This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Augmenting Cognitive Training In Older Adults (NCT02851511), a randomized na study. The primary outcome is Improvement in Cognitive Ability..
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02851511 |
| Phase | NA |
| Condition | Aging |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 379 |
| Arms in the primary outcome | 2 |
| Lead sponsor | University of Florida |
| Results posted | Yes |
2. Clinical Question
Population
Older adults enrolled in a study of cognitive and educational training with transcranial direct current stimulation (tDCS). The primary outcome description covers participants who received cognitive training across Phase I and Phase II; it reports N=334, with Phase I N=42 and Phase II N=292.
Intervention
Cognitive training combined with active tDCS. The registry describes cognitive training as a behavioral intervention and active tDCS as a device intervention.
Comparator
Cognitive training combined with sham tDCS. The comparison therefore concerns active versus sham stimulation among participants receiving cognitive training, not cognitive training versus educational training.
Primary question
What was the change in a composite measure of cognitive ability from baseline to the post assessment at 3 months, and how did the mean change compare between cognitive training paired with active stimulation and cognitive training paired with sham stimulation?
The registry describes a broader study of cognitive training (CT), educational training (ET), active tDCS, and sham tDCS. Its stated hypotheses concern whether tDCS augments CT, whether effects persist after training, and whether neuroimaging biomarkers predict individual response. The primary endpoint considered in this comparison is narrower: it is the reported change in the NIH toolbox fluid cognition fully corrected T-score for the cognitive-training participants. It does not, by itself, answer every question in the broader study description.
3. Trial Design
The registry identifies this as a randomized, double-masked, parallel trial and describes it as a two-phase adaptive randomized clinical trial. The study status is completed. The record lists an enrollment of 379 and Aging as the condition. The sponsor is the University of Florida. The listed study start date is 2017-08-08, and the primary completion date is 2022-04-30. The phase field is NA.
The intervention framework combines two behavioral activities—cognitive training and educational training—with active or sham tDCS. The four named arms are cognitive training with active stimulation, cognitive training with sham stimulation, educational training with active stimulation, and educational training with sham stimulation. The primary comparison described in the posted results is between the two cognitive-training arms. The primary endpoint description says that it includes people who received cognitive training across Phase I and Phase II, with N=334, Phase I N=42, and Phase II N=292.
The trial description says that cognitive and brain function were assessed using neurocognitive, clinical, and multimodal neuroimaging measures. It names functional magnetic resonance imaging (FMRI) during working memory, attention, and memory encoding tasks, and proton magnetic resonance spectroscopy (MRS) to assess cerebral metabolites, including GABA concentrations. These are stated aims and assessment areas; the primary result is the cognitive ability composite, not an imaging endpoint.
The registry record does not report the allocation ratio, the procedures used to maintain masking, the detailed adaptive rules, or the original sample-size assumptions. It also does not report the full schedule of assessments beyond the specified primary endpoint timeframe.
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 (Phase I + Phase II)
| Stage | Cognitive Training + Active Stimulation | Cognitive Training + Sham Stimulation | Educational Training + Active Stimulation | Educational Training + Sham Stimulation |
|---|---|---|---|---|
| STARTED | 168 | 166 | 23 | 22 |
| COMPLETED | 126 | 127 | 23 | 18 |
| NOT COMPLETED | 42 | 39 | 0 | 4 |
Reasons for not completing this period:
| Reason | Cognitive Training + Active Stimulation | Cognitive Training + Sham Stimulation | Educational Training + Active Stimulation | Educational Training + Sham Stimulation |
|---|---|---|---|---|
| Physician Decision | 18 | 16 | 0 | 1 |
| Withdrawal by Subject | 20 | 17 | 0 | 3 |
| COVID-19 lockdown, no reason specified | 4 | 5 | 0 | 0 |
| Lost to Follow-up | 0 | 1 | 0 | 0 |
Phase I
| Stage | Cognitive Training + Active Stimulation | Cognitive Training + Sham Stimulation | Educational Training + Active Stimulation | Educational Training + Sham Stimulation |
|---|---|---|---|---|
| STARTED | 21 | 21 | 23 | 22 |
| COMPLETED | 19 | 20 | 23 | 18 |
| NOT COMPLETED | 2 | 1 | 0 | 4 |
Reasons for not completing this period:
| Reason | Cognitive Training + Active Stimulation | Cognitive Training + Sham Stimulation | Educational Training + Active Stimulation | Educational Training + Sham Stimulation |
|---|---|---|---|---|
| Physician Decision | 0 | 0 | 0 | 1 |
| Withdrawal by Subject | 2 | 1 | 0 | 3 |
Phase II
| Stage | Cognitive Training + Active Stimulation | Cognitive Training + Sham Stimulation | Educational Training + Active Stimulation | Educational Training + Sham Stimulation |
|---|---|---|---|---|
| STARTED | 147 | 145 | 0 | 0 |
| COMPLETED | 107 | 107 | 0 | 0 |
| NOT COMPLETED | 40 | 38 | 0 | 0 |
Reasons for not completing this period:
| Reason | Cognitive Training + Active Stimulation | Cognitive Training + Sham Stimulation | Educational Training + Active Stimulation | Educational Training + Sham Stimulation |
|---|---|---|---|---|
| Physician Decision | 18 | 16 | 0 | 0 |
| Withdrawal by Subject | 18 | 16 | 0 | 0 |
| COVID-19 lockdown, no reason specified | 4 | 5 | 0 | 0 |
| Lost to Follow-up | 0 | 1 | 0 | 0 |
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.
