Effect of an Antioxidants Mix on Cognitive Performance and Well Being: The Bacopa, Licopene, Astaxantina, Vitamin B12: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effect of an Antioxidants Mix on Cognitive Performance and Well Being: The Bacopa, Licopene, Astaxantina, Vitamin B12 (NCT03825042), a randomized na study. The primary outcome is Change in Trail Making Test (TMT) B Between Baseline and End of Treatment.

2. Clinical Question

3. Trial Design

The registry describes a randomized, quadruple-masked, parallel-arm superiority study comparing a food supplement with placebo. The supplement combined bacopa, lycopene, astaxanthin and vitamin B12. Both arm descriptions specify tablets taken once daily for 8 weeks. The brief summary calls the study a nine-weeks study, while the arm descriptions and primary outcome timeframe describe 8 weeks of treatment. The registry record does not explain this difference in wording.

The stated aim was to examine cognitive performance, mood state and well-being in people aged at least 60 years with no evidence of cognitive dysfunction. The primary outcome was change in Trail Making Test B score from baseline (V2) to the end-of-treatment assessment at 8 weeks (V4). The brief summary places this outcome first in a hierarchical sequence that also includes TMT-A and TMT B-A. Other planned objectives included cognitive tests, assessments of psychological well-being and mood, sexual satisfaction, metabolic measures and plasma markers of oxidative stress. Results for secondary outcomes are not posted in the registry record.

The registry lists enrollment of 80 and marks the study completed. The posted outcome summaries give 38 participants for the food supplement group and 40 for placebo. The primary outcome population is labeled intention to treat, but the registry record does not describe how that population was defined or how missing outcome measurements were handled. The phase is listed as NA. Details such as the recruitment setting, participant characteristics at baseline and the people covered by quadruple masking 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: Subjects who provided written informed consent have been subjected to the screening assessments. Subjects who met all inclusion criteria and none of the exclusion criteria have been eligible for the study and have proceeded with the randomization visit after 7 days. No wash-out or run-in period was used in this study. 8

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Intention To Treat

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 Change in Trail Making Test (TMT) B Between Baseline and End of Treatment, measured over 8 weeks - from baseline to end of study.

The primary endpoint is change in Trail Making Test (TMT) B score, measured in seconds, between baseline (V2) and 8 weeks of treatment (V4). The TMT-B task requires a participant to complete a sequence, and the registry describes a reduction in the time taken as an improvement in cognitive function. The endpoint therefore records a continuous measure: a time value, rather than a count of events or a yes-or-no outcome.

Change from baseline is used to describe how the measured score differs between the start and end of treatment. The registry’s posted arm summaries report mean changes, with standard deviations describing variation among observations within each arm. The change in the food supplement arm is -17.63 seconds, and the change in the placebo arm is 3.46 seconds. These are group averages; they do not indicate that every participant changed by the same amount.

The primary objective lists TMT-B first in a hierarchical order followed by TMT-A and TMT B-A. The posted primary result concerns TMT-B. The registry’s description connects a shorter test time with improvement, but the endpoint alone is a measure of performance on this particular test. It does not, on its own, describe every aspect of cognition, mood or well-being, nor does it establish how changes relate to participants’ everyday functioning.

7. Results Posted in the Registry

• Food Supplement: mean -17.63 versus 3.46 on control; difference -21.09 (95% CI -28.35 to -13.83), standardized effect d = -1.30; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is continuous because TMT-B is recorded as time in seconds. The registry reports each arm’s mean change and standard deviation. In general, a mean gives the average observed value, while a standard deviation describes how spread out observations are around that average. A group mean does not show the pattern of every participant’s result, and the standard deviation is not the uncertainty interval for the difference between groups.

What does the unadjusted comparison represent?

The recalculated comparison uses the posted summary statistics to contrast the arm mean changes. Its estimate is -21.09 seconds, with an interval from -28.35 to -13.83. This is an unadjusted comparison: it describes the difference between the posted group summaries without accounting for covariates through a model. The reported unadjusted p-value is <0.001. A p-value measures how inconsistent data are with a specified null model under the assumptions of the analysis; it is not the probability that the null hypothesis is true, nor a measure of the size or practical importance of the difference.

What does ANCOVA add?

The sponsor reports an analysis using ANCOVA, with a mean difference in final values of -21.01 seconds, a 95% confidence interval from -26.80 to -15.20, and p< 0.001. ANCOVA is a model-based method that can compare groups while accounting for covariates included in the model. Which covariates were included, how they were specified and how the model was checked are not reported in the registry record. The sponsor’s final-values estimate should therefore be distinguished from the unadjusted recalculation based on mean changes.

