Obesity and Nonalcoholic Fatty Liver Disease: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Obesity and Nonalcoholic Fatty Liver Disease (NCT00262964), a randomized na study. The primary outcome is Hepatic Insulin Sensitivity Index (HISI).

2. Clinical Question

The trial’s broader goals concerned the biology of NAFLD in people with obesity and the effects of marked weight loss on liver and metabolic abnormalities. Its listed hypotheses addressed liver fat accumulation, glucose production, liver protein synthesis, lipid peroxidation, inflammation, necrosis, fibrosis, and weight loss. Those aims provide context, but the posted primary result is a baseline comparison of HISI between NAFLD participants and controls. It does not by itself test whether weight loss, niacin, fenofibrate, or placebo changed HISI.

3. Trial Design

The registry identifies this as a completed, randomized, single-masked, factorial study with phase listed as not applicable. Enrollment was 51. The recorded start was 2004-10 and primary completion was 2008-12. The sponsor was Washington University School of Medicine. Although the overall study is described as randomized and factorial, the primary result is a baseline cross-sectional comparison between participants classified as having NAFLD and controls; it is not a randomized treatment contrast.

The NAFLD group combined participants assigned to different study conditions for its baseline characteristics. The registry describes a niacin regimen lasting 16 weeks, a nightly fenofibrate regimen lasting eight weeks, and an eight-week placebo course. It also says placebo participants’ baseline data were included with those for the two intervention groups in the overall NAFLD baseline characteristics. Controls were selected for intrahepatic triglyceride content below the study’s 10% threshold, measured by magnetic resonance spectroscopy. The record does not establish that controls were randomized to the drug interventions.

The primary endpoint timeframe is “baseline cross-sectional data.” The analysis population is described as per protocol, with 34 participants in the NAFLD group and 17 in the control group. The primary outcome is a continuous measure reported as a mean with standard error. The registry lists 12 outcome measures and 20 analyses, and identifies five secondary outcome titles. The original design’s allocation details, masking procedures, and statistical-analysis plan beyond the posted descriptions 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.

Before assignment: We screened 138 subjects. 80 would-be participants failed the screening. This was often due to not having Non-alcoholic Fatty Liver Disease. Other subjects were excluded due to use of various medications or the presence of some excluded disease such as type 2 diabetes. Of the 58 that passed screening 51 chose to enroll in the study.

Overall Study

Analysis population for the primary outcome, as defined in the registry: number of subjects determined by power calculations. Analysis was per protocol. Intrahepatic triglyceride was determined by magnetic resonance spectroscopy.

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 Hepatic Insulin Sensitivity Index (HISI), measured over baseline cross-sectional data.

The primary endpoint is the Hepatic Insulin Sensitivity Index (HISI), reported in [10000/(μmol/min)x(mU/L)]. It is intended to represent hepatic insulin sensitivity using the rate of glucose production and plasma insulin concentration. The registry describes HISI as the reciprocal of glucose rate of appearance multiplied by insulin concentration. The factor 10000 is described as a conventional adjustment to make the measure more readable.

HISI is used as a surrogate marker: it offers a quantitative way to characterize hepatic insulin sensitivity from these metabolic measurements. The registry cautions that it has not been validated and that no normal range is established. Consequently, the value should be interpreted as an index used for comparison in this study, not as a clinical threshold or a direct measure with an established normal-versus-abnormal interpretation.

The endpoint was measured at baseline, and the posted primary comparison is between the NAFLD group and controls. It therefore describes a cross-sectional difference in the index. It does not estimate change over time, nor does it isolate the effect of any of the listed drug interventions. The registry’s broader interest in liver pathology and metabolic abnormalities does not change what this particular endpoint directly measures.

7. Results Posted in the Registry

• NAFLD: mean 0.80 versus 1.40 on control; difference -0.60 (95% CI -1.18 to -0.02), standardized effect d = -0.66; z-test p = 0.042.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Very Low Density Lipoprotein - Triglyceride Production Rate

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
• Result:
  • NAFLD: mean 6.70 versus 3.80 on control; difference 2.90 (95% CI 1.76 to 4.04), standardized effect d = 1.16; z-test p = <0.001.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for NAFLD than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The secondary outcome titles cover VLDL-triglyceride production, VLDL apolipoprotein B production, VLDL-triglyceride clearance, VLDL-triglyceride production rate, and VLDL-triglyceride concentration. These measures relate to aspects of lipid transport and metabolism, which are relevant to the study’s broader interest in metabolic abnormalities associated with NAFLD. They address different quantities from HISI, so they provide context rather than a direct replication of the primary endpoint.

