Lipoic Acid and Omega-3 Fatty Acids for Cognitive Impairment in Multiple Sclerosis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Lipoic Acid and Omega-3 Fatty Acids for Cognitive Impairment in Multiple Sclerosis (NCT02133664), a randomized phase 1, phase 2 study. The primary outcome is Paced Auditory Serial Addition Task (PASAT).

2. Clinical Question

3. Trial Design

The registry record describes a randomized, triple-masked, parallel-group Phase 1 and Phase 2 trial. The planned comparison was lipoic acid plus omega-3 fatty acids against placebo. The record does not identify which individuals or groups were masked, how randomization was implemented, or whether allocation was concealed. Those details are not reported in the registry record.

Enrollment was 54. The primary outcome results include 21 participants in the combination group and 21 in the placebo group. The outcome description says that only participants who completed PASAT at both baseline and 12 weeks were analyzed. The registry record does not explain the difference between total enrollment and the number included in the reported outcome, or describe reasons for missing outcome observations.

The study start is recorded as 2014-06, and primary completion as 2016-05. Its status is completed. The registry lists multiple sclerosis and cognition as conditions. It does not report the study setting, recruitment locations, detailed eligibility criteria, intervention doses, adherence measures, or follow-up beyond the primary outcome timeframe.

The registry record identifies the study’s primary aim as collecting data to determine an effect size for planning a larger study. That aim provides context for interpreting the estimates: the reported comparison is an estimate from a relatively small analyzed group, rather than a definitive answer about cognitive outcomes. The trial’s original sample-size assumptions and justification are not reported in the registry record. A separate planning illustration based on the observed effect is not the original trial design rationale.

The registry lists four outcome measures, while no secondary outcome results are posted. One analysis is listed. The analysis population is restricted for the primary outcome to participants with PASAT measurements at both specified time points; other analysis populations 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: 49 participants were excluded from the study for the following: did not meet inclusion criteria (i.e. test scores too high, colorblindness, unclear cognitive status), declined to participate, could not consent, lost to follow-up, and started fish oil.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Only participants who completed PASAT at both baseline and 12 weeks were analyzed.

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 Paced Auditory Serial Addition Task (PASAT), measured over Baseline to 12 weeks.

The primary endpoint was change in the total number of correct responses on the Paced Auditory Serial Addition Task (PASAT) from baseline to 12 weeks. Results are expressed as mean change in correct responses with standard deviations for the two groups. The registry record says that only participants who completed the PASAT at both time points were included in this outcome analysis.

The PASAT is described as a measure of working memory and sustained attention, and is frequently used in multiple sclerosis treatment outcome studies. During the task, an examinee hears a series of numbers at 2 second intervals and responds by adding the last two numbers before the next number is presented. The outcome therefore represents correct task responses over the assessment, not a broad measure of every aspect of cognition.

Using change from baseline is intended to describe how the measure differs over the stated assessment period. General statistical context: a change score summarizes within-participant movement between measurements, while a comparison of group means asks whether the average changes differ between groups. That group comparison can be imprecise, particularly when the analyzed groups are small or individual responses vary widely. The registry record does not report a clinically meaningful threshold for PASAT change, so the practical importance of a given difference cannot be established from this endpoint description alone.

7. Results Posted in the Registry

• Lipoic Acid and Omega-3 Fatty Acids: mean 2.24 versus 3.38 on control; difference -1.14 (95% CI -4.22 to 1.94), standardized effect d = -0.22; z-test p = 0.468.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: it records a count of correct responses, and the registry summarizes it using means and standard deviations. A mean describes the center of the observed values. A standard deviation describes how spread out individual values are around that mean. General statistical context: a mean difference compares group averages, while the standard deviation describes variability within a group; they answer related but different questions.

What the recalculated comparison represents

The recalculated estimate is an unadjusted difference in mean change scores, with the combination group subtracted from the placebo group. The posted estimate is -1.14 correct responses. A negative sign indicates that the observed average change was lower in the combination group than in the placebo group under that subtraction convention. This is a description of the sample estimate, not a statement about cause or clinical importance.

The recalculation uses the group summaries and a pooled standard deviation of 5.09. Its 95% confidence interval is -4.218 to 1.938, and its two-sided p-value is 0.468. General statistical context: a confidence interval describes the range of effect values reasonably compatible with the data and the method used. It is not a range containing a fixed proportion of individual participants’ responses, nor does it give the probability that the true effect lies within the interval.