In general, adjustment can change an estimate and its precision, depending on the covariates and their relation to the outcome. The closeness of the two reported estimates is descriptive; it does not reveal which covariates were used or establish that the modeling assumptions were satisfied. The registry labels the sponsor analysis as a superiority analysis, but does not provide the full statistical analysis plan or further detail about the model.

How should the stated hierarchy be understood?

The brief summary lists TMT-B, TMT-A and TMT B-A in hierarchical order for the primary objective. In general, a prespecified hierarchy can guide the order in which outcomes are tested and can be part of a strategy for handling multiple statistical tests. The registry record does not report the decision rules for the hierarchy, whether testing proceeded to later outcomes, or the multiplicity procedure used. The posted primary result concerns TMT-B; results for the other listed measures are not reported in the registry record.

The record describes a randomized parallel-arm comparison with quadruple masking. Random allocation is generally intended to make treatment groups comparable with respect to measured and unmeasured characteristics, on average. Masking is generally intended to reduce the influence of expectations on participants, clinicians or outcome assessment. The registry does not identify which parties were masked or give further detail about how randomization and masking were implemented. These design labels should not be mistaken for a complete account of implementation.

What remains unknown about analysis?

The primary outcome population is labeled intention to treat. In general, this approach aims to analyze participants according to their assigned group, but the record does not explain its precise definition, the number included in the sponsor analysis, or the handling of participants without an outcome measurement. Missing-data procedures, model diagnostics, distributional checks, protocol deviations and sensitivity analyses are not reported in the registry record. The listed arm sizes for the posted outcome are 38 for the food supplement group and 40 for placebo; the registry does not explain the relationship between those figures and its enrollment listing.

The registry lists 3 outcome measures and 3 analyses, while the posted secondary outcome count is 0. These record-level counts do not supply the missing results or clarify the full analysis plan. In general, a complete statistical assessment would consider the endpoint definition, estimand, analysis population, missing-data approach, model specification and multiplicity strategy together. The available record supports a description of the posted TMT-B estimates, but not a reconstruction of all planned or performed analyses.

10. Confidence Intervals and Precision

The recalculated, unadjusted comparison has an interval from -28.35 to -13.83 seconds around the mean difference of -21.09 seconds. This interval describes the uncertainty in the estimated group contrast under the recalculation’s assumptions. In general, a confidence interval is a range produced by a statistical procedure; it is not a range containing every participant’s result, and it does not show the full spread of individual outcomes. The confidence level for this recalculated interval is not reported in the registry record.

The sponsor’s ANCOVA analysis reports a 95% confidence interval from -26.80 to -15.20 seconds around the mean difference of -21.01 seconds. In general, an interval’s width reflects both the observed data and the method used to estimate uncertainty. A narrower interval indicates greater statistical precision for the modeled estimate, but precision is not the same as clinical importance or freedom from bias.

Both reported intervals lie on the negative side of the null value for a difference, consistent with the negative estimates. The endpoints of the intervals are not identical because the unadjusted recalculation and sponsor ANCOVA analysis use different approaches. The registry record does not give the ANCOVA covariates or the confidence level for the recalculated interval, which limits a direct assessment of why their interval widths differ.

The arm standard deviations are 18.93 seconds for the food supplement group and 13.08 seconds for placebo. These describe variation in the group outcome summaries, not the precision of the between-group estimate. The registry record does not report confidence intervals for the individual arm means. Precision should therefore be interpreted from the intervals attached to the comparisons, while recognizing that the posted record does not document every modeling or missing-data assumption underlying them.

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 event counts. They are illustrations based on the observed effect, rather than the trial’s original design assumptions. 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 to a stated fraction of the observed effect.

For planning for 100% of the observed effect, the figures are 10 participants per arm for 80% power and 13 participants per arm for 90% power. For planning for 75% of the observed effect, they are 17 participants per arm for 80% power and 23 participants per arm for 90% power. For planning for 50% of the observed effect, they are 38 participants per arm for 80% power and 50 participants per arm for 90% power.

In plain language, the 80% power column gives the illustrated participants per arm for a design with an 80% chance of detecting the specified effect under the stated assumptions. The 90% power column gives the corresponding planning figure for a higher target chance of detection. Smaller effects need more participants to detect under otherwise unchanged assumptions. These figures are not observed power; they are planning illustrations based on the observed effect, not a description of the trial’s original design. The registry record does not report the trial’s own sample-size justification or original planning assumptions.