The registry lists five secondary outcome titles, but a complete numerical pattern across all of them cannot be assessed from the available posted results. A detailed comparison is available for VLDL-triglyceride production rate; the remaining endpoints’ estimates and uncertainty are not reported in the registry record. Therefore, the available information does not establish whether the secondary outcomes consistently support, qualify, or contradict the primary group difference.

Unadjusted secondary results generally carry less weight when several outcomes or analyses are examined, because the chance of at least one apparently notable result can increase across repeated testing. Whether the study adjusted for multiple comparisons, prioritized secondary outcomes, or used a prespecified testing sequence is not reported in the registry record. The secondary findings should consequently be interpreted as exploratory context, not as independent confirmation of the baseline HISI contrast or evidence about the effects of the listed treatments.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Very Low Density Lipoprotein - Triglyceride Production Rate
• Change From Baseline in Very Low Density Lipoprotein Apolipoprotein B Production Rate
• Change From Baseline in VLDL-Tg Clearance Rate
• Change From Baseline in VLDL-Tg Production Rate
• Change From Baseline in Very Low-density Lipoprotein Triglyceride Concentration

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous and is summarized as a mean with standard error. A mean describes the group’s central value for the measure. A standard error describes the precision of the estimated mean, rather than the range of values among participants. The registry gives a mean HISI of 0.8 with standard error 0.14 for the NAFLD group and 1.4 with standard error 0.26 for controls.

What does the mean difference represent?

The mean difference compares the NAFLD group’s mean with the control group’s mean, using the direction stated for the comparison. Its estimate is -0.6. A negative estimate means the NAFLD group’s mean was lower than the control group’s mean on this index. The estimate is expressed in the endpoint’s units; it is not a percentage change, a treatment effect, or a statement about the difference for every participant.

How should the interval be read?

A confidence interval is a range of values compatible with the observed estimate under the assumptions of the calculation. In general, a narrower interval indicates greater precision, while a wider interval leaves more uncertainty about the size of the contrast. The recalculated interval extends from -1.179 to -0.021. Its position on the negative side of zero accords with the direction of the estimated difference. The registry’s sponsor-reported analysis identifies a 95% confidence level, but gives no confidence limits for that analysis.

What does the p-value address?

A p-value describes how unusual results at least as inconsistent with a specified null comparison would be if that null model and its assumptions held. It does not measure the probability that the null is true, the probability that the finding is due to chance, or the clinical importance of the estimate. The recalculated unadjusted p-value is 0.042. The sponsor-reported two-sided t-test gives p <0.019. The reason these reported values differ is not reported in the registry record.

The sponsor’s method is identified as a two-sided t-test. “Two-sided” means the test considers differences in either direction, rather than testing only whether one group has a larger value. A t-test compares group means while accounting for their variability and sample sizes. The registry does not give the test statistic, detailed assumptions, or additional model specifications. The recalculation uses posted summary statistics and is unadjusted; it is not a substitute for the sponsor’s analysis.

Why does study design matter?

Random assignment can help make treatment groups comparable for estimating intervention effects, but the primary contrast is between participants with NAFLD and controls at baseline. NAFLD status was not described as randomized. The observed contrast may therefore reflect group differences that cannot be separated from disease status using the posted summary alone. The word “factorial” is the registry’s design label; details sufficient to reconstruct the design or its analysis are not reported in the registry record.

General statistical context: variability among individual observations and uncertainty in a group mean are different quantities. The posted summaries provide standard errors, not standard deviations. The recalculated comparison includes a pooled standard deviation of 0.908 and standardized mean difference of -0.661, but these are derived summaries, not the endpoint values themselves. Standardized effects can express a difference relative to variability; they do not resolve the cross-sectional design or establish clinical importance.

General statistical context: over-dispersion matters when a model assumes less variability than the data contain, because standard errors can then be too small and confidence intervals too narrow. The primary outcome is analyzed with a t-test, and the registry does not report an over-dispersion assessment or a count-data model for this endpoint. There is no basis in the registry record to claim that over-dispersion was present or that it affected this comparison.

11. Confidence Intervals and Precision

The recalculated mean difference is -0.6, with an interval from -1.179 to -0.021. The interval gives a range of plausible values for the group contrast under the recalculation’s assumptions. It lies on the negative side of zero, consistent with the lower mean in the NAFLD group. Because its upper limit is close to zero, the range also indicates that the estimated contrast is not precisely separated from a null difference. The interval does not establish the clinical importance of any value within it.

The group means are estimated with standard errors of 0.14 for NAFLD and 0.26 for controls. These standard errors describe uncertainty in each mean, not how widely participants’ individual HISI values vary. The group sizes are 34 and 17, respectively. The smaller control group and the difference between group sizes are relevant context for the precision of the comparison, but do not by themselves identify the source of uncertainty.

