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 Effect of Noninvasive Electrical Brain Stimulation on Memory at Different Times of Day in Younger and Older Adults (NCT03723850), a randomized na study. The primary outcome is Episodic Memory Performance.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03723850 |
| Phase | NA |
| Condition | Effect of tDCS on Memory in Older and Younger Adults |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 271 |
| Arms in the primary outcome | 5 |
| Lead sponsor | University of Chicago |
| Results posted | Yes |
2. Clinical Question
Population
Cognitively normal adults, including younger adults aged 18-30 and older adults aged 60-75. The registry record describes these age groups in the arm descriptions and identifies the primary outcome population as cognitively-normal adults.
Intervention
Active transcranial direct current stimulation (tDCS), delivered to the left dorsolateral prefrontal cortex (dlPFC) for older adults and for one younger-adult group. A separate younger-adult group received active stimulation at the left parietal cortex.
Comparator
Sham tDCS. The older-adult sham group received stimulation at the left dlPFC. The younger-adult sham group is described as having stimulation at either the left dlPFC or the left parietal cortex.
Primary question
How does tDCS relate to episodic memory performance in younger and older adults when memory is tested after sessions scheduled in the morning and afternoon? Posted results report average performance by arm and unadjusted comparisons with the older-adult sham group.
The central research question concerns memory performance after noninvasive electrical stimulation and whether the observed pattern varies with age group and time of day. According to the registry summary, participants completed one morning session and another session on a separate afternoon for the described arms. The outcome was assessed immediately after stimulation. The record does not report a statistical test of the specific interaction between treatment, age, and time of day, so the arm means and posted comparisons should not be read as establishing such an interaction.
The comparison structure requires care. The older-adult active group is compared with older-adult sham participants, while each younger-adult group is compared with the older-adult sham group. Those comparisons therefore differ not only in stimulation assignment but also in age group. They describe differences between the reported arms; they do not isolate a treatment effect among younger adults against a younger-adult sham comparator. The younger sham group also encompasses two electrode locations in its arm description.
3. Trial Design
The registry record describes a randomized, double-masked, parallel-group study with an enrollment of 271 and a completed status. The sponsor is the University of Chicago. The listed phase is not applicable. The registry gives study start and primary completion dates as 2019-03-08 and 2022-12-15.
Five arms appear in the posted primary outcome results: older adults receiving active tDCS at the dlPFC, older adults receiving sham stimulation at the dlPFC, younger adults receiving active tDCS at the dlPFC, younger adults receiving sham stimulation at the dlPFC or parietal cortex, and younger adults receiving active tDCS at the parietal cortex. Arm descriptions state that participants received two sessions, one in the morning and another on a separate afternoon. The record does not give a complete description of the stimulation schedule for every arm, so details beyond the posted descriptions are not assumed.
The primary outcome results include 46 older adults in the active dlPFC arm and 45 in the older sham dlPFC arm. The younger active dlPFC and younger sham dlPFC/parietal arms each include 51 participants; the younger active parietal arm includes 48. These outcome-specific counts need not match enrollment or safety counts, because they refer to different record entries and analysis measures.
Random assignment and masking describe design features, not a guarantee that the reported comparisons are unbiased in every respect. The registry record does not report the allocation procedure, how masking was maintained or assessed, the original sample-size justification, or a detailed prespecified statistical analysis plan. It also does not post sponsor-reported statistical analyses for the primary outcome. The contrasts discussed in the interpretation are simple, unadjusted recalculations from the posted arm summaries, rather than results attributed to a reported sponsor analysis.
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: Participants have the right to end their participation at any time. In addition, the PI may terminate participation if a participant is in obvious non-compliance with the study procedures (e.g., responding randomly or sleeping during the cognitive task) or shows signs of moderate or severe adverse events associated with the study procedures (e.g., excessive discomfort with the tDCS electrodes). Enrolled participants may not continue in the study if they meet any of our exclusion criteria.
Overall Study
| Stage | Older, Active tDCS, dlPFC | Older, Sham tDCS, dlPFC | Younger, Active tDCS, dlPFC | Younger, Sham tDCS, dlPFC/Parietal | Younger, Active tDCS, Parietal Cortex |
|---|---|---|---|---|---|
| STARTED | 49 | 45 | 54 | 52 | 51 |
| COMPLETED | 46 | 45 | 51 | 51 | 48 |
| NOT COMPLETED | 3 | 0 | 3 | 1 | 3 |
Analysis population for the primary outcome, as defined in the registry: Cognitively-normal adults.
