 8, with 4 participants in each arm. This provides a small basis for characterizing a binary outcome, and the registry record does not report a sample-size justification or planned detectable effect. The enrollment should not be taken as evidence that the study was adequately sized for its primary comparison.

The registry record gives no comparative estimate, confidence interval, p-value, or detailed statistical analysis. It also does not report an analysis plan, participant flow, analysis population, or the handling of missing outcomes. Therefore, it is not possible to assess whether the posted counts include all randomized participants under a prespecified approach or how unavailable measurements were treated.

The endpoint definition is incomplete for replication and detailed clinical interpretation. Normalization is described as having liver enzyme levels within a normal laboratory range, but the enzymes, numerical reference limits, and rules for multiple measurements are not reported. The timeframe is up to 12 months from entry, without a more specific assessment schedule in the registry record.

There is also a population-description inconsistency: the official title refers to children, while the primary outcome description refers to young adults. Ages and an explanation for the difference are not reported in the registry record. The masking description says quadruple but does not identify the masked roles. Finally, numerical findings for the listed lipid and insulin-resistance outcomes are not reported. These limitations restrict interpretation of both the primary result and the broader study aims.

16. Related Tutorials

17. Related Statistical Calculators

18. Sources

• ClinicalTrials.gov: Fish Oil and Nonalcoholic Fatty Liver Disease (NAFLD) Study — NCT01285362.
• Registry record last updated 2022-05-05; status last verified 2022-05.
• Results first posted 2022-05-05.
• 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.

19. Record Summary

The registry record describes NCT01285362, a completed randomized, quadruple-masked, parallel-group study sponsored by Columbia University. Recorded enrollment was 8. The recorded start was 2013-03, and primary completion was 2014-09.

The study compared fish oil supplementation with placebo supplementation using corn oil capsules. The primary outcome counted participants with liver enzyme levels within a normal laboratory range, during a timeframe of up to 12 months from study entry. The posted counts were 0 of 4 in the fish oil group and 0 of 4 in the placebo group. No comparative analysis result is reported.

Two secondary outcomes were listed: normalization of plasma lipid levels and attenuation of insulin resistance. Their numerical results are not reported in the registry record. Safety figures report no serious adverse events, other adverse events, or deaths in either group. Important details—including the statistical analysis plan, missing-data handling, analysis population, and explanation of the age-description discrepancy—are not reported in the registry record.