CogT BEEM Study (a tDCS Study): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for CogT BEEM Study (a tDCS Study) (NCT04099524), a randomized na study. The primary outcome is Change of C3 Activation (NPS-shared Neural Circuit Measure.

2. Clinical Question

3. Trial Design

The registry identifies NCT04099524 as the CogT BEEM Study (a tDCS Study), sponsored by the University of Rochester. It lists the study as completed, with an enrollment of 40 and phase recorded as NA. The start date is 2019-12-06, and the primary completion date is 2022-01-19. The design was randomized, double-masked, and parallel-group, comparing active tDCS with sham tDCS.

The study summary describes a Stage 0 pilot randomized control trial in older adults with informant-rated neuropsychiatric symptoms that had worsened in the past 2 years. Participants were assigned to active anodal or sham left precentral gyrus stimulation for 4 weeks. The study planned assessments of resting-state and visual-attention task-related functional MRI and informant-rated symptoms at baseline, the end of week 4, and week 8; diffusion MRI was planned at baseline. The posted primary endpoint concerns the visual-attention task-related activation measure from baseline to post-intervention at 4 weeks.

The registry reports primary-outcome analysis data from 35 subjects, with 18 in the intervention group and 17 in the control group. It also states that one participant withdrew and one participant’s data were excluded for excessive motion during MRI. The enrollment figure and analysis populations should therefore be read as different features of the record, not as interchangeable counts. The registry does not report the original sample-size justification, the allocation procedure in further detail, or the full masking procedures. The exact schedule of stimulation sessions and adherence to the planned intervention 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: all participants enrolled were assigned to groups.

Overall Study

Analysis population for the primary outcome, as defined in the registry: AR(1) covariance matrix with Generalized Estimating Equation (GEE) model. Data from 35 subjects (18 from intervention and 17 from control) were included in the data analysis on LSMC: in addition to the one participant that withdrew, one participant's data was excluded for excessive motion during MRI scanning, two for issues with co-registration and normalization, and one did not complete MRI scanning at timepoint 2 due to claustrophobia.

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: We conducted group comparisons of baseline characteristics.

6. Primary Endpoint

The registry lists the primary outcome as Change of C3 Activation (NPS-shared Neural Circuit Measure, measured over from baseline to post-intervention (4 weeks).

The primary endpoint is titled “Change of C3 Activation” and described as change in arbitrary-unit left precentral gyrus activation in response to a visual-attention task, measured using task-related functional MRI. The timeframe is baseline to post-intervention at 4 weeks. The registry states that the scale has no theoretical minimum or maximum, so the magnitude is expressed in arbitrary units rather than on a bounded clinical scale.

The measure was chosen to address the study’s mechanistic question. The study summary describes a proposed neural circuit shared across neuropsychiatric symptoms and identifies the left precentral gyrus as a target region involved in visual attention. A change in task-related activation could therefore serve as an indicator of neural response to stimulation. It is a biological or functional imaging measure, however, not itself a direct measure of daily functioning or symptom burden. The registry separately lists patient-reported and informant-rated neuropsychiatric symptom outcomes.

The record’s title for the endpoint uses “C3 Activation,” while its unit and description refer to left precentral gyrus activation. The exact reason for that naming difference is not reported in the registry record. The primary outcome is a change score, but the posted sponsor analyses are described as mean differences in final values; those are not necessarily the same estimand as a difference in change scores.

7. Results Posted in the Registry

• Active tDCS: mean -0.15 versus 0.01 on control; difference -0.16 (95% CI -0.40 to 0.08), standardized effect d = -0.44; z-test p = 0.189.

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.

Change of Patient-report NPS

• 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:
  • Active tDCS: mean -0.22 versus -1.01 on control; difference 0.79 (95% CI -0.37 to 1.95), standardized effect d = 0.44; z-test p = 0.180.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Active tDCS and the control. The interval gives the range of effects that remain compatible with the data.