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.
| Characteristic | Unit | Older, Active tDCS, dlPFC | Older, Sham tDCS, dlPFC | Younger, Active tDCS, dlPFC | Younger, Sham tDCS, dlPFC/Parietal | Younger, Active tDCS, Parietal Cortex | Total |
|---|---|---|---|---|---|---|---|
| Participants analysed | 46 | 45 | 51 | 51 | 48 | 241 | |
| Age, Categorical: <=18 years | Participants | 0 | 0 | 0 | 0 | 0 | 0 |
| Age, Categorical: Between 18 and 65 years | Participants | 0 | 0 | 51 | 51 | 48 | 150 |
| Age, Categorical: >=65 years | Participants | 46 | 45 | 0 | 0 | 0 | 91 |
| Age, Continuous | years | 67.56 (SD 4.58) | 67.06 (SD 4.61) | 20.80 (SD 2.90) | 20.90 (SD 3.23) | 21.40 (SD 3.06) | 39.54 (SD 3.68) |
| Sex: Female, Male: Female | Participants | 31 | 29 | 30 | 31 | 27 | 148 |
| Sex: Female, Male: Male | Participants | 15 | 16 | 21 | 20 | 21 | 93 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 3 | 1 | 9 | 11 | 14 | 38 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 40 | 38 | 41 | 38 | 34 | 191 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 3 | 6 | 1 | 2 | 0 | 12 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Asian | Participants | 0 | 0 | 12 | 17 | 10 | 39 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 22 | 22 | 7 | 2 | 5 | 58 |
| Race (NIH/OMB): White | Participants | 19 | 22 | 24 | 29 | 27 | 121 |
| Race (NIH/OMB): More than one race | Participants | 5 | 1 | 6 | 1 | 4 | 17 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 2 | 2 | 2 | 6 |
| Region of Enrollment: United States | participants | 46 | 45 | 51 | 51 | 48 | 241 |
6. Primary Endpoint
The registry lists the primary outcome as Episodic Memory Performance, measured over This task is performed immediately after tDCS is administered, and lasts approximately 20 minutes..
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | proportion of items |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is episodic memory performance, measured as a mean proportion of items. Participants studied picture and word stimuli and later completed a retrieval task. The task asked them to distinguish studied from non-studied items and, for studied items, to recall the original format. Participants also made confidence judgments. The registry defines the primary dependent variable as the proportion of studied items assigned to the correct source minus the proportion of nonstudied items incorrectly assigned to that same source.
This scoring approach is intended to capture memory for the source or format of studied material while accounting for incorrect source attribution to nonstudied material. It is a continuous outcome, with larger values reflecting a greater net proportion under the stated scoring definition. The posted results give the mean and standard deviation for each arm. They do not provide confidence limits for the individual arm means.
The task was performed immediately after tDCS and lasted approximately 20 minutes. That timing makes the endpoint a measure of performance soon after the stimulation session, not a measure of memory over a longer follow-up period. The registry also lists working memory as a secondary outcome, but that is a separate measure and should not be conflated with the episodic memory endpoint.
As a general statistical point, a mean summarizes the average outcome in a group, while a standard deviation describes how dispersed individual scores are around that average. Neither the mean nor the standard deviation alone shows whether a difference between groups is distinguishable from sampling uncertainty; the comparison estimate and its confidence interval help describe that uncertainty.
7. Results Posted in the Registry
- Older, Active tDCS, dlPFC: mean 0.34 versus 0.32 on control; difference 0.02 (95% CI -0.08 to 0.12), standardized effect d = 0.08; z-test p = 0.703.
- Younger, Active tDCS, dlPFC: mean 0.46 versus 0.32 on control; difference 0.14 (95% CI 0.04 to 0.24), standardized effect d = 0.55; z-test p = 0.007.
- Younger, Sham tDCS, dlPFC/Parietal: mean 0.50 versus 0.32 on control; difference 0.18 (95% CI 0.08 to 0.28), standardized effect d = 0.75; z-test p = <0.001.
- Younger, Active tDCS, Parietal Cortex: mean 0.49 versus 0.32 on control; difference 0.17 (95% CI 0.07 to 0.27), standardized effect d = 0.69; z-test p = <0.001.