How to read the p-value

The p-value of 0.468 is calculated for a test of no mean difference under the assumptions of the specified comparison. General statistical context: a p-value measures how unusual data at least as discrepant as those observed would be under a null model. It does not measure the probability that the null hypothesis is true, the probability that a result occurred by chance, or the size or importance of an effect. The p-value should be read alongside the point estimate and confidence interval, rather than as a standalone verdict.

The recalculation is described as unadjusted. The registry record does not report adjustment for baseline values, stratification factors, or other covariates in this calculation. General statistical context: adjustment can account for prespecified variables and may change an estimate or its precision, but whether it is appropriate depends on the study design and analysis plan. No such plan is reported in the registry record.

Why variability matters

The standard deviations, 4.69 and 5.46, are larger than the absolute size of the recalculated mean difference. This indicates substantial variation in individual change scores compared with the difference between group averages. General statistical context: greater variability makes it harder to estimate a group contrast precisely, because participants’ outcomes are less tightly clustered around their group mean. The confidence interval reflects that uncertainty.

The registry describes a t-test for the sponsor’s analysis. A t-test compares group means under assumptions about the outcome distribution and observations. The sponsor analysis is reported for final values, not change scores, and its estimate and uncertainty should be interpreted as a separate analysis. The registry record does not report enough detail to determine whether additional modeling, covariate adjustment, or other procedures were used alongside that test.

What the analysis population means

The outcome description limits analysis to participants with PASAT assessments at both baseline and 12 weeks. This is a complete-measurement analysis for the specified outcome. General statistical context: excluding participants without both assessments can affect the estimate if the availability of measurements is related to outcomes or participant characteristics. The registry record does not report missingness reasons, imputation, sensitivity analyses, or an intention-to-treat analysis for this endpoint. The reported results therefore apply directly to the participants included in the posted analysis, not automatically to everyone enrolled.

The registry’s trial design is randomized, but the posted outcome summaries do not themselves show how randomization was implemented or whether group comparability was assessed. General statistical context: random allocation is intended to make groups comparable on average, while masking can reduce some forms of bias; the specific conduct and success of these procedures cannot be evaluated from the details. The identities of the masked parties and the allocation procedure are not reported in the registry record.

10. Confidence Intervals and Precision

The recalculated mean difference in change scores is -1.14 correct responses, with a 95% confidence interval from -4.218 to 1.938. The confidence interval includes zero and spans estimates in both directions. The data therefore do not pin down the direction or size of the difference precisely. The point estimate is only one value among a range of values compatible with the observed data under the calculation’s assumptions.

General statistical context: a confidence interval reflects sampling uncertainty, not every source of uncertainty. Its width depends on factors including sample size, outcome variability, and the analysis method. A narrower interval would indicate greater precision under the same method, while a wider interval leaves more uncertainty about the underlying effect. The observed standard deviations, 4.69 in the combination group and 5.46 in the placebo group, indicate variability in participants’ change scores.

The recalculated interval differs from the sponsor-reported interval because the registry describes different outcome quantities: the recalculation compares change scores, while the sponsor analysis reports a comparison of final values. The sponsor’s 95% confidence interval is -2.03 to 4.32. It also includes zero. These intervals should not be substituted for one another, since they correspond to different analyses.

The registry record does not report a clinically meaningful difference threshold. Consequently, the confidence interval cannot be classified as excluding or including a prespecified threshold for a meaningful change. Nor does the interval describe certainty about effects on cognitive domains beyond the PASAT or beyond the baseline-to-12-week timeframe.

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 sample-size figures are planning illustrations based on the observed effect, not the original trial’s sample-size rationale. The assumptions listed for the illustration are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses the stated fraction of the observed effect as the effect to detect. The trial’s own design assumptions and sample-size justification are not reported in the registry record.

The entries are participants per arm, not total participants and not total events. The 80% power column gives the estimated number of participants per arm for a design with an 80% chance of detecting the specified effect under the planning assumptions, if that effect is the true one. The 90% power column gives the corresponding planning number for a 90% chance. Power is a property of a planned design under assumed conditions; it is not a description of what happened in this completed trial.

The scenarios use 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. The listed requirements are 313 and 419 participants per arm for 100% of the observed effect; 557 and 745 for 75% of the observed effect; and 1,252 and 1,676 for 50% of the observed effect, for the 80% and 90% power columns, respectively. Smaller effects require more participants under these assumptions, because a smaller group difference is harder to distinguish from sampling variation.

These figures are not observed power. They are planning illustrations calculated from the observed estimate and the stated assumptions. They do not establish what sample size would be appropriate for a future study without a defensible target effect, design details, and analysis plan.