Change of Informant-rated NPS

• 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:
  • Active tDCS: mean -0.04 versus -0.87 on control; difference 0.83 (95% CI 0.07 to 1.59), standardized effect d = 0.70; z-test p = 0.032.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for Active tDCS than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The secondary outcome pattern is not uniform across patient report and informant report. The recalculated patient-report comparison is uncertain, with a confidence interval that includes zero. The informant-rated comparison has a confidence interval that does not include zero, and its direction differs from the primary activation comparison’s point estimate when expressed as active relative to sham. These secondary findings concern symptom ratings, whereas the primary outcome is a functional imaging measure, so they address related but distinct questions.

The secondary outcomes can help show whether the proposed neural measure is accompanied by changes in reported symptoms, but they do not establish that a change in activation caused a symptom change. The posted record does not report a mediation analysis or a formal test linking individual changes in the imaging measure to changes in symptom ratings. The summaries therefore support descriptive comparison, not a causal account of how the outcomes may be related.

Unadjusted secondary results carry less weight when multiple outcomes or analyses are examined, because the chance of observing at least one nominally notable result can increase as more tests are considered. This is a general statistical concern. The registry lists multiple analyses and does not report a multiplicity adjustment or identify a prespecified hierarchy for interpreting the secondary outcomes. The registry-reported secondary analyses should therefore be regarded as exploratory evidence rather than standalone confirmation. Their mixed pattern also makes it inappropriate to summarize the secondary outcomes as a single consistent signal.

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

• Change of Patient-report NPS
• Change of Informant-rated NPS

9. Statistical Interpretation

10. Statistical Methods Explained

What does the primary comparison estimate?

The posted primary summaries give a mean change for each group, and the recalculation contrasts those means as active stimulation relative to sham. In general, a mean difference expresses the average separation between groups on the measured scale. A negative estimate means the active-group change was lower than the sham-group change as encoded by the comparison. Because the activation scale is in arbitrary units and has no theoretical minimum or maximum, the sign and magnitude describe the measured scale; they do not automatically translate into a clinical benefit or harm.

The recalculation uses the reported group means and standard deviations as an unadjusted comparison. It does not reproduce the registry’s stated generalized estimating equation analysis with an AR(1) covariance matrix. In general, an adjusted or repeated-measures model may use information across measurements and account for within-person correlation, while a simple summary-statistic comparison does not model those features. The methods target can differ, especially when the posted sponsor analysis is described in terms of final values rather than change scores.

What does a confidence interval convey?

In general, a confidence interval expresses uncertainty around an estimate under the assumptions of the method used to calculate it. A narrower interval indicates greater precision; a wider interval leaves more uncertainty about the effect’s size and direction. For a difference, an interval spanning zero is compatible with both a negative and a positive difference, as well as no difference. It is not proof that there is no effect. The interval should be considered alongside the estimate, the measurement scale, and the study design.

The primary interval is reported from -0.399 to 0.079. Since it spans zero, it does not support a clear directional conclusion from the unadjusted calculation. Its width also illustrates that the estimate is not very precise. The p-value of 0.189 is an unadjusted value for this recalculation; it does not measure the probability that the null hypothesis is true or the probability that the result arose by chance.

Why might repeated-measures methods matter?

The primary-outcome population description reports an AR(1) covariance matrix with a generalized estimating equation model. In general, repeated observations from the same participant may be correlated rather than independent. An AR(1) structure represents a pattern in which measurements closer together in time are treated as more strongly related than measurements farther apart. Generalized estimating equations use a specified correlation structure to estimate an average relationship across participants. The registry does not report enough detail to reproduce the sponsor model, including the model specification beyond the named covariance structure and method.

In general, over-dispersion occurs when observed variability exceeds what a model’s assumed distribution would predict. If present and not accommodated, standard errors can be too small and uncertainty can be understated. The record does not report an over-dispersion assessment or whether this issue applied to the analyses, so it is not possible to say that it affected these results.

How should the p-values be understood?

In general, a p-value measures how incompatible the observed data are with a specified null model, conditional on the model and its assumptions. It is not an effect-size measure and does not show whether a result is clinically important. The recalculated primary p-value is 0.189. The registry’s mixed-model entries report p <0.05, but do not provide confidence intervals or enough outcome-level detail to interpret those entries as replacements for the recalculated change-score comparison.