Mean difference: Older, Active tDCS, dlPFC
95% CI: -0.08 to 0.12
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 |
|---|---|---|---|---|
| Working Memory Performance | Continuous Endpoint | Mean difference | 0.00 (-0.13 to 0.13) | n/a |
Working Memory Performance
- 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:
- Older, Active tDCS, dlPFC: mean 0.60 versus 0.60 on control; difference 0.00 (95% CI -0.13 to 0.13), standardized effect d = 0.00; z-test p = 1.000.
- Younger, Active tDCS, dlPFC: mean 0.60 versus 0.60 on control; difference 0.00 (95% CI -0.12 to 0.12), standardized effect d = 0.00; z-test p = 1.000.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Older, Active tDCS, dlPFC and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Younger, Active tDCS, dlPFC and the control. The interval gives the range of effects that remain compatible with the data.
The registry record lists working memory performance as a secondary outcome. The posted arm means are close in broad terms, ranging from 0.58 to 0.6, and the comparisons that are reported have recalculated mean differences of 0.0. Their confidence intervals include zero and their unadjusted p-values are 1.0. The record does not post comparison analyses for every secondary arm contrast, so the available summaries do not establish a complete pattern across all possible pairwise comparisons.
At a high level, the working-memory summaries do not show the same pattern of positive cross-age contrasts that appears in the recalculated episodic-memory comparisons. This is a broad descriptive observation, not a formal test that the primary and secondary outcomes differ from one another. A difference between whether separate outcomes cross a statistical threshold is not itself evidence of a difference in effects across those outcomes; that would require a suitable direct analysis.
The secondary measure was performed after the episodic-memory task, approximately 20 minutes after the end of the tDCS session, and lasted approximately 10 minutes. Its timing and construct differ from the primary endpoint, so results should not be treated as interchangeable measures of memory. The registry record does not report a secondary-outcome analysis plan or adjustment for examining multiple outcomes and contrasts.
Unadjusted secondary results generally carry less inferential weight when many outcomes or comparisons may be considered, because the chance of observing apparently notable results can increase across repeated testing. This is a general statistical concern, not evidence that any particular result is false. With no reported multiplicity strategy and no posted sponsor analysis, the secondary summaries are best regarded as descriptive context rather than confirmatory evidence.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Working Memory Performance
9. Statistical Interpretation
For older adults, the active dlPFC arm had a mean episodic memory score of 0.34, compared with 0.32 in the older sham dlPFC arm. The recalculated unadjusted mean difference was 0.02, with a 95% confidence interval from -0.083 to 0.123 and p = 0.703. This interval includes both negative and positive differences, and the estimate is imprecise enough that the posted summaries do not sharply distinguish the direction of the underlying difference.
For younger adults receiving active dlPFC stimulation, the reported mean was 0.46, compared with 0.32 in the older sham group. The recalculated unadjusted mean difference was 0.14, with a 95% confidence interval from 0.038 to 0.242 and p = 0.007. The younger sham dlPFC/parietal group had a mean of 0.5; its unadjusted difference from older sham was 0.18, with a 95% confidence interval from 0.084 to 0.277 and p < 0.001. The younger active parietal group had a mean of 0.49; its unadjusted difference from older sham was 0.17, with a 95% confidence interval from 0.070 to 0.270 and p < 0.001.
These comparisons are descriptive contrasts with the older sham group, not like-for-like estimates of active versus sham stimulation within younger adults. In particular, the differences involving younger groups combine age-group differences with differences in assigned stimulation and, for the younger sham arm, variation in stimulation location. The contrasts therefore cannot by themselves establish that active stimulation caused the observed differences, nor do they directly answer whether treatment effects vary by age or time of day.
The record states that the outcome task followed stimulation sessions scheduled at different times. However, the posted primary results are arm-level summaries, and the registry record does not report estimates separating morning from afternoon performance or a treatment-by-time-of-day analysis. The reported means consequently do not reveal whether any group performed differently at one time of day than another, or whether time of day changed the relationship between stimulation and memory.
The p-values and confidence intervals are unadjusted recalculations from the posted summary statistics. The registry record contains no reported primary-outcome analyses, so these should not be mistaken for the sponsor's own inferential analysis. The differences describe what the posted group summaries imply under a simple comparison; they do not account for any unreported modeling, covariates, repeated-session structure, or multiplicity procedures. The values should be interpreted as evidence about the precision and direction of these particular crude contrasts, rather than as a complete answer to the study's broader research question.