The sponsor’s analysis reports a 95% confidence level and p <0.019, but its confidence limits are not reported in the registry record. The recalculated p-value is 0.042, and the recalculated interval is based on posted summary statistics. These outputs should not be merged into a single estimate of precision when the reason for their differing p-values is not available. Both the surrogate nature of HISI and the cross-sectional comparison limit what precision can say about clinical effects or causes.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total events. They are illustrations based on the observed effect and are not the original trial’s sample-size justification. The stated assumptions are a two-sided significance level of 0.05, equal allocation between two arms, a normal approximation, and an effect to detect set at the stated fraction of the observed effect. The original study’s own design assumptions and detailed power calculations are not reported in the registry record.

The 80% power column gives the planned number of participants per arm for a design that would have an 80% chance of detecting the specified effect under the stated assumptions, if that effect and assumptions were correct. The 90% power column represents a higher target probability of detecting that effect and generally requires a larger planned sample. The table considers planning for 100%, 75%, and 50% of the observed effect. Smaller effects need more participants to detect under the same planning assumptions, which is why the participant requirements increase as the target effect becomes smaller.

These are planning illustrations, not observed power and not a retrospective verdict on whether the study was adequately designed. They use the observed effect as an input, so they do not establish the true effect in a future study. The table’s arm-based counts also assume equal allocation, which is distinct from the analyzed group sizes in this baseline comparison.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so 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 = -0.600; pooled standard deviation σ = 0.908.
2. n = 2 × (1.96 + 0.842)² × 0.908² / -0.600² = 35.9, rounded up to 36 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 <- -0.6                      # observed difference in means
sigma <- 0.907771435765544                     # 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(262964)
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 = 36 (80% power), 49 (90% power)
 75% of observed effect: n per arm = 64 (80% power), 86 (90% power)
 50% of observed effect: n per arm = 144 (80% power), 193 (90% power)
power.t.test: 36.9 
Simulated power at n = 36 per arm: 0.788 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Analyses Reported by the Sponsor

The registry reports that the sponsor’s primary analysis used a two-sided t-test and gives p <0.019 for the comparison between the NAFLD and control groups. It does not report the sponsor’s confidence limits, test statistic, or fuller analysis details. The posted summaries support a simple unadjusted recalculation, which gives a mean difference of -0.6, an interval from -1.179 to -0.021, and p=0.042.

The sponsor-reported p-value and the recalculated p-value are not the same. The registry record does not report why they differ, so no explanation should be inferred. The recalculation is based on the posted group means, standard errors, and sample sizes; it is not a reconstruction of any unreported adjustments or analysis choices. The sponsor’s result remains the result reported by the trial record, while the recalculation is a separate descriptive check on the posted summaries. The discrepancy flag is not raised for this record.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 12 outcome measures and 20 analyses, and identifies five secondary outcome titles. The posted primary comparison has an unadjusted recalculated p-value. The multiplicity strategy for the full set of outcomes and analyses is not reported in the registry record. It is therefore not possible to determine whether the primary result was protected by a prespecified testing hierarchy or whether secondary comparisons were adjusted for multiple testing.

The registry describes the primary analysis population as per protocol. It does not report the number of participants excluded from that analysis, reasons for exclusion, missing endpoint values, or how missing data were handled. It also does not provide enough information to determine whether the analyzed population differs from all enrolled participants or whether an intention-to-treat analysis was conducted. These details matter because exclusions and missing measurements can affect the comparability and representativeness of analyzed groups.

The record says the number of subjects was determined by power calculations, but the original calculation’s target effect, power, significance level, allocation assumptions, and analysis assumptions are not reported in the registry record. The planning figures elsewhere are illustrations computed from the observed effect, not evidence of the original design rationale. Interim analyses, stopping rules, protocol deviations, and the full statistical analysis plan are also not reported in the registry record. Without those details, the registry results cannot establish how all analytic decisions were set before outcome data were examined.

16. 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 2% reporting threshold.

Most frequent non-serious adverse event terms

The serious adverse event counts are zero in each listed group: NAFLD-fenofibrate, NAFLD-niacin, NAFLD-no drug, and controls. The numbers at risk for serious adverse events were 11, 11, 12, and 17, respectively. These figures describe what was reported for the listed groups; they do not establish that no unrecorded or unobserved events occurred.

For other adverse events, one event is listed in the fenofibrate group, with zero listed in the niacin, no-drug, and control groups. The registry record does not report the type of that event in the information available. Death counts are not reported in the registry record. These small group counts are descriptive and should not be interpreted as a comparative safety estimate or as evidence that one group has a different risk.