Population: The study is a 2-phase adaptive design study. After first phase, 2 education arms were dropped. all participants were randomly assigned to 2 cognitive training groups in Phase II.
| Characteristic | Unit | Cognitive Training + Active Stimulation | Cognitive Training + Sham Stimulation | Educational Training + Active Stimulation | Educational Training + Sham Stimulation | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 168 | 166 | 23 | 22 | 379 | |
| Age, Continuous | years | 71.5 (SD 5.4) | 71.5 (SD 4.8) | 70.0 (SD 5.1) | 73.1 (SD 4.7) | 71.5 (SD 5.1) |
| Sex: Female, Male: Female | Participants | 104 | 111 | 10 | 11 | 236 |
| Sex: Female, Male: Male | Participants | 64 | 55 | 13 | 11 | 143 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 14 | 8 | 1 | 2 | 25 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 154 | 158 | 22 | 20 | 354 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 3 | 5 | 1 | 0 | 9 |
| Race (NIH/OMB): Asian | Participants | 0 | 3 | 1 | 0 | 4 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 1 | 0 | 1 |
| Race (NIH/OMB): Black or African American | Participants | 11 | 8 | 0 | 2 | 21 |
| Race (NIH/OMB): White | Participants | 146 | 148 | 20 | 18 | 332 |
| Race (NIH/OMB): More than one race | Participants | 5 | 2 | 0 | 2 | 9 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 3 | 0 | 0 | 0 | 3 |
| Region of Enrollment: United States | participants | 168 | 166 | 23 | 22 | 0 |
| Years of Education | years | 16.3 (SD 2.3) | 16.4 (SD 2.4) | 16.7 (SD 2.1) | 15.6 (SD 2.4) | 16.3 (SD 2.4) |
| MOCA Total Score | units on a scale | 26.7 (SD 2.0) | 26.8 (SD 1.9) | 26.9 (SD 1.7) | 26.1 (SD 2.1) | 26.7 (SD 1.9) |
| Average POSIT z-score: | z-score | -0.18 (SD 0.44) | -0.20 (SD 0.46) | -0.11 (SD 0.47) | -0.44 (SD 0.55) | -0.20 (SD 0.46) |
| BDI-II Total Score | units on a scale | 4.0 (SD 4.8) | 3.4 (SD 3.9) | 2.4 (SD 3.1) | 3.1 (SD 3.7) | 3.6 (SD 4.3) |
6. Primary Endpoint
The registry lists the primary outcome as Improvement in Cognitive Ability., measured over Change from baseline to post assessment (3 months)..
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | units on a scale |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is improvement in cognitive ability, measured as change from baseline to the post assessment at 3 months. The registry describes the measure as a composite based on the NIH toolbox fluid cognition fully corrected T-score. It is a continuous measure reported in units on a scale, with the mean and standard deviation used to describe the groups. Higher scores indicate a better outcome.