10. Statistical Methods Explained
Statistical interpretation begins with the outcome's scale and the comparison being made. Episodic memory is recorded as a proportion-based continuous measure. For each arm, the posted mean is the average outcome and the standard deviation describes participant-to-participant variability. A mean difference subtracts one arm mean from another; the recalculated comparisons use the older sham dlPFC arm as the reference. These are unadjusted contrasts, not estimates from a reported regression or other sponsor analysis.
What does a confidence interval communicate?
As a general explanation, a confidence interval expresses the uncertainty around an estimate under the method used to construct it. A narrower interval indicates greater precision on that scale, while a wider interval indicates that a broader range of differences remains compatible with the data and calculation. It is not a guarantee that the true value lies inside the particular interval, and it does not remove bias caused by design or analysis choices. For the older active versus older sham comparison, the interval ranges from -0.083 to 0.123 and includes zero. The intervals for the three younger-arm comparisons with older sham are entirely above zero. These interval patterns characterize the recalculated contrasts, but the age-group and comparator differences remain important when interpreting them.
How should a p-value be read?
As a general explanation, a p-value measures how unusual data at least as incompatible with a specified null hypothesis would be if that hypothesis and the model assumptions were true. It is not the probability that the null hypothesis is true, the probability that results arose by chance, or a measure of clinical importance. The recalculated p-values are unadjusted: p = 0.703 for older active versus older sham, p = 0.007 for younger active dlPFC versus older sham, and p < 0.001 for each of the younger sham dlPFC/parietal and younger active parietal comparisons versus older sham.
Those p-values use simple two-group comparisons based on the posted means, standard deviations, and sample sizes. The record does not report the sponsor's model, any adjustment for covariates, or an analysis that accounts for both sessions within a participant. It also does not report a prespecified multiplicity procedure. Thus, the recalculated p-values should be treated as exploratory summaries, particularly because several arms and outcomes are involved.
Why does the comparator define the interpretation?
A contrast only answers the question embodied by its two groups. The older active and older sham comparison holds the described age group and stimulation location constant while changing active versus sham assignment, so it is the most direct posted contrast for active versus sham stimulation among older participants at the dlPFC. The younger-arm comparisons instead use older sham participants as the comparator. Because age group changes along with arm assignment, those comparisons do not isolate stimulation assignment in younger adults. A direct younger active-versus-younger sham estimate is not among the posted primary comparisons.
The younger sham description includes stimulation at either the dlPFC or parietal cortex. The record notes that these locations were represented in that arm, but it does not provide separate outcome summaries for the two younger sham locations. This limits the specificity of a comparison against that arm and prevents assessing whether the location subgroups differed.
What does standard deviation add?
As a general explanation, the standard deviation measures spread among individual observations, rather than uncertainty in the group mean. A standard error instead describes the estimated sampling variability of a statistic such as a mean. The recalculated contrasts use the arm-level standard deviations and counts to estimate uncertainty in the difference. Participants' scores can vary substantially even when a group mean is estimated with reasonable precision; conversely, a small observed mean difference can have an interval that remains broad when variability is large relative to the amount of information.
The posted primary standard deviations range from 0.23 to 0.26 across the five arms. These values show appreciable individual variability on the outcome scale, but they do not alone establish whether the task was reliable or whether the mean differences are meaningful. The registry record does not report psychometric reliability or a threshold for an important difference.
What can and cannot be inferred from the design?
Randomization can support causal comparisons when the groups being contrasted were randomized against one another and the analysis respects the assigned design. The older active and older sham groups are described as randomized arms. The younger comparisons presented in the recalculation use an older group as reference, so randomization across the overall trial does not make those cross-age contrasts equivalent to an active-versus-sham treatment comparison in younger adults.
The study is described as parallel-group, but participants are also described as receiving sessions at different times on separate days. The registry record does not report whether the primary outcome analysis accounted for within-person measurements, session order, or potential carryover. Nor does it report the analysis population, handling of missing outcomes, or adjustment for multiple comparisons. These omissions matter because an analysis of repeated observations can differ from an analysis that reduces data to a single arm-level summary.
