Brain Stimulation and Enhancing Cognition in Older Adults: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Brain Stimulation and Enhancing Cognition in Older Adults (NCT03653351), a randomized na study. The primary outcome is Cognitive and Memory Function.

2. Clinical Question

3. Trial Design

The registry describes a randomized, parallel-group trial with quadruple masking. Enrollment was 26, with 14 participants randomized to sham tDCS and MBSR and 12 to active tDCS and MBSR. The study is marked completed. Its recorded start date is 2018-06-27 and its primary completion date is 2019-04-22. The phase is listed as NA.

Both arms combined MBSR with a form of tDCS. The sham arm received 8 weeks of in-class group MBSR plus sham tDCS, as well as daily at-home MBSR plus sham tDCS. The active arm received the corresponding MBSR schedule with active tDCS. Thus, the principal randomized contrast is between active and sham stimulation while the MBSR component is present in both assigned regimens. The record does not describe an MBSR-only group, a tDCS-only group, or a group receiving neither component.

The registry’s description of quadruple masking does not identify which roles or groups were masked. Details of the randomization procedure, allocation concealment, adherence, treatment fidelity, and the exact timing of the 8-week assessment beyond its stated timeframe are not reported in the registry record. The record identifies Washington University School of Medicine as sponsor.

The primary outcome is a continuous score reported as a mean and standard deviation. There is one primary outcome, and no secondary outcomes were reported. Although a group comparison is posted for the primary outcome, the registry lists zero analyses. The statistical analysis plan, including model specification and the population used for analysis, is 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.

Overall Study

Analysis population for the primary outcome, as defined in the registry: Twenty-six participants enrolled in the study: 14 were randomized to sham tDCS and 12 to active tDCS.

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 Cognitive and Memory Function, measured over 8 weeks.

The primary endpoint is Cognitive and Memory Function, measured with the NIH Toolbox Fluid Cognition Composite Score at 8 weeks. It provides a global assessment of general fluid cognition. The registry describes fluid abilities as those used to solve problems, think and act quickly, and encode new episodic memories. It also notes that these abilities are presumed to be especially influenced by biological processes and less dependent on past exposure or learning experiences.

The measure is a continuous score: the posted group summaries are means and standard deviations. Higher scores indicate higher levels of cognitive functioning. The registry gives a reference point of a score at or near 100 as average compared with others nationally, and describes scores around 115 as above average and around 130 as superior, in the top 2 percent nationally. It describes a score around 85 as below average and a score in the range of 70 or below as suggesting significant impairment, which may also indicate difficulties in general functioning.

These reference points help explain the scale’s interpretation but do not establish the participants’ baseline status or the meaning of an individual participant’s score in this study. The posted primary comparison concerns group means at the 8-week timeframe. No secondary outcomes were reported.

7. Results Posted in the Registry

• Active tDCS and MBSR: mean 49.80 versus 56.50 on control; difference -6.70 (95% CI -12.08 to -1.32), standardized effect d = -0.97; z-test p = 0.015.

8. Statistical Interpretation

9. Statistical Methods Explained

A continuous endpoint is commonly summarized by its mean and standard deviation. The mean describes the group’s average score, while the standard deviation describes how spread out participant scores are around that average. These summaries answer different questions: the mean locates the group average on the scale, and the standard deviation indicates variability among scores. The registry posts a mean and standard deviation for each randomized arm at the 8-week endpoint.

What does a mean difference represent?

The mean difference compares the group averages in the order active tDCS and MBSR versus sham tDCS and MBSR. A negative value means the first group’s posted mean is lower. The reported estimate is -6.7. This is an unadjusted group contrast as presented in the registry; the adjustment status beyond that description and the model used to obtain the estimate are not reported in the registry record. A group mean difference is not the same as a change from baseline, and the registry does not post baseline values or a baseline-adjusted estimate.

In a randomized study, the assigned groups are intended to support a comparison of assigned regimens. The registry identifies randomized allocation, but it does not describe the randomization sequence or the analysis population. Interpretation therefore rests on the posted group summaries and cannot establish from the record whether all randomized participants contributed outcome data or whether any additional analysis choices were made.

How should a confidence interval be understood?