A composite can bring together information from multiple cognitive tasks into a single outcome, which may offer a broad measure of cognitive ability rather than focusing on performance in one task alone. The registry’s study description emphasizes working memory, attention, and memory encoding as abilities trained by cognitive training, and describes wider neurocognitive and brain-function assessments. The listed endpoint provides a way to quantify cognitive change over the specified assessment period.
The registry gives the possible change range as -13 to 26 and reports group-specific observed minimum and maximum values in the outcome description. Those ranges describe the scale and recorded observations; they do not establish what magnitude of change would be important to participants or clinicians. A threshold for clinically meaningful change is not reported in the registry record.
The endpoint description states that the analysis includes people who received cognitive training in both phases. It does not provide details about how missing baseline or post-assessment values were handled, or whether the analysis used an intention-to-treat population. Those details matter when interpreting a change outcome, because the analysis population and missing-data approach affect which observations contribute to the estimate.
7. Results Posted in the Registry
- Cognitive Training + Active Stimulation: mean 4.70 versus 4.50 on control; difference 0.20 (95% CI -1.15 to 1.55), standardized effect d = 0.03; z-test p = 0.772.
Mean difference: Cognitive Training + Active Stimulation
95% CI: -1.15 to 1.55
Recalculated from the posted summary statistics
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.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Phase I POSIT BrainHQ Cognitive Training Composite Performance Measure.(Phase I POSIT Z-Score) | Continuous Endpoint | Mean difference | -1.01 (-1.20 to -0.82) | 4 per arm |
Phase I POSIT BrainHQ Cognitive Training Composite Performance Measure.(Phase I POSIT Z-Score)
- 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 deviations.
- Result:
- Education Training: mean -0.06 versus 0.95 on control; difference -1.01 (95% CI -1.20 to -0.82), standardized effect d = -2.28; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Education Training than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The registry lists one secondary outcome: a Phase I POSIT BrainHQ Cognitive Training Composite Performance Measure, described as a Z-score assessed from baseline to the post assessment at 3 months. Its posted group summaries compare cognitive training with educational training. This differs from the primary comparison, which concerns active versus sham stimulation among participants receiving cognitive training.
Because only one secondary endpoint is listed, there is no broad pattern across multiple secondary outcomes to characterize. The secondary measure addresses performance on the cognitive-training composite in Phase I; it is not another estimate of the primary NIH toolbox fluid cognition endpoint, and it does not directly answer whether active tDCS adds to cognitive training. The registry record contains no sponsor-reported analysis for this secondary endpoint, so the relationship between it and the primary sponsor analysis cannot be established from a shared adjusted modeling framework.
Secondary outcomes can offer complementary information, but their results generally carry less confirmatory weight when they are not the primary question or when the analysis plan and multiplicity approach are not available. Testing multiple outcomes can increase the chance that at least one result appears notable by chance. The registry record does not report whether any adjustment for multiple comparisons was planned or applied. The secondary result should therefore be interpreted as supportive or exploratory rather than as an independent confirmation of the primary comparison.
The secondary measure is based on Phase I, whereas the primary outcome description includes cognitive-training participants from Phase I and Phase II. Differences in the outcome, phase, and comparison mean that the secondary result cannot simply be used to validate or contradict the primary result. A clear assessment of consistency would require prespecified relationships between endpoints and details of the analysis populations, neither of which is reported in the registry record.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Phase I POSIT BrainHQ Cognitive Training Composite Performance Measure.(Phase I POSIT Z-Score)
9. Statistical Interpretation
For the primary comparison, the reported group means were 4.7 for cognitive training with active stimulation and 4.5 for cognitive training with sham stimulation. The posted unadjusted recalculation gives a mean difference of 0.2, with a 95% confidence interval from -1.152 to 1.552 and an unadjusted p-value of 0.772. This interval includes zero and is compatible with a range of differences on either side of zero. The result does not precisely distinguish a small positive difference from no difference or a small negative difference.
The registry also reports a sponsor analysis using linear regression. It gives a slope of 0.33, a 95% confidence interval from -0.91 to 1.56, and p <0.05. The reported interval includes zero, while the reported p-value is below 0.05. Those two features do not align under the usual two-sided interpretation of a confidence interval and test of the same effect. The registry’s sponsor analysis takes precedence over the simple unadjusted recalculation, but the apparent inconsistency within the sponsor-reported statistics should be kept in view. The record does not explain it.