Finally, the statistical methods discussed for the primary comparisons are recalculations, not a reconstruction of unreported protocol decisions. The registry record does not report the original sample-size rationale, planned primary contrast, or any interim-analysis plan. The posted summaries support cautious descriptions of arm averages and simple pairwise uncertainty, but not claims that require those absent design and analysis details.
11. Confidence Intervals and Precision
The confidence intervals give a useful sense of how precisely the mean differences are estimated from the posted summaries. For older active dlPFC versus older sham dlPFC, the estimate is 0.02 and the 95% confidence interval extends from -0.083 to 0.123. The interval spans zero, so the summary data are compatible with a negative difference as well as a positive one. The point estimate alone should not be treated as a precise estimate of the direction or size of the contrast.
For younger active dlPFC versus older sham, the recalculated estimate is 0.14, with an interval from 0.038 to 0.242. The younger sham dlPFC/parietal comparison has an estimate of 0.18, with an interval from 0.084 to 0.277. The younger active parietal comparison has an estimate of 0.17, with an interval from 0.070 to 0.270. Those intervals are above zero, but their interpretation remains limited by the cross-age comparisons and by the unadjusted recalculation method.
As a general statistical point, interval width reflects sampling precision under the calculation, not the importance of an outcome or the quality of the study as a whole. An interval can be narrow around a contrast that is not the scientifically relevant comparison, and a point estimate can be statistically distinguishable from zero without being meaningful to participants. The registry record does not report a threshold for an important episodic-memory difference.
The intervals also do not incorporate uncertainty from unreported modeling decisions, missing-data handling, or multiplicity adjustment. They should therefore be read as precision summaries for simple comparisons of posted means, rather than as a complete account of uncertainty about the research question.
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 | 2,453 | 3,284 |
| 75% of the observed effect | 4,361 | 5,838 |
| 50% of the observed effect | 9,812 | 13,135 |
The sample-size illustrations are planning calculations based on the observed effect, not the trial's original design justification. The record does not report the original sample-size assumptions. The stated illustration assumes a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each planning row uses a stated fraction of the observed effect as the effect to detect. The displayed figures are participants per arm, not total participants across both arms; the distinction between per-arm participant counts and total event counts applies generally, and this trial's illustrations are for participants per arm.
The 80% power column gives the approximate number of participants per arm for a design with an 80% chance of rejecting the null hypothesis under the assumed effect and calculation. The 90% power column gives the corresponding per-arm number for a design with a 90% chance under those same assumptions. Power is a design property conditional on the assumed effect, analysis, and error rate; it does not describe the probability that a finding is true.
Rows planning for 75% or 50% of the observed effect require more participants per arm than rows planning for 100% of the observed effect. This follows the general relationship between effect size and sample size: smaller effects are harder to distinguish from variability and therefore require more information to detect with the same target power. For example, the older active-versus-sham illustration lists 2,453 participants per arm for 80% power when planning for 100% of the observed effect, and 9,812 for 50% of that effect. These are planning illustrations only; they are not observed power, and they should not be read as evidence about the adequacy of the original trial's design.
Because the calculations take observed differences as their starting point, they inherit uncertainty and possible bias in those estimates. The registry record does not report the original sample-size justification or whether its planning used a different outcome, contrast, or target effect.
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 = 0.020; pooled standard deviation σ = 0.250.
- n = 2 × (1.96 + 0.842)2 × 0.2502 / 0.0202 = 2,452.8, rounded up to 2,453 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 <- 0.02 # observed difference in means
sigma <- 0.25 # 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(3723850)
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 = 2,453 (80% power), 3,284 (90% power)
75% of observed effect: n per arm = 4,361 (80% power), 5,838 (90% power)
50% of observed effect: n per arm = 9,812 (80% power), 13,135 (90% power)
power.t.test: 2453.7
Simulated power at n = 2,453 per arm: 0.797 (20000 replicates)
The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Multiplicity, Missing Data and Analysis Populations
The registry record lists a primary episodic-memory outcome and a secondary working-memory outcome, but does not report a multiplicity-adjustment plan. It also does not report a prespecified hierarchy for comparing the several treatment and age arms. The recalculated p-values are unadjusted, meaning they do not account for the number of contrasts or outcomes considered. When multiple hypotheses are tested, unadjusted results can make the overall chance of at least one small p-value larger than the nominal rate for a single test. This is a general issue in multiple testing; the record does not establish which procedure, if any, was planned.