Different methods can yield different estimates or p-values because they may use different outcome definitions, data, covariates, correlation assumptions, or analysis populations. The sponsor analyses are identified as mixed models of final values, whereas the recalculation is an unadjusted comparison of posted change summaries. The record does not give the full model specification or enough information to reconcile the results. A reader should therefore distinguish the sponsor-reported model results from the recalculated summary-statistic results rather than blending them into a single estimate.

What is the role of a pilot trial?

In general, a pilot study can assess feasibility and produce preliminary estimates for a larger investigation. Estimates from small studies can be unstable, and observed effects may differ from effects in a later study. The registry describes this as a Stage 0 pilot and proof-of-concept mechanistic intervention study. It does not report the original sample-size justification, any interim analyses, or a prespecified statistical analysis plan. The posted sample-size illustrations are based on the observed effect and are not evidence of the study’s original planning process.

11. Confidence Intervals and Precision

The primary recalculated mean difference is -0.16, with a 95% confidence interval from -0.399 to 0.079. The interval crosses zero, so the data are compatible with differences in either direction as well as no group difference. Its span indicates substantial uncertainty around the point estimate relative to the precision needed for a firm conclusion. The unadjusted p-value is 0.189, but the interval gives a more direct view of the range of effects compatible with this calculation.

The group standard deviations are 0.39 for active stimulation and 0.33 for sham stimulation. These describe variation in participant changes within each group; they are not confidence limits around the group means. The registry does not report arm-specific confidence intervals for the primary means. The recalculated interval is based on the posted summary statistics and is not the interval from the sponsor’s generalized estimating equation model.

Confidence intervals are useful because they show both the estimated direction and uncertainty, but they depend on the analysis assumptions. Here, the primary analysis description names a repeated-measures GEE approach with an AR(1) covariance matrix, while the recalculation is an unadjusted comparison of group summaries. The record does not report a sponsor-model confidence interval or the detail needed to reproduce that model. Thus, the recalculated interval should be interpreted as a simple summary-based estimate, not as a reconstruction of the sponsor’s model-based uncertainty.

The primary endpoint uses arbitrary units, with no theoretical scale limits. Consequently, the interval’s numerical width cannot be translated directly into a clinically meaningful threshold from the record. A clinically important difference is not reported in the registry record. Precision about the statistical difference and evidence about clinical relevance are separate questions.

12. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm for this continuous-outcome comparison, not total events. They are illustrations based on the observed effect, with two-sided significance level 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses the stated fraction of the observed effect as the effect to detect. The original trial’s own design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm under the stated assumptions for a design with an 80% chance of detecting the specified effect if that effect were the true one. The 90% power column gives the corresponding per-arm planning figure for a design with a 90% chance under those assumptions. These are prospective planning concepts, not guarantees that a future study will reach a particular result.

The rows for planning for 100%, 75%, and 50% of the observed effect illustrate how the assumed target effect changes the required sample size. A smaller effect is harder to distinguish from random variation, so detecting it generally requires more participants. The figures are tied to the observed estimate, which may be unstable in a pilot study, and the registry does not establish that any of these effects is clinically important.

This is not observed power. It is a planning illustration generated from a stated effect assumption and analysis framework, not a retrospective measure of how informative the completed trial was. The primary result’s uncertainty is better assessed from its estimate and confidence interval than from a post hoc power calculation.

13. How the Sample Size Is Derived

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

Formula

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

Worked calculation for this trial

1. Observed difference Δ = -0.160; pooled standard deviation σ = 0.362.
2. n = 2 × (1.96 + 0.842)² × 0.362² / -0.160² = 80.4, rounded up to 81 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 <- -0.16                      # observed difference in means
sigma <- 0.362152654904731                     # 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(4099524)
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 = 81 (80% power), 108 (90% power)
 75% of observed effect: n per arm = 143 (80% power), 192 (90% power)
 50% of observed effect: n per arm = 322 (80% power), 431 (90% power)
power.t.test: 81.4 
Simulated power at n = 81 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

The registry lists mixed-model analyses for the active and sham groups, reporting mean differences in final values of -0.18 and 0.20, each with p <0.05. Confidence intervals are not reported for these entries. The posted analysis descriptions do not identify which outcome corresponds to each estimate, so the outcome-level interpretation cannot be determined from those entries alone.