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 = -21.090; pooled standard deviation σ = 16.194.
2. n = 2 × (1.96 + 0.842)² × 16.194² / -21.090² = 9.3, rounded up to 10 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 <- -21.09                      # observed difference in means
sigma <- 16.194187919387                     # 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(3825042)
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 = 10 (80% power), 13 (90% power)
 75% of observed effect: n per arm = 17 (80% power), 23 (90% power)
 50% of observed effect: n per arm = 38 (80% power), 50 (90% power)
power.t.test: 10.3 
Simulated power at n = 10 per arm: 0.787 (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 reported analysis is an ANCOVA comparison of final values. It gives a mean difference of -21.01 seconds, a 95% confidence interval from -26.80 to -15.20 and a p-value of < 0.001. The unadjusted recalculation from posted summary statistics gives a mean difference of -21.09 seconds, an interval from -28.35 to -13.83 and an unadjusted p-value of <0.001. The estimates are similar in direction and magnitude, but the analyses are not interchangeable: one is a sponsor-reported ANCOVA of final values, and the other is an unadjusted recalculation using posted mean changes.

The registry record does not report the ANCOVA covariates or enough detail to reproduce that model. The sponsor’s analysis is the trial’s reported analysis; the recalculation is a separate, simple comparison of the posted summaries. The record marks the discrepancy flag as false, so no conflict is identified between the reported and recalculated estimates. That does not make the recalculation a replacement for the sponsor’s analysis, nor does it supply the omitted model details.

The sponsor labels the analysis as superiority. Its result should be read as a modeled group comparison on the stated endpoint, with the reported interval and p-value, rather than as a complete account of all outcomes or analyses. Results for the other measures in the stated primary hierarchy and for secondary outcomes are not reported in the registry record.

14. Multiplicity, Missing Data and Analysis Populations

The primary objective describes a hierarchical order: TMT-B, TMT-A and TMT B-A. The posted primary result is for TMT-B. In general, testing several outcomes can increase the chance of at least one apparently strong result if the testing strategy is not accounted for. A hierarchy can be one way to organize testing, but its meaning depends on the prespecified sequence and rules for moving from one test to another. Those rules and any formal multiplicity adjustment are not reported in the registry record.

The registry reports no posted secondary outcomes, although the brief summary describes secondary objectives including verbal fluency, MoCA, MMSE, AVLT, psychological well-being, mood, sexual satisfaction, metabolic parameters and oxidative-stress markers. Results for these measures are not reported in the registry record. The record therefore does not allow assessment of results across the full set of described outcomes or whether other analyses were conducted.

The primary outcome population is labeled intention to treat. The registry does not define the analysis population in operational terms, state how many participants contributed to the reported ANCOVA, or describe how missing TMT-B observations were addressed. Missing-data methods, imputation, sensitivity analyses and the handling of protocol deviations are not reported in the registry record. Without those details, the consequences of incomplete measurements for the estimates cannot be assessed from the posted results.

The record lists outcome arm sizes of 38 for the food supplement group and 40 for placebo, while enrollment is listed as 80. These figures are not accompanied by a participant flow account explaining screening, allocation, follow-up or analysis inclusion. The record also does not report whether the primary hierarchy and analysis population were finalized before results were examined. These omissions do not invalidate the posted statistics, but they limit independent evaluation of how the analysis was conducted and how broadly it represents the stated objectives.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: hepatitis e (2.5%).

The registry lists serious adverse events for the food supplement group as 1 affected among 40 at risk, and for placebo as 0 affected among 40 at risk. Deaths are listed as 0 in both groups. For other adverse events, the record lists 1 affected among 40 at risk in the food supplement group and 0 affected among 40 at risk in placebo. These are counts in the posted safety record, not a complete description of every event or its clinical course.

The registry identifies Hepatitis E as the top serious adverse event term and lists 2.5%. It does not provide further context for that term in the posted safety summary, such as a detailed event narrative or relationship to treatment. The record does not state whether the reported events were considered related to the supplement or placebo, or provide additional information about severity, timing or outcome.

These figures should be read as descriptive safety counts within the registry record. They do not establish whether an event was caused by an intervention, and the absence of a listed event in an arm is not proof that no risk exists. The registry record does not report a fuller safety analysis or follow-up beyond the stated trial record.

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

The posted TMT-B results show a negative mean change in the food supplement group and a positive mean change in the placebo group. The unadjusted difference in mean changes is -21.09 seconds, and the sponsor’s ANCOVA estimate is -21.01 seconds. The endpoint description says that a reduction in the time required for the test represents improvement in cognitive function. The comparison therefore describes a difference in test-time change favoring a larger reduction in the supplement arm within the posted result.