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

The posted primary data show a lower mean HISI in the NAFLD group than in controls at baseline: 0.8 compared with 1.4, with a mean difference of -0.6. The recalculated interval extends from -1.179 to -0.021, and the unadjusted recalculated p-value is 0.042. The sponsor separately reports a two-sided t-test with p <0.019. The reason the reported p-values differ is not reported in the registry record.

This is a group-level, cross-sectional finding. It does not establish that NAFLD caused the difference, because the primary contrast is not a randomized comparison of NAFLD status. It does not show that niacin, fenofibrate, placebo, or weight loss changed HISI, because the primary endpoint is baseline data. It also does not establish that the observed index difference corresponds to a clinical benefit, harm, or meaningful threshold.

The endpoint’s interpretation is limited by its status as an unvalidated surrogate with no normal range, as stated in the registry. The estimate and interval describe the measured contrast and its statistical precision, not liver histology, future disease course, or an individual participant’s prognosis. The broader study hypotheses concern liver fat and metabolic and histologic abnormalities, but this result alone does not answer all of those questions.

For readers, the most defensible conclusion is narrow: the analyzed NAFLD and control groups had different baseline mean values on the posted HISI measure, with the NAFLD group’s mean lower. The magnitude is uncertain, the sponsor’s reported p-value is distinct from the unadjusted recalculation, and neither result converts this observational contrast into a treatment-effect estimate.

18. Why This Trial Matters Statistically

This trial illustrates why the study’s overall design label and the specific analysis must be read separately. The registry calls the study randomized and factorial and lists several drug interventions, yet the primary endpoint is baseline cross-sectional data comparing NAFLD participants with controls. That comparison is informative about group differences at baseline, but it does not estimate the effect of randomized treatment. Identifying the estimand—the quantity a result is intended to estimate—is essential before interpreting a p-value or mean difference.

The endpoint also illustrates the difference between a statistical measure and a validated clinical measure. HISI combines glucose production and insulin concentration into a surrogate index, but the registry states that the index has not been validated and has no normal range. A statistically distinguishable group mean therefore does not automatically imply a clinically interpretable threshold or a patient-level consequence.

Finally, the record shows why reported analyses and summary-statistic recalculations should be kept distinct. The sponsor’s two-sided test and the unadjusted recalculation produce different p-values, while the reason is not reported. The group summaries still permit an independent description of the estimated contrast and its precision, but they do not reveal unreported analytic choices. Together, these features make the trial a useful example of interpreting results in light of endpoint validity, comparison structure, and incomplete statistical reporting.

19. 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 primary comparison is cross-sectional and contrasts participants with NAFLD against controls, rather than randomized treatment groups. It cannot establish that NAFLD caused the observed HISI difference. The analyzed group sizes are 34 and 17, and the registry describes the analysis as per protocol without explaining exclusions or how missing measurements were handled.

HISI is a surrogate measure that the registry says has not been validated and has no normal range. Its clinical interpretation is therefore limited, even when a group contrast is statistically distinguishable. The primary endpoint concerns baseline data, so it does not address change following the listed interventions or the effect of weight loss.

The sponsor’s reported p-value differs from the unadjusted recalculation based on posted summary statistics, and the reason is not reported in the registry record. The sponsor’s confidence limits and full analytic details are absent. Multiplicity handling, the original sample-size assumptions, the full statistical plan, interim analyses, and missing-data procedures are also not reported in the registry record. These omissions limit assessment of how robust the result is to analysis choices and how it fits into the study’s broader set of outcomes.

Finally, the available secondary results do not permit a comprehensive assessment of consistency across the listed secondary endpoints. The safety counts are descriptive, and the registry does not provide event types or death counts in the information available. These constraints call for a narrow interpretation of the posted baseline comparison.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Obesity and Nonalcoholic Fatty Liver Disease — NCT00262964.
• Registry record last updated 2018-07-11; status last verified 2018-06.
• Results first posted 2010-06-28.
• 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.

23. Record Summary

NCT00262964, “Obesity and Nonalcoholic Fatty Liver Disease,” is listed as completed, randomized, single-masked, and factorial, with enrollment of 51. Its primary endpoint is baseline HISI, compared between participants with NAFLD and controls. The reported means are 0.8 and 1.4, respectively, and the recalculated mean difference is -0.6, with an interval from -1.179 to -0.021 and an unadjusted p-value of 0.042. The sponsor reports a two-sided t-test with p <0.019; the reason for the difference is not reported in the registry record.

The result is a cross-sectional group comparison on an unvalidated surrogate with no established normal range, not an estimate of intervention effect. The record’s missing details on multiplicity, missing data, and the original statistical plan limit further interpretation.