A confidence interval expresses uncertainty around an estimated quantity. In repeated use of a method under its assumptions, intervals constructed at a stated confidence level would cover the target quantity at that level. It is not a range of scores containing a stated proportion of individual participants, nor does it assign a probability to a particular fixed treatment effect after the data are observed. For this comparison, the posted 95% confidence interval extends from -12.08 to -1.323. Both limits are negative, which conveys that the interval produced by the posted analysis lies on the side where the active-group mean is lower.

The confidence interval’s meaning depends on the statistical method and its assumptions. Those details, including whether the calculation accounted for baseline values or other covariates, are not reported in the registry record. General statistical interpretation should therefore be separated from claims about exactly how the interval was calculated.

What does the p-value add?

The unadjusted p-value is 0.015. In general, a p-value measures how incompatible the observed data, or data more extreme, are with a specified null hypothesis under the statistical model. It is not the probability that the null hypothesis is true, and it does not quantify the magnitude or practical importance of a difference. “Unadjusted” indicates that the posted value is not described as adjusted for multiple comparisons. The registry reports one primary outcome and no secondary outcomes, but does not explain any multiplicity procedure or provide a detailed analysis plan.

The registry lists zero analyses even though a primary outcome comparison is posted. This is a feature of the record as displayed, not enough information to reconstruct the analysis. The specific test, model, degrees of freedom, handling of missing outcomes, and analysis population are not reported in the registry record. No particular statistical test should be inferred from the presence of a mean difference, confidence interval, and p-value alone.

Why can score variability matter?

General statistical principle: when participant scores vary substantially, a group mean is estimated less precisely than when scores are more tightly clustered, all else being equal. The posted standard deviations are 6.7 for sham and 7.2 for active tDCS. A pooled standard deviation of 6.934 is also reported for the comparison. Pooling is a way to represent variability across groups for certain standardized comparisons, but the registry does not provide a detailed explanation of its calculation or its role in the primary analysis.

Over-dispersion is a general concern when a statistical model assumes less variability than the data actually contain. In that situation, standard errors can be too small and uncertainty can be understated. The posted endpoint is continuous, and the record does not report an over-dispersion assessment or a model that would make such an assessment relevant. It is therefore more appropriate to treat this as a general statistical concept than to assert that over-dispersion affected this result.

Finally, statistical significance and estimation are distinct. The p-value provides a test-related summary, while the point estimate and confidence interval describe the direction, scale, and uncertainty of the group contrast. None of these alone establishes clinical importance. The registry does not report a threshold for a clinically meaningful difference, and the posted comparison addresses only the stated endpoint and timeframe.

10. Confidence Intervals and Precision

The mean difference is -6.7, and its 95% confidence interval ranges from -12.08 to -1.323. The interval communicates uncertainty around the estimated group contrast: values throughout it are negative, so the posted interval is consistent with a lower mean in the active tDCS and MBSR group than in the sham tDCS and MBSR group. The interval does not describe the spread of individual participants’ scores; the arm-specific standard deviations describe that aspect of the data.

Precision is not determined by the point estimate alone. Enrollment was 14 in the sham group and 12 in the active group, and the posted standard deviations were 6.7 and 7.2, respectively. In general, estimates from limited numbers of participants tend to be more sensitive to the observed data than estimates from larger studies. The confidence interval is therefore an important part of interpretation, not merely an optional addition to the mean difference.

The registry does not state a clinically meaningful difference for the score. Consequently, the interval cannot be translated from this record into a judgment that all values within it would matter clinically, or that some would not. Nor does it establish precision for other populations, timeframes, or treatment settings. The method used to construct the interval is not reported in the registry record, so its assumptions cannot be independently assessed from the record alone.

The p-value of 0.015 is a separate summary and does not replace the interval. The interval shows the range of estimates associated with the reported uncertainty calculation; the p-value addresses compatibility with a null hypothesis under a statistical model. Both should be interpreted cautiously given the limited enrollment and the absence of a reported analysis plan.

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 own design assumptions. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; each row uses the stated fraction of the observed effect as the effect to detect. The trial’s original sample-size justification and design assumptions are not reported in the registry record.

For planning for 100% of the observed effect, the illustration gives 17 participants per arm for 80% power and 23 participants per arm for 90% power. For planning for 75% of the observed effect, it gives 30 participants per arm for 80% power and 41 participants per arm for 90% power. For planning for 50% of the observed effect, it gives 68 participants per arm for 80% power and 91 participants per arm for 90% power.