The recalculated estimate is based on group summary statistics and is unadjusted. It is not a replacement for the sponsor’s regression analysis, which may reflect an analysis specification not recoverable from the posted summaries. The registry does not report the regression covariates or other modeling details. The difference between the recalculated mean difference and the reported regression slope should therefore not be interpreted as proof that one analysis is erroneous; the estimands and methods may differ, and the record does not give enough detail to reconcile them.
The reported group standard deviations, 6.5 and 6.1, are large relative to the mean difference. This indicates substantial variability in individual changes around the group averages. A small difference between averages does not mean that individual responses were uniform, and these summary results do not describe the distribution of individual outcomes or identify who may have experienced larger or smaller changes.
The record’s primary comparison concerns active versus sham stimulation when both groups received cognitive training. It does not directly compare cognitive training with educational training in the primary endpoint result. Nor does this estimate settle the broader hypotheses about maintaining effects up to 12 months or using neuroimaging biomarkers to predict individual response. Such conclusions would require the corresponding outcomes and analyses, which are not reported in the primary comparison.
Accordingly, the result should be read as an estimate with appreciable uncertainty, alongside a sponsor-reported regression result whose interval and p-value are difficult to reconcile from the registry record alone. It does not establish equivalence, and it should not be converted into a claim that active stimulation does or does not work. The registry record does not report a clinically meaningful threshold for this scale, which also limits interpretation of the size of the mean difference.
10. Statistical Methods Explained
The primary outcome is continuous, so the registry reports group means and standard deviations. A mean describes the average change in a group; a standard deviation describes how spread out individual changes are around that average. Neither statistic alone shows the full shape of the outcome distribution. The group sizes and standard deviations help indicate how much information contributes to the comparison, but they do not replace details about the analysis population or missing observations.
What does a mean difference represent?
The unadjusted recalculation compares the average change in the active-stimulation cognitive-training group with the average change in the sham-stimulation cognitive-training group. The reported mean difference is 0.2. Its direction is defined by the comparison as presented: the active-stimulation group mean is higher than the sham-stimulation group mean. This is a simple comparison of posted summary statistics, not an adjusted estimate. It does not control for covariates or account for any modeling choices that may have been used in the sponsor’s analysis.
In general, a mean difference is an estimate of the difference between group averages on the outcome’s scale. Its interpretation depends on the endpoint definition, the direction of the scale, and the analysis population. Here, the registry states that higher scores mean a better outcome, but does not report a threshold for a clinically meaningful difference. Statistical evidence about the estimate therefore should not be conflated with evidence about its practical importance.
Why is a confidence interval useful?
A confidence interval describes the uncertainty around an estimated effect under the assumptions of the analysis. The posted recalculated interval is -1.152 to 1.552. Because it includes zero, the data summaries are compatible with no mean difference as well as with differences in either direction within the interval. The interval’s width also shows that the recalculated estimate is not highly precise. A confidence interval is not a guarantee that the true effect lies in the interval, and it does not account for unreported sources of bias or analysis decisions.
The reported sponsor analysis is a linear regression with a slope estimate. Regression can estimate an association or group contrast while accounting for variables included in a model. The registry gives the method and result, but does not report the model specification, covariates, treatment of missing observations, or other details. Consequently, the slope cannot be fully interpreted as adjusted or unadjusted on the basis of the record alone. The sponsor’s analysis takes precedence over the simple summary-statistic recalculation, while the discrepancy between its reported p-value and confidence interval remains unresolved.
What does the p-value say?
A p-value describes how unusual data at least as inconsistent with a specified null hypothesis would be if that null hypothesis and the test’s assumptions were true. It is not the probability that the null hypothesis is true, and it does not measure the probability that a result is due to chance. The unadjusted recalculation reports p=0.772. The sponsor analysis reports p <0.05. These are results from different analyses, and the sponsor’s p-value is paired in the record with an interval that includes zero. The record does not explain that mismatch, so the sponsor result should be reported as recorded rather than silently corrected.
In general, p-values do not measure effect size or precision. The estimate and its confidence interval are needed to understand the range of effects compatible with the data. A small p-value alone does not establish clinical importance, while a larger p-value does not prove that groups are equivalent. A prespecified equivalence or non-inferiority framework is not reported in the registry record.
Why can over-dispersion matter?