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 = -1.140; pooled standard deviation σ = 5.090.
2. n = 2 × (1.96 + 0.842)² × 5.090² / -1.140² = 312.9, rounded up to 313 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 <- -1.14                      # observed difference in means
sigma <- 5.08958249761216                     # 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(2133664)
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 = 313 (80% power), 419 (90% power)
 75% of observed effect: n per arm = 557 (80% power), 745 (90% power)
 50% of observed effect: n per arm = 1,252 (80% power), 1,676 (90% power)
power.t.test: 313.9 
Simulated power at n = 313 per arm: 0.797 (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 a sponsor analysis using a two-sided t-test of mean differences in final values. It gives a mean difference of 1.14, a 95% confidence interval from -2.03 to 4.32, and p = 0.05. The registry does not provide further detail about the calculation beyond identifying the test and the final-value parameter.

The recalculated comparison instead uses the posted change-score summaries from baseline to 12 weeks. Its mean difference is -1.14, its 95% confidence interval is -4.218 to 1.938, and its p-value is 0.468. Because the sponsor’s analysis concerns final values and the recalculation concerns change scores, they do not estimate precisely the same quantity. Their different signs and p-values should not be interpreted as a direct contradiction without further analysis details.

The sponsor-reported confidence interval spans zero, as does the recalculated interval. Neither posted interval gives a precise estimate of the direction and magnitude of a difference. The registry record does not report a reconciliation of the two analyses, an explanation of their differing results, or additional details that would permit a more complete comparison. The sponsor analysis and the unadjusted recalculation should therefore remain clearly distinguished.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists four outcome measures, but no secondary outcome results are posted. One analysis is listed. The record identifies the PASAT as the primary outcome, but does not report a complete statistical analysis plan, a hierarchy of outcomes, or a multiplicity adjustment strategy. It is therefore not possible to determine from the registry record whether other analyses were planned, whether other outcomes were assessed, or how multiple comparisons were intended to be handled.

General statistical context: multiplicity arises when several outcomes, time points, subgroups, or analyses are tested. Conducting many tests can increase the chance of at least one apparently notable result. Prespecified outcome priorities and analysis procedures help readers understand how results should be interpreted. No such detailed plan is reported in the registry record, so no claim about multiplicity control can be made.

The primary outcome analysis includes only participants who completed PASAT at both baseline and 12 weeks. The record does not report how many participants lacked one or both assessments, why measurements were missing, or whether missing data were imputed. It also does not report sensitivity analyses to examine whether conclusions change under alternative assumptions about missing outcomes. General statistical context: a complete-measurement analysis can be biased if the likelihood of having both measurements is related to the outcome or to factors associated with it. Without missing-data details, the impact of excluded observations cannot be assessed.

The registry record does not report whether an intention-to-treat analysis was performed, or whether the reported analysis followed a prespecified population definition beyond requiring the two PASAT assessments. The primary results should consequently be read as applying to the participants analyzed, rather than automatically to all randomized participants. Further details about analysis populations, missingness, and planned comparisons are not reported in the registry record.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: kidney infection (3.8%), deafness unilateral (3.8%).

The registry reports serious adverse events among 26 participants at risk in the lipoic acid and omega-3 fatty acids group, with 2 participants affected. In the placebo group, 28 participants were at risk and 0 were affected. Deaths are reported as 0 in both groups. These are descriptive counts from the safety record; they do not by themselves establish whether an event was caused by an intervention.

Other adverse events are reported for 21 of 26 participants at risk in the combination group and 12 of 28 participants at risk in the placebo group. The record also lists kidney infection and unilateral deafness among the top serious adverse-event terms, each at 3.8%. It does not provide enough detail in this summary to connect those terms to a particular group or to establish their causes.

The safety counts use different group sizes from the primary PASAT analysis, which includes 21 participants per group. The registry record does not explain the difference in denominators or provide additional details about event timing, severity grading, relatedness assessments, or exposure duration. The counts should be interpreted as recorded adverse-event information, not as a comparative estimate of risk or proof of safety.

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

The posted PASAT data describe mean change in correct responses between baseline and 12 weeks among participants with measurements at both time points. The recalculated estimate is -1.14 for the combination group relative to placebo, with a 95% confidence interval from -4.218 to 1.938. This interval includes zero and spans values in either direction. The estimate is therefore imprecise, and the data do not establish a clear direction or magnitude of the group difference.