The record reports no sponsor-conducted statistical analyses for the primary endpoint and no reported analyses for the secondary endpoint. It does not state whether the reported arm summaries use an intention-to-treat population, a per-protocol population, or another analysis set. The posted outcome counts are lower than the overall enrollment, but enrollment and outcome-specific denominators alone do not explain why individuals are absent from a particular measure or whether missingness affected the estimates.
Missing-data methods are not reported in the registry record. There is no stated approach to incomplete outcome measurements, exclusions, or sensitivity analyses. Without that information, it is not possible to determine whether the posted means represent all randomized participants or a subset with available outcomes, nor to evaluate whether missingness could have influenced comparisons.
The registry record also does not report an interim-analysis plan, stopping boundaries, or adjustments related to interim monitoring. No such procedures should be assumed. Similarly, the original statistical analysis plan, model specification, and any covariate adjustment are not reported in the registry record. These missing details limit how fully the recalculated comparisons can be aligned with the study's planned inferential aims.
15. 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 |
|---|---|---|---|
| Older, Active tDCS, dlPFC | 0 | 49 | 0.0% |
| Older, Sham tDCS, dlPFC | 0 | 45 | 0.0% |
| Younger, Active tDCS, dlPFC | 0 | 54 | 0.0% |
| Younger, Sham tDCS, dlPFC/Parietal | 0 | 52 | 0.0% |
| Younger, Active tDCS, Parietal Cortex | 0 | 51 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Older, Active tDCS, dlPFC | 0 of 49 |
| Older, Sham tDCS, dlPFC | 0 of 45 |
| Younger, Active tDCS, dlPFC | 0 of 54 |
| Younger, Sham tDCS, dlPFC/Parietal | 0 of 52 |
| Younger, Active tDCS, Parietal Cortex | 0 of 51 |
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 |
|---|---|
| Older, Active tDCS, dlPFC | 49 of 49 |
| Older, Sham tDCS, dlPFC | 45 of 45 |
| Younger, Active tDCS, dlPFC | 54 of 54 |
| Younger, Sham tDCS, dlPFC/Parietal | 52 of 52 |
| Younger, Active tDCS, Parietal Cortex | 47 of 51 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Older, Active tDCS, dlPFC | Older, Sham tDCS, dlPFC | Younger, Active tDCS, dlPFC | Younger, Sham tDCS, dlPFC/Parietal | Younger, Active tDCS, Parietal Cortex |
|---|---|---|---|---|---|---|
| Non-Serious Adverse Events | Investigations | 49 of 49 | 45 of 45 | 54 of 54 | 52 of 52 | 47 of 51 |
For the serious adverse event summaries, each of the five reported groups has zero affected participants, with the listed number at risk varying by group. No deaths are listed in any group. These entries describe what was recorded for the reported safety categories and denominators; they do not establish that no serious events could occur or that the groups have equivalent safety profiles.
As a general statistical point, observing zero events in a group does not mean the underlying event risk is known to be zero. The precision of an event estimate depends on how many participants were observed and how events were ascertained and reported. The registry record does not provide further detail about event definitions, duration of safety follow-up, or the process used to collect adverse-event information.
The counts for adverse-event reporting differ from the outcome-specific sample sizes. Safety denominators should not be substituted for the numbers contributing to the memory summaries. The record also lists other adverse events in most participants in the groups, but the serious-event figures and the other-event category are distinct reporting measures and should not be conflated.
16. What the Result Does, and Does Not, Mean
The posted results describe average episodic-memory scores in five randomized arms and simple unadjusted contrasts using older sham participants as the reference. The older active and older sham means are close, while the younger-arm means are higher than the older sham mean in the reported summaries. Confidence intervals indicate that the older active-versus-sham contrast is imprecise and includes zero; the three younger-arm contrasts with older sham have intervals above zero.
These statements do not establish that active tDCS improved memory. The most direct active-versus-sham comparison in the posted primary results is among older adults at the dlPFC. The younger comparisons use an older sham reference, so age and assigned arm change together. The record does not provide a direct younger active-versus-younger sham comparison in the primary contrast set. The younger sham group also includes stimulation locations described as dlPFC or parietal cortex.
The study's stated interest includes time of day, but arm-level means do not show separate morning and afternoon estimates. The registry record does not report an analysis of time-of-day differences or of an interaction between time of day, age, and stimulation. It is therefore not possible to infer from these arm summaries whether the relationship between stimulation and memory changes across the day.