For continuous outcomes, greater variability means that individual observations are more dispersed around the group means. When variability is large relative to the mean contrast, estimates can be less precise unless the study has enough information to distinguish the contrast from that background variation. The reported standard deviations describe variability in this endpoint. In other settings, over-dispersion refers to observed variation exceeding what a model assumes; that can make standard errors and tests unreliable if the model does not account for it. The registry does not report a dedicated assessment of over-dispersion for this outcome, and it should not be assumed to have occurred.
Finally, the primary outcome is change from baseline to a post assessment. A change score summarizes within-participant change, but interpreting a between-group contrast still requires knowing which participants contributed paired measurements and how missing values were handled. Those details are not reported in the registry record. The stated comparison and its uncertainty can be described, but conclusions about robustness to alternative missing-data or modeling assumptions cannot be drawn from the posted information.
11. Confidence Intervals and Precision
The recalculated mean difference for the primary comparison is 0.2, with a 95% confidence interval from -1.152 to 1.552. The interval extends across zero, so the posted summary statistics do not precisely locate the group contrast on one side of zero. It also spans values in both directions on the endpoint scale. This is a measure of statistical uncertainty around the unadjusted estimate, not a range of individual participant outcomes.
The reported standard deviations, 6.5 and 6.1, indicate substantial variation in cognitive change within each group compared with the small difference between their means. When individual outcomes vary considerably, a modest difference in group averages can be difficult to estimate precisely. The confidence interval reflects this uncertainty under the recalculation’s assumptions. It does not address uncertainty caused by unreported design, missing-data, or model choices.
The sponsor’s regression estimate is 0.33, with a 95% confidence interval from -0.91 to 1.56. That interval also includes zero. The accompanying sponsor-reported p-value is p <0.05, which is not conventionally consistent with an interval including zero for the same two-sided test. The registry record offers no explanation, so the discrepancy limits how confidently the sponsor result can be interpreted from the record alone.
Neither interval establishes equivalence or rules out effects of practical importance. The registry does not report a clinically meaningful threshold for the composite score. Judging whether the interval is narrow enough to exclude meaningful benefit or harm therefore is not possible from the posted information alone.
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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 15,598 | 20,881 |
| 75% of the observed effect | 27,730 | 37,122 |
| 50% of the observed effect | 62,392 | 83,524 |
The planning illustrations express sample size as participants per arm, not as total events. They use 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. These assumptions describe the planning illustration; the trial’s own original design assumptions are not reported in the registry record.
For the primary comparison, the illustration based on 100% of the observed effect gives 15,598 participants per arm for 80% power and 20,881 participants per arm for 90% power. Planning for 75% of the observed effect gives 27,730 participants per arm for 80% power and 37,122 participants per arm for 90% power. Planning for 50% of the observed effect gives 62,392 participants per arm for 80% power and 83,524 participants per arm for 90% power.
In general, power is the probability that a planned study will detect an effect of the specified size under the assumed model and significance level. The 80% column represents a design targeting an 80% chance of detecting that effect; the 90% column represents a design targeting a 90% chance. The 90% target requires more participants per arm than the 80% target in these illustrations. Smaller assumed effects require more participants because they are harder to distinguish from random variation.
These values are planning illustrations derived from the observed effect, not observed power. They should not be read as the sample size the trial actually planned to recruit, as evidence that the trial was adequately or inadequately powered, or as a reconstruction of its adaptive design. The observed effect may itself be uncertain, and the registry does not report the original sample-size justification.
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 z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = 0.200; pooled standard deviation σ = 6.304.
- n = 2 × (1.96 + 0.842)2 × 6.3042 / 0.2002 = 15,597.8, rounded up to 15,598 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 <- 0.2 # observed difference in means
sigma <- 6.304377901339 # 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(2851511)
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 = 15,598 (80% power), 20,881 (90% power)
75% of observed effect: n per arm = 27,730 (80% power), 37,122 (90% power)
50% of observed effect: n per arm = 62,392 (80% power), 83,524 (90% power)
power.t.test: 15598.7
Simulated power at n = 15,598 per arm: 0.800 (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
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Regression, Linear | Slope 0.33 | -0.91 to 1.56 | < 0.050 |
The registry reports a sponsor analysis of the primary comparison using linear regression. The reported slope is 0.33, with a 95% confidence interval from -0.91 to 1.56 and p <0.05. The simple recalculation from the posted group summaries gives a mean difference of 0.2, with a 95% confidence interval from -1.152 to 1.552 and an unadjusted p-value of 0.772.