The result does not establish that the groups are equivalent. An inconclusive difference estimate is not the same as evidence that two interventions have the same effect. Equivalence or non-inferiority requires a prespecified margin and an analysis designed for that question; neither is reported in the registry record. No threshold for a clinically meaningful PASAT change is reported either, limiting interpretation of the numerical scale in practical terms.

The finding is specific to PASAT performance over the stated timeframe. The registry describes the task as measuring working memory and sustained attention, but it does not establish that the result represents every aspect of cognition. The posted result also does not answer questions about other outcomes, longer follow-up, or effects in people outside the analyzed group.

The sponsor’s final-value analysis is a distinct result from the change-score recalculation. It reports a mean difference of 1.14, with a 95% confidence interval from -2.03 to 4.32 and p = 0.05. Because the analyses address different quantities, neither should be used as a simple replacement for the other. The registry record does not explain the difference between these estimates.

Overall, the registry result is best understood as an uncertain estimate from a small analyzed group, in a study whose stated purpose included gathering effect-size information for a larger study. It does not establish a treatment benefit or lack of benefit, and it does not support conclusions about clinical recommendations.

17. Why This Trial Matters Statistically

This trial is statistically informative because it illustrates the difference between estimating an effect and obtaining a precise estimate. The observed group means and recalculated contrast provide a numerical description of PASAT change in the analyzed participants. The confidence interval, however, is wide enough to include values favoring either group. A point estimate alone would conceal that uncertainty.

The study’s stated aim was to collect data to determine the correct effect size for designing a larger study. That makes the uncertainty especially relevant: planning depends on assumptions about the size of an effect worth detecting, as well as variability and the intended analysis. The planning illustration demonstrates that smaller target effects require more participants under its stated assumptions. Those estimates are not the original trial’s design justification.

The record also presents two different types of group comparison: a recalculation of change scores and a sponsor analysis of final values. Keeping the estimands distinct is important. Different choices about whether to compare change or final values can produce different numerical summaries, and the registry does not provide enough methodological detail to reconcile them.

Finally, the primary outcome analysis is limited to participants with measurements at both time points. The registry does not report the reasons for missing measurements or the methods used to address them. Such information is important when judging how well an analyzed sample represents the randomized participants. These features make the record useful for understanding effect estimation and uncertainty, while also identifying what additional reporting would be needed for a fuller statistical assessment.

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 primary outcome is reported for participants who completed PASAT at both baseline and 12 weeks, with 21 participants in each group. Total enrollment was 54. The registry record does not explain why the analyzed outcome groups are smaller than enrollment, how many participants lacked measurements, or whether missingness differed by group. The impact of missing outcomes cannot be evaluated from the posted information.

The registry reports a recalculated change-score comparison and a sponsor analysis of final values. These analyses address different quantities, and the record does not report a reconciliation or enough detail to assess all analytical choices. The original statistical analysis plan, covariate adjustments, allocation procedures, masking details, and sample-size justification are not reported in the registry record.

The record does not report a clinically meaningful threshold for PASAT change. That limits interpretation of whether the estimated differences would matter in practice, even apart from their statistical uncertainty. The result also concerns one measure and the baseline-to-12-week interval; broader cognitive outcomes and longer-term results cannot be inferred from it.

No secondary outcome results are posted, although the registry lists four outcome measures. The record does not provide details of multiplicity control or sensitivity analyses. Safety information is reported with denominators that differ from the primary outcome analysis, but the reason for that difference is not explained. Additional adverse-event detail, including event timing and assessments of relatedness, is not reported in the registry record.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Lipoic Acid and Omega-3 Fatty Acids for Cognitive Impairment in Multiple Sclerosis — NCT02133664.
• Registry record last updated 2017-06-02; status last verified 2017-05.
• Results first posted 2017-05-03.
• 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

NCT02133664 is a completed randomized, triple-masked, parallel Phase 1 and Phase 2 trial sponsored by Oregon Health and Science University. It compared lipoic acid and omega-3 fatty acids with placebo for cognitive impairment in multiple sclerosis. The study start is recorded as 2014-06, and primary completion as 2016-05. Enrollment was 54.

The primary outcome was PASAT change in correct responses from baseline to 12 weeks. The recalculated unadjusted mean difference was -1.14, with a 95% confidence interval from -4.218 to 1.938 and p = 0.468. The registry also reports a distinct sponsor analysis of final values: mean difference 1.14, 95% confidence interval -2.03 to 4.32, and p = 0.05.

The record’s stated aim included gathering effect-size information to inform a larger study. Secondary results and several details needed to assess missing data, analysis planning, and the difference between the reported analyses are not reported in the registry record.