The recalculated primary comparison uses the posted group change means and standard deviations. It is an unadjusted summary-statistic estimate of -0.16, with a 95% confidence interval from -0.399 to 0.079 and p=0.189. It differs in method and stated outcome form from the sponsor’s mixed-model analyses, which are described as comparisons of final values. A comparison of change scores and a model of final values are not necessarily estimating the same quantity.

The registry does not report enough model detail or outcome mapping to reproduce or reconcile the sponsor analyses. The discrepancy flag is false, but that does not make the methods interchangeable. The sponsor’s analyses should be read as the registry-reported model results; the recalculation is a separate, simple unadjusted check based on posted summaries. Neither should be presented as if it directly validates or replaces the other.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists four outcome measures and five analyses, and it posts two secondary outcomes. The record does not report whether the analyses were organized into a prespecified hierarchy, which outcomes were designated confirmatory beyond the stated primary endpoint, or whether any correction for multiple comparisons was planned or applied. Without that information, the statistical family of tests is not clear. In general, testing multiple outcomes can increase the chance of a nominally small p-value even when no true effect is present; adjustments or prespecified priorities can help control how such results are interpreted.

The primary analysis description identifies an AR(1) covariance matrix and a generalized estimating equation model. It also states that data from 35 subjects, with 18 in the intervention group and 17 in the control group, were included in the analysis. The description mentions one withdrawal and one participant excluded because of excessive motion during MRI. The record does not explain the missing-data handling method, whether all randomized participants were included in any other analysis, or how missing observations at other measurement times were handled.

The secondary outcome summaries use different analysis populations from the primary outcome description. The registry does not report a complete participant flow or the reasons for all differences in available outcome data. It also does not report whether analyses followed an intention-to-treat principle, whether any imputation was used, or whether sensitivity analyses examined missing-data assumptions. These omissions matter because conclusions can depend on who contributes data and how unavailable measurements are treated.

The registry gives no information on interim analyses, stopping rules, or a full statistical analysis plan. Their presence or absence cannot be inferred from the posted endpoint summaries. The results are therefore best interpreted with attention to the stated analysis populations and methods, while recognizing that the multiplicity and missing-data procedures are not fully documented in the registry record.

16. 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.

The serious adverse event summary lists 20 participants at risk in the active tDCS group and 20 in the sham tDCS group. The number affected by a serious adverse event is reported as 0 in each group, and deaths are reported as 0 in each group. The registry also reports 0 affected by other adverse events in each group among the listed participants at risk.

These figures describe what was recorded in the registry’s adverse-event summary for the stated groups. A zero count means no events of that category were reported in that summary; it does not establish that the intervention is free of risk. The registry does not provide event-level details, severity breakdowns beyond the serious-event category, or information about ascertainment procedures. The adverse-event population counts also should not be assumed to match the analysis populations for each outcome.

The study was a pilot, and the safety counts should be read as descriptive observations rather than a precise estimate of uncommon harms. No broader safety conclusion follows from these counts alone.

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

The primary result is an estimate of change in task-related left precentral gyrus activation over the intervention period, not a direct measure of overall cognitive function, daily independence, or neuropsychiatric symptom burden. The unadjusted comparison is imprecise, and its confidence interval includes zero. The result therefore does not establish a clear difference between active and sham groups on this measure, but it also does not show that the groups are identical.

The secondary outcomes assess patient-reported and informant-rated neuropsychiatric symptoms. They provide additional descriptions of reported symptom change, but do not demonstrate that stimulation-induced neural changes caused symptom changes. No formal analysis linking the imaging and symptom outcomes is reported in the registry record. The record’s mechanistic hypothesis is a rationale for the study, not a conclusion established by these summaries.