The recalculation is an unadjusted comparison based on group means, standard deviations, and group sizes. It is not a substitute for the sponsor’s regression analysis. The sponsor’s estimate may reflect modeling choices that are not described in the registry record, including any covariates or other adjustments; the record does not state which were used. For that reason, the sponsor’s own analysis takes precedence over the simple recalculation.
There is also an internal inconsistency in the sponsor-reported statistics: its confidence interval includes zero, while its p-value is below 0.05. Under the usual two-sided interpretation, those results would not ordinarily convey the same conclusion for one estimate. The registry record does not explain the difference, so it is not appropriate to choose one statistic and disregard the other or to infer the sponsor’s intended result. The unadjusted recalculation helps readers understand the posted group summaries, but it cannot resolve that inconsistency.
15. Multiplicity, Missing Data and Analysis Populations
The registry describes several hypotheses and assessment areas, including cognitive function, brain function, functional outcomes, maintenance of effects up to 12 months, and neuroimaging biomarkers. It lists one secondary endpoint in addition to the primary endpoint. The multiplicity strategy—whether outcomes or tests were prioritized, whether an adjustment was made, or how confirmatory conclusions were protected across analyses—is not reported in the registry record. Without that information, isolated p-values should be treated cautiously, particularly for secondary or exploratory analyses.
Missing-data handling is also not reported. The record does not say how participants without a post assessment were treated, whether imputation was used, or what assumptions were made about missingness. It does not report whether the analysis included all randomized participants, only participants with observed outcome data, or another analysis population. Although the primary outcome description identifies participants who received cognitive training and gives the phase-specific counts, it does not establish an intention-to-treat analysis or explain exclusions.
The registry reports a linear regression for the sponsor’s primary comparison but does not report the covariates, model diagnostics, or the handling of repeated measurements and baseline values. The posted recalculation is an unadjusted comparison of summary statistics and cannot answer those methodological questions. The record also does not report sensitivity analyses that might show whether conclusions change under alternative missing-data assumptions or model specifications.
These omissions do not establish that the trial lacked such procedures; they mean that the procedures are not reported in the registry record. They limit the ability to assess whether the reported estimate is robust to multiplicity, incomplete outcome data, or analytic choices. The reported results can be described, but a full evaluation of the analysis plan and its execution is not possible from the registry information alone.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Cognitive Training + Active Stimulation | 16 | 168 | 9.5% |
| Cognitive Training + Sham Stimulation | 19 | 166 | 11.4% |
| Educational Training + Active Stimulation | 4 | 23 | 17.4% |
| Educational Training + Sham Stimulation | 5 | 22 | 22.7% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Cognitive Training + Active Stimulation | 0 of 168 |
| Cognitive Training + Sham Stimulation | 0 of 166 |
| Educational Training + Active Stimulation | 0 of 23 |
| Educational Training + Sham Stimulation | 0 of 22 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Cognitive Training + Active Stimulation | 69 of 168 |
| Cognitive Training + Sham Stimulation | 75 of 166 |
| Educational Training + Active Stimulation | 12 of 23 |
| Educational Training + Sham Stimulation | 12 of 22 |
Most frequent serious adverse event terms
| Event term | Organ system | Cognitive Training + Active Stimulation | Cognitive Training + Sham Stimulation | Educational Training + Active Stimulation | Educational Training + Sham Stimulation |
|---|---|---|---|---|---|
| Chest Pain | Cardiac disorders | 1 of 168 | 1 of 166 | 0 of 23 | 1 of 22 |
| Fall | General disorders | 0 of 168 | 2 of 166 | 1 of 23 | 0 of 22 |
| Skin cancer spot removal | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 1 of 168 | 0 of 166 | 1 of 23 | 1 of 22 |
| Bronchitis | Respiratory, thoracic and mediastinal disorders | 1 of 168 | 1 of 166 | 0 of 23 | 0 of 22 |