In plain language, the 80% power column describes the per-arm enrollment used by the planning calculation to have an 80% chance of detecting the assumed effect under its stated assumptions; the 90% column uses a higher target chance of detection. These values are planning illustrations, not observed power for the completed study. The progression also illustrates a general relationship: smaller effects require more participants to detect under otherwise unchanged assumptions. The calculations use the observed effect as their starting point, so they should not be treated as a validated enrollment recommendation for a future study.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -6.700; pooled standard deviation σ = 6.934.
2. n = 2 × (1.96 + 0.842)² × 6.934² / -6.700² = 16.8, rounded up to 17 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 <- -6.7                      # observed difference in means
sigma <- 6.933643823176                     # 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(3653351)
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 = 17 (80% power), 23 (90% power)
 75% of observed effect: n per arm = 30 (80% power), 41 (90% power)
 50% of observed effect: n per arm = 68 (80% power), 91 (90% power)
power.t.test: 17.8 
Simulated power at n = 17 per arm: 0.777 (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. Multiplicity, Missing Data and Analysis Populations

The registry identifies one primary outcome, Cognitive and Memory Function, and reports no secondary outcomes. A single prespecified primary endpoint can reduce the number of outcome comparisons that need to be considered, but the registry does not report whether this endpoint was prespecified in a protocol or analysis plan. It also does not describe an adjustment for multiple testing, a hierarchy of hypotheses, or any other multiplicity strategy. The posted p-value is explicitly unadjusted.

The record lists zero analyses, while also presenting a mean difference, confidence interval, and unadjusted p-value for the primary outcome. It does not explain this difference in reporting. The statistical test or model, covariate adjustment, handling of repeated measurements if any, and exact analysis population are not reported in the registry record. The posted arm summaries and comparison can be described, but they do not disclose enough to reconstruct the analysis.

Missing outcome data are not described. The record does not state how many participants contributed 8-week scores, whether any measurements were missing, why data might have been missing, or how missing values were handled. It is also not reported whether the analysis followed randomized assignment regardless of adherence, included only participants with available measurements, or used another population definition. These details matter because the observed group summaries may depend on which participants contributed data.

Masking is listed as quadruple, but the record does not identify who was masked or describe how masking was maintained. There is no reported protocol-level detail about interim analyses, stopping decisions, or adjustments related to multiple looks at the data. Those matters should be regarded as not reported in the registry record rather than assumed absent. With these analysis details unavailable, statistical interpretation is limited to the posted endpoint summaries and comparison values.

14. 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 non-serious adverse event terms

The serious adverse event figures are reported by randomized group. In the sham tDCS and MBSR group, 0 of 14 participants were recorded with a serious adverse event; in the active tDCS and MBSR group, 0 of 12 were recorded with a serious adverse event. The registry also records 0 deaths in each group. No serious adverse event terms are listed.

The record separately gives other adverse event counts: 7 of 14 in the sham group and 6 of 12 in the active group. These are not the serious adverse event counts and should not be conflated with them. The registry does not describe the types, severity, timing, duration, or relationship to study components for those other events.

These figures are counts in a study with enrollment of 26. Having no serious adverse events recorded in either group does not establish that serious events cannot occur, and it does not by itself provide a complete assessment of safety. The registry does not report detailed methods for adverse-event collection or adjudication, and it does not describe follow-up beyond the information in the record. The counts should therefore be read as the posted observations, not as a guarantee about risk.

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

The result describes an 8-week comparison of the mean NIH Toolbox Fluid Cognition Composite Score between participants assigned to active tDCS plus MBSR and those assigned to sham tDCS plus MBSR. The posted means were 49.8 and 56.5, respectively, and the mean difference for active versus sham was -6.7. The reported 95% confidence interval was -12.08 to -1.323, and the unadjusted p-value was 0.015.

Because MBSR was part of both assigned regimens, the comparison does not estimate MBSR versus no MBSR. It also does not establish the effect of tDCS without MBSR, or whether the effect of one component depends on the other. The contrast pertains to the two combined regimens in this randomized study and to the stated endpoint and timeframe.