Statistical significance and practical importance are different questions. A p-value does not measure the size or importance of a memory difference, and the record does not report a threshold for a meaningful change. Conversely, an interval that includes zero does not prove that two groups are identical; it indicates that the simple estimate remains uncertain under the calculation used.
The reported comparisons are recalculated from posted summary statistics rather than taken from a sponsor-reported analysis. The record does not provide the full analysis plan, missing-data methods, multiplicity adjustment, or analysis population. These limitations mean the results are most appropriately read as descriptive evidence about the posted arm summaries, not as a definitive causal conclusion about tDCS, age, or time of day.
17. Why This Trial Matters Statistically
This study is statistically interesting because its central question involves several dimensions at once: stimulation assignment, age group, time of day, and memory domain. Those factors make the choice of comparison especially important. An arm-level difference can be calculated precisely, yet still fail to isolate the scientific question if the groups differ on more than the factor of interest.
The older active-versus-sham contrast is more directly aligned with a treatment comparison within a described age group than the younger-versus-older contrasts. The latter comparisons mix age and arm assignment. This illustrates a general principle of trial interpretation: randomization is valuable, but causal meaning depends on which randomized groups are compared and whether the analysis matches the question.
The study also highlights the distinction between a primary outcome and a broader research aim. Episodic memory is the primary measure, while the registry summary describes interest in time-of-day effects. The posted results do not report a time-specific analysis, so the arm means alone cannot answer the full question about performance at different times. A clearly defined estimand and analysis that directly represents age, stimulation, and timing would be needed to assess that interaction.
Finally, the record demonstrates why estimates, confidence intervals, and analysis details should be considered together. The unadjusted recalculations offer a transparent view of the arm summaries, but absent protocol details constrain confirmatory interpretation. These considerations apply broadly to clinical and behavioral research: statistically legible summaries are useful, but the design and comparison structure determine what those summaries can support.
18. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
Several limitations specific to this record affect interpretation. First, the posted primary comparisons use older sham participants as the reference for all other arms. The younger-arm contrasts therefore combine age-group differences with arm differences, rather than isolating active-versus-sham stimulation among younger adults. No direct younger active-versus-younger sham primary contrast is reported in the listed comparisons.
Second, the younger sham arm is described as including stimulation at either the dlPFC or parietal cortex, but the posted primary outcome summary does not separate those locations. This makes the comparator less specific for evaluating a particular stimulation site. The arm descriptions for some groups are also incomplete in the registry record, so details not fully stated cannot be assumed.
Third, the stated research interest includes performance at different times of day, but the posted results do not break out morning and afternoon outcomes or report an analysis of time-of-day effects. The record also does not report whether session order or repeated measurements were incorporated into the outcome analysis.
Fourth, the recalculated comparisons are unadjusted and use only posted summary statistics. The registry record does not report the sponsor's analysis, prespecified model, analysis population, missing-data approach, covariate adjustment, or multiplicity procedure. The original sample-size rationale and any interim-analysis plan are also not reported. These omissions prevent a full assessment of how the posted summaries relate to the intended inferential analysis.
Finally, the endpoint is measured immediately after stimulation, and no longer-term episodic-memory outcome is described in the posted primary measure. The record does not report a threshold for an important difference or the reliability of the memory task. Thus, statistical contrasts cannot be translated into a judgment about practical importance from the information recorded.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: Effect of Noninvasive Electrical Brain Stimulation on Memory at Different Times of Day in Younger and Older Adults — NCT03723850.
- Registry record last updated 2024-05-14; status last verified 2024-04.
- Results first posted 2024-05-14.
- 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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22. Record Summary
The registry record describes a completed randomized, double-masked, parallel-group study of tDCS and memory performance in younger and older adults. Five arms are represented in the primary results, with active and sham stimulation at the dlPFC and active parietal stimulation in a younger group. Participants in the described arms completed morning and afternoon sessions on separate days.
The primary endpoint is episodic memory, reported as an arm mean and standard deviation. Recalculated unadjusted comparisons show a small, uncertain older active-versus-older sham difference and positive contrasts between each younger arm and the older sham reference. Those cross-age contrasts do not isolate stimulation effects in younger adults. Working memory is listed as a secondary outcome, while sponsor-reported analyses and key analysis-plan details are not reported in the registry record.