| Cyst removal | Skin and subcutaneous tissue disorders | 1 of 168 | 0 of 166 | 1 of 23 | 0 of 22 |
| Shingles | Skin and subcutaneous tissue disorders | 0 of 168 | 2 of 166 | 0 of 23 | 0 of 22 |
| Stomach pain | Gastrointestinal disorders | 1 of 168 | 1 of 166 | 0 of 23 | 0 of 22 |
| Tachycardia | Cardiac disorders | 1 of 168 | 1 of 166 | 0 of 23 | 0 of 22 |
| Transient ischemic attack | Vascular disorders | 1 of 168 | 0 of 166 | 0 of 23 | 1 of 22 |
| Vertigo | Nervous system disorders | 1 of 168 | 1 of 166 | 0 of 23 | 0 of 22 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Cognitive Training + Active Stimulation | Cognitive Training + Sham Stimulation | Educational Training + Active Stimulation | Educational Training + Sham Stimulation |
|---|---|---|---|---|---|
| Skin cancer spot removal | Surgical and medical procedures | 19 of 168 | 24 of 166 | 4 of 23 | 3 of 22 |
| Arthritis | Musculoskeletal and connective tissue disorders | 8 of 168 | 8 of 166 | 0 of 23 | 2 of 22 |
| Migraine headache | Nervous system disorders | 6 of 168 | 10 of 166 | 1 of 23 | 1 of 22 |
| Cataract surgery | Surgical and medical procedures | 10 of 168 | 6 of 166 | 1 of 23 | 0 of 22 |
| Urinary tract infection | Renal and urinary disorders | 3 of 168 | 9 of 166 | 1 of 23 | 3 of 22 |
| High Cholesterol | General disorders | 3 of 168 | 7 of 166 | 0 of 23 | 0 of 22 |
| High Blood Pressure | Cardiac disorders | 6 of 168 | 1 of 166 | 0 of 23 | 1 of 22 |
| Colonoscopy | Surgical and medical procedures | 3 of 168 | 2 of 166 | 0 of 23 | 1 of 22 |
| Anxiety and Depression | Psychiatric disorders | 2 of 168 | 2 of 166 | 0 of 23 | 1 of 22 |
| Vertigo | Nervous system disorders | 4 of 168 | 1 of 166 | 0 of 23 | 0 of 22 |
Serious events with the highest arm-level rate: cat bite (4.5%), chest pain (4.5%), hernia (4.5%), pulmonary embolism (4.5%), skin cancer spot removal (4.5%).
The registry reports serious adverse events and other adverse events separately for the four named arms. For the two cognitive-training arms relevant to the primary comparison, serious adverse events affected 16 participants in the active-stimulation arm and 19 in the sham-stimulation arm. Other adverse events affected 69 participants in the active-stimulation arm and 75 in the sham-stimulation arm. The record reports zero deaths in each of the four arms.
For educational training, serious adverse events affected 4 participants with active stimulation and 5 with sham stimulation; other adverse events affected 12 participants in each arm. The listed top serious adverse-event terms are Cat bite, Chest Pain, Hernia, Pulmonary Embolism, Skin cancer spot removal, and Transient ischemic attack, each reported as 4.5%.
These counts describe reported events, not evidence that a particular intervention caused them. The registry record does not provide enough detail to assess event timing, relatedness to study intervention, severity definitions, or comparative risk. The adverse-event figures should therefore be read descriptively and in the context of the reported group sizes, without inferring causation from the counts alone.
17. What the Result Does, and Does Not, Mean
The primary result is an estimate of average change in a cognitive composite after training, comparing cognitive training paired with active stimulation against cognitive training paired with sham stimulation. The unadjusted recalculation gives a small mean difference and a confidence interval that includes zero. The sponsor’s regression result also has a confidence interval that includes zero, but its reported p-value is inconsistent with that interval under the usual two-sided interpretation. The registry record does not resolve this issue.
These results do not establish that active stimulation has no effect, nor do they establish that it improves cognitive ability. A confidence interval including zero is not proof of equivalence. Demonstrating equivalence would require a prespecified margin and an analysis designed for that purpose; such a margin or analysis is not reported in the registry record. The results also do not show whether any change is clinically meaningful, because the record gives no threshold for meaningful change on the composite measure.
The primary comparison is not a direct test of cognitive training against educational training. It isolates active versus sham stimulation among the cognitive-training arms as described in the posted primary outcome. The trial’s broader hypotheses include combined intervention effects, persistence after training, and neuroimaging biomarkers, but those questions need their own reported endpoints and analyses. They cannot be answered by the primary comparison alone.