The findings also do not establish whether an observed difference is clinically important. The imaging endpoint is expressed in arbitrary units, and the registry reports no clinically meaningful threshold for it. The study summary describes a proof-of-concept Stage 0 pilot, so its results are preliminary and should be interpreted in that context. The posted data do not establish how results would generalize beyond the studied population or intervention conditions.

These results are not medical advice and should not be used alone to make decisions about care. They describe the outcomes recorded for this study and the precision of the posted comparisons. A clear understanding of the results requires keeping the primary imaging outcome distinct from symptom outcomes, the sponsor’s model-based analyses distinct from the unadjusted recalculations, and statistical evidence distinct from clinical importance.

18. Why This Trial Matters Statistically

This trial raises a useful statistical challenge: a mechanistic study may measure a biological response and symptom outcomes at the same time, but those outcomes do not answer the same question. The primary endpoint concerns task-related fMRI activation in a proposed neural-circuit target. Patient- and informant-reported outcomes concern symptoms. A difference in one does not automatically imply a difference in the other, and parallel changes would not alone establish a causal link between them.

The record also illustrates why estimates and uncertainty matter more than a binary reading of significance. The primary recalculated estimate is accompanied by an interval that spans zero, so the data are compatible with a range of possible group differences. The pilot design can generate estimates for future research, but those estimates need to be interpreted cautiously because uncertainty is substantial and the study’s own sample-size justification is not reported.

Finally, the record includes both sponsor-reported mixed-model analyses and simple recalculations from group summaries. Comparing them requires attention to the stated endpoint, outcome form, analysis population, and model. When those details are incomplete, apparent differences between results cannot be resolved by treating one estimate as a direct reproduction of the other. This is a general lesson in clinical biostatistics: transparent estimands, analysis plans, and uncertainty reporting are essential for interpreting complex pilot trials.

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 study’s primary imaging measure is expressed in arbitrary units, and the registry states that the scale has no theoretical minimum or maximum. A clinical interpretation threshold is not reported in the registry record. The primary interval is relatively broad and includes zero, limiting precision about the direction and magnitude of the group difference.

The record describes the primary analysis as a GEE model with an AR(1) covariance matrix, but the full model specification and confidence interval for the sponsor analysis are not reported. The sponsor’s entries are described as mean differences in final values, while the summary-based recalculation contrasts change scores. The outcome mapping for the sponsor entries is also not clear from the posted analysis descriptions. These differences prevent a direct reconciliation.

The analysis populations vary across the posted outcomes. The primary-outcome description reports 35 subjects in the analysis and mentions a withdrawal and an MRI-motion exclusion, while the secondary outcome summaries list different group counts. A complete participant flow, detailed missing-data procedures, and sensitivity analyses are not reported. The original sample-size justification, the full statistical analysis plan, and multiplicity procedures are also not reported in the registry record.

As a pilot mechanistic study, the trial’s findings are preliminary. The registry does not report a formal analysis connecting the neural measure with symptom changes, nor does it establish clinical importance or generalizability beyond the study population and conditions. The safety summary is descriptive and cannot precisely characterize uncommon events.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: CogT BEEM Study (a tDCS Study) — NCT04099524.
• Registry record last updated 2023-11-07; status last verified 2023-11.
• Results first posted 2023-11-07.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

23. Record Summary

NCT04099524, the CogT BEEM Study (a tDCS Study), is listed as a completed, randomized, double-masked, parallel-group study sponsored by the University of Rochester. The registry reports enrollment of 40 and a comparison of active with sham tDCS in older adults with mild cognitive impairment and worsening informant-rated neuropsychiatric symptoms.

The primary endpoint assessed change in task-related left precentral gyrus activation from baseline to post-intervention at 4 weeks. The unadjusted recalculation gives a mean difference of -0.16, with a 95% confidence interval from -0.399 to 0.079 and p=0.189. The interval includes zero, indicating uncertainty about the direction and size of the difference. Secondary symptom outcomes show a mixed pattern, and multiplicity and missing-data details are not fully reported.

The posted findings are preliminary and should be interpreted as results from a pilot mechanistic study, not as proof of clinical importance or a causal link between neural activation and symptom change.