That statistical description is limited to TMT-B at the stated assessment. It does not establish effects on other cognitive measures, mood, well-being, metabolic measures, oxidative stress or sexual satisfaction. Although the registry summary describes these secondary objectives, their results are not reported in the registry record. Results for TMT-A and TMT B-A, which are included in the stated primary hierarchy, are also not posted.

The estimated difference and its confidence intervals describe the size and precision of a group contrast under the analyses reported. They do not show that all participants experienced the average change, and the registry does not provide a threshold for clinical importance. The record also lacks the detailed analysis plan, covariate specification, missing-data approach and participant flow needed for a complete appraisal of how the result was obtained.

Accordingly, the result should be understood as a statistical finding about the posted TMT-B endpoint in this trial, not as a conclusion about every aspect of cognitive function or well-being. It does not by itself establish the importance of the observed difference in daily life, the durability of any change beyond the assessment period, or the balance of benefits and harms. Those questions require evidence and context not reported in the registry record.

17. Why This Trial Matters Statistically

This trial illustrates why the endpoint definition matters when interpreting a reported treatment comparison. The outcome is test time in seconds, and the registry explicitly states that a reduction in time represents improvement on the TMT. Without that direction-of-meaning information, a negative change or difference could be easy to misread. Translating the estimate back into the endpoint’s units and direction makes the contrast interpretable without treating it as a broad measure of all cognition.

The result also illustrates the distinction between an unadjusted comparison of change scores and a sponsor-reported ANCOVA of final values. Both estimates are close in magnitude, but they are generated by different methods and are accompanied by different intervals. Reporting both requires clarity about the analysis method, its inputs and its assumptions. The registry record names ANCOVA but does not identify its covariates, illustrating how a method label alone may not permit full reproduction.

The stated hierarchy highlights the role of multiplicity planning. TMT-B is placed before TMT-A and TMT B-A, but the record does not explain the testing rules or show the other results. A hierarchy can shape interpretation only when its decision procedure is clear and results are available. Missing details about the hierarchy, secondary outcomes and missing-data handling leave important uncertainty beyond the numerical estimate.

Finally, the sample-size illustrations are based on the observed effect and are not evidence about the original design’s adequacy. They show how planning figures depend on the effect a future study aims to detect and the chosen power target. Keeping planning illustrations separate from observed results helps prevent post hoc planning calculations from being mistaken for properties of the completed trial.

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 provides a limited account of the primary analysis. Although the sponsor reports ANCOVA, the covariates, model specification and diagnostic checks are not reported. The record does not describe how missing measurements were handled, how the intention-to-treat population was defined, or how many participants contributed to the sponsor analysis. There is also no participant flow account explaining the outcome arm sizes in relation to enrollment.

The study summary describes a hierarchy across TMT-B, TMT-A and TMT B-A, but only the TMT-B primary result is posted. No secondary outcome results are posted despite the listed secondary objectives. The registry record does not report the multiplicity strategy or the rules for interpreting the hierarchy. Consequently, the posted estimate cannot be considered alongside the full set of described outcomes or a complete testing plan.

The record calls the study nine-weeks in the brief summary, while intervention descriptions and the primary endpoint timeframe specify 8 weeks of treatment. It does not explain the difference. Participant characteristics beyond the intended age and cognitive-status description, the recruitment setting, and details of randomization and masking are not reported. The people included in quadruple masking are not identified.

The safety summary gives counts and a serious adverse event term, but not event narratives, attribution, timing or detailed follow-up. No threshold for a clinically important TMT-B change is reported. These limitations are specific to the available registry account and restrict interpretation of the posted results; they do not, by themselves, determine what the full trial documentation may contain.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Effect of an Antioxidants Mix on Cognitive Performance and Well Being: The Bacopa, Licopene, Astaxantina, Vitamin B12 — NCT03825042.
• Registry record last updated 2020-07-27; status last verified 2019-02.
• Results first posted 2020-07-27.
• 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 randomized, quadruple-masked, parallel-arm superiority study of a supplement containing bacopa, lycopene, astaxanthin and vitamin B12 versus placebo. Enrollment is listed as 80, and the study status is completed. The intended population was people aged at least 60 years with no evidence of cognitive dysfunction.

The primary posted outcome is change in TMT-B time from baseline to 8 weeks. The unadjusted mean difference is -21.09 seconds, with an interval from -28.35 to -13.83 and p <0.001. The sponsor’s ANCOVA reports -21.01 seconds, a 95% confidence interval from -26.80 to -15.20 and p< 0.001. Secondary results and details needed to reconstruct the full analysis plan are not reported in the registry record.