Group averages do not describe each participant’s experience. The reported standard deviations indicate variability, but the record does not provide distributions or individual response patterns. Nor does the primary estimate establish that effects are maintained up to 12 months; the stated primary timeframe is the post assessment at 3 months. The interpretation should remain confined to the reported outcome, comparison, and timeframe, while recognizing the uncertainty and the unresolved inconsistency in the sponsor statistics.
18. Why This Trial Matters Statistically
This trial is statistically informative because its design separates two behavioral activities and two stimulation conditions, while the primary comparison focuses on active versus sham stimulation within cognitive training. That structure makes clear why results must be tied to a specific contrast: a finding about stimulation added to cognitive training is not the same question as cognitive training compared with educational training.
The study description also illustrates how a clinical trial may have a broad scientific program while reporting a narrower primary endpoint. Cognitive performance, brain response, cerebral metabolites, longer-term maintenance, and individual prediction are distinct questions requiring distinct outcomes and analysis plans. Keeping the reported primary endpoint separate from the broader hypotheses prevents a single estimate from being stretched beyond what it measures.
From a biostatistical perspective, the case also highlights why effect estimates and confidence intervals matter alongside p-values. The simple recalculation and sponsor regression result are not identical analyses, and the registry’s sponsor-reported p-value and confidence interval appear inconsistent. Transparent reporting of the model, analysis population, missing-data approach, and multiplicity plan would help readers understand how the sponsor estimate was obtained and how strongly it supports an inference.
Finally, the planning illustrations demonstrate that sample-size requirements depend on the effect assumed for planning and the desired power. They do not reveal the original design justification or the adequacy of the completed trial. Separating design planning from observed results is essential when interpreting a completed study, particularly when the observed estimate itself is uncertain.
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 registry record leaves several trial-specific interpretive questions unanswered. It describes a two-phase adaptive randomized trial but does not report the adaptive decision rules, how phase-specific information was combined, or whether the primary analysis accounted for the adaptive design. The phase field is NA, and the original sample-size justification and design assumptions are not reported.
The primary outcome description gives a cognitive-training population spanning both phases, while the group summaries report the two cognitive-training arms. The record does not explain the relationship between the outcome population and all randomized participants, whether participants were excluded, or how incomplete assessments were handled. Missing-data methods and the analysis population are not reported. This limits assessment of selection and attrition effects.
The sponsor’s analysis is identified as linear regression, but model details are absent. The record does not report covariate adjustment, baseline handling, model diagnostics, or sensitivity analyses. In addition, the reported sponsor confidence interval includes zero while the reported p-value is below 0.05, and no explanation is given. This discrepancy makes the sponsor result harder to interpret without further information.
The registry record does not state a clinically meaningful threshold for the cognitive composite, so the practical importance of the estimated difference cannot be judged from the scale alone. It also does not report a multiplicity strategy despite multiple stated hypotheses and assessment domains. The primary comparison addresses a 3-month outcome and cannot establish the separate hypothesis about maintenance up to 12 months. These are limits on interpretation of the registry record, not claims that the trial protocol or full analysis lacked the relevant procedures.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Augmenting Cognitive Training In Older Adults — NCT02851511.
- Registry record last updated 2024-04-17; status last verified 2023-06.
- Results first posted 2023-07-17.
- 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.
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23. Record Summary
The registry describes a completed, randomized, double-masked, parallel, two-phase adaptive trial sponsored by the University of Florida. The study evaluates cognitive and educational training paired with active or sham tDCS. The primary endpoint is change in NIH toolbox fluid cognition fully corrected T-score from baseline to post assessment at 3 months.
For cognitive training with active versus sham stimulation, the posted group means are 4.7 and 4.5. The unadjusted recalculation reports a mean difference of 0.2, with a 95% confidence interval from -1.152 to 1.552 and p=0.772. The sponsor’s regression analysis reports a slope of 0.33, a 95% confidence interval from -0.91 to 1.56, and p <0.05. The interval and p-value are not conventionally consistent, and the registry does not explain the discrepancy; the sponsor’s analysis takes precedence over the simple recalculation.
The record lists one secondary cognitive-training measure, adverse-event counts for four arms, and planning illustrations based on the observed effect. Original design assumptions, multiplicity procedures, missing-data handling, and detailed sponsor-model specifications are not reported in the registry record.