Enhancing Spatial Navigation Using Non-Invasive Brain Stimulation: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Enhancing Spatial Navigation Using Non-Invasive Brain Stimulation (NCT01958437), a randomized na study. The primary outcome is Accuracy in Centimeters From Target Location for Allocentric.

2. Clinical Question

3. Trial Design

This was a randomized, double-masked, crossover study of tDCS. The registry lists enrollment as 44 and status as completed. The listed start date is 2013-10-01, and the primary completion date is 2017-03-23. The phase is listed as NA, and the sponsor is the VA Office of Research and Development.

The primary outcome description states that each participant completed one active tDCS session and one sham tDCS session for each measure. Outcome assessment took place after each of the two sessions, estimated within 1 week of each other. In a crossover design, a participant can contribute observations under both conditions. This differs from a design in which separate groups receive only one condition, and it means that within-person information can matter to the analysis.

The posted outcome groups include cognitively intact participants and participants with MCI, each represented under active and sham conditions. The listed group counts are 22 for each cognitively intact condition and 20 for each MCI condition. Computer errors caused missing outcome data for a subset of participants, and the record says those data were omitted from the analyses. The listed enrollment and outcome-group counts should not be treated as a complete account of the crossover data structure.

The registry lists Alzheimer's disease among the conditions, while the posted primary outcome groups are cognitively intact participants and participants with MCI. Whether people with Alzheimer's disease were enrolled or contributed to these posted outcome groups is not reported in the registry record. The randomization sequence, masking procedures, period effects, carryover assessment, washout interval, and original design assumptions are also not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Computer errors caused missing data for a subset (n=4) of participants; those data have simply been omitted from analyses below.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Accuracy in Centimeters From Target Location for Allocentric, measured over Outcome assessed after each of 2 sessions (estimated within 1 week of each other).

The primary endpoint is accuracy in centimeters from the target location for allocentric navigation. Participants used a touchscreen to document the location of a landmark; the distance between its actual location and the selected location was the dependent measure. This is a continuous outcome reported as a mean and standard deviation for each condition.

Distance is used as a direct measure of spatial-location error: a smaller distance represents a selection closer to the actual landmark location, while a larger distance represents a greater spatial discrepancy. The measure addresses allocentric navigation, which the registry describes as using landmarks and spatial knowledge to form and use a mental map. The registry's rationale contrasts this flexible strategy with egocentric navigation, which relies on learned associations between features and directions.

The outcome was assessed after each of the two sessions, one active and one sham. Four participants' outcome data were omitted because of computer errors. The record does not describe the exact landmark task beyond the touchscreen procedure, nor does it report a threshold for a meaningful difference in centimeters. Therefore, the posted means and their uncertainty describe measured location error, but the registry record does not establish what size of difference would be important for participants.

7. Results Posted in the Registry

• Cognitively Intact ACTIVE tDCS: mean 13.24 versus 14.22 on control; difference -0.98 (95% CI -3.00 to 1.04), standardized effect d = -0.29; z-test p = 0.342.
• MCI ACTIVE tDCS: mean 15.38 versus 14.22 on control; difference 1.16 (95% CI -0.33 to 2.65), standardized effect d = 0.47; z-test p = 0.127.
• MCI SHAM tDCS: mean 15.03 versus 14.22 on control; difference 0.81 (95% CI -0.59 to 2.21), standardized effect d = 0.34; z-test p = 0.256.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a mean difference represent?

A mean difference expresses the separation between the average outcome in one condition and the average in its comparator, in the outcome's original units. Here, those units are centimeters of distance from the target location. The recalculated contrast uses active tDCS as the first condition and sham tDCS as the reference in the cognitively intact comparison. A negative estimate means the active-condition average is lower in centimeters; a positive estimate means it is higher. For this endpoint, lower distance corresponds to greater location accuracy.

The posted recalculations are unadjusted comparisons based on summary statistics. They are not the sponsor's ANCOVA results. An unadjusted summary comparison does not necessarily reproduce an adjusted model, and the available summary statistics do not encode all features of a crossover analysis. In particular, the within-person covariance between a participant's active and sham observations is not reported in the registry record. That information can affect the uncertainty of a crossover contrast.

What does a confidence interval communicate?

A confidence interval describes uncertainty around an estimated effect under the assumptions of the method used to construct it. A narrower interval indicates greater precision than a wider interval on the same scale. An interval that includes zero is compatible with no mean difference under the analysis, as well as with differences in either direction that fall within the interval. It is not proof that the conditions are equivalent. Establishing equivalence would require a prespecified margin and an analysis designed to assess it; neither is reported in the registry record.

The recalculated intervals for the active-versus-sham comparisons include zero. The sponsor's ANCOVA p-values do not come with a reported estimate or confidence interval in the registry record. A p-value describes how compatible the data are with a specified null model under the analysis assumptions; it does not measure the probability that the null hypothesis is true, the