The posted result does not establish whether the group difference is clinically important. The registry describes score reference points but gives no threshold for a clinically meaningful difference. It does not report baseline cognitive scores, change from baseline, individual participant outcomes, or results at later timeframes. The group means should not be treated as a description of every participant’s function or as proof of change over time.

The record also does not provide enough analysis detail to determine precisely how the estimate and interval were calculated, how missing data were handled, or which participants were included in the analysis. Enrollment was 26, and the group sizes were 14 and 12. These features warrant attention to uncertainty and to the limits of generalization. The registry result is a statistical account of the posted comparison, not a treatment recommendation or a definitive claim about outcomes beyond this study.

16. Why This Trial Matters Statistically

This trial raises several useful statistical distinctions. First, it compares two combined regimens rather than testing MBSR against no MBSR. Both groups received an MBSR schedule, while assigned stimulation was active or sham. Defining the contrast precisely prevents the result from being attributed to an intervention component that was not independently compared.

Second, the result is an estimate, not only a test outcome. The mean difference of -6.7 and its confidence interval from -12.08 to -1.323 convey direction and uncertainty, while the unadjusted p-value of 0.015 addresses a different statistical question. Neither the p-value nor the confidence interval establishes clinical importance; the record does not specify a meaningful-difference threshold.

Third, the enrollment of 26 makes precision and analysis transparency especially relevant. The posted arm sizes are 14 and 12. The registry gives group means, standard deviations, a comparison, and adverse-event counts, but it does not report the analysis population, missing-data handling, or the method behind the comparison. Readers can describe the posted statistics while recognizing that the record does not permit a full reconstruction of the analysis.

Finally, planning from an observed effect is different from documenting the original design. The registry includes planning illustrations under explicit assumptions, but the original sample-size justification is not reported. Keeping those planning figures distinct from observed study results avoids treating a post hoc illustration as a design rationale or as observed power. These distinctions make the result easier to interpret without extending it beyond what the record supports.

17. 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 study enrolled 26 participants, with 14 randomized to sham tDCS and MBSR and 12 to active tDCS and MBSR. This limited enrollment means the estimated group contrast is based on a small number of participants, and its uncertainty should remain central to interpretation. The posted confidence interval provides one expression of that uncertainty, but the analysis method underlying it is not described in the registry record.

The primary assessment is stated at 8 weeks. The registry does not report later outcomes, so the record cannot establish whether the observed group contrast persisted, changed, or was limited to that timeframe. Baseline scores and changes from baseline are also not reported. Although the endpoint has national reference points, the record does not provide details that would allow a full assessment of how the enrolled participants compared with those reference values.

Both randomized groups received MBSR, with active or sham tDCS. This design does not separately estimate MBSR’s effect against no MBSR, nor does it isolate stimulation outside the MBSR regimen. The record does not describe intervention adherence, attendance, fidelity, or the amount of home practice completed, so the extent of exposure to the described regimens cannot be assessed.

Additional limitations arise from missing reporting detail. The registry does not report the analysis population, missing-outcome counts or handling, the statistical model, multiplicity procedures, or the original sample-size justification. It lists zero analyses despite posting a primary comparison. The degree to which these omissions affect interpretation cannot be determined from the registry record. These limitations concern the available record and do not, by themselves, establish that a particular procedure was or was not used.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Brain Stimulation and Enhancing Cognition in Older Adults — NCT03653351.
• Registry record last updated 2021-07-08; status last verified 2021-07.
• Results first posted 2021-06-29.
• 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.

21. Record Summary

NCT03653351 is a completed randomized, parallel-group trial sponsored by Washington University School of Medicine. It enrolled 26 participants: 14 were assigned to sham tDCS with MBSR and 12 to active tDCS with MBSR. The registry lists quadruple masking.

The single primary outcome was Cognitive and Memory Function, measured with the NIH Toolbox Fluid Cognition Composite Score at 8 weeks. The posted means were 56.5 for sham tDCS and MBSR and 49.8 for active tDCS and MBSR. The mean difference for active versus sham was -6.7, with a 95% confidence interval from -12.08 to -1.323 and an unadjusted p-value of 0.015. No secondary outcomes were reported.

The record reports 0 serious adverse events and 0 deaths in each group. It does not report the original sample-size justification, analysis population, missing-data handling, or detailed statistical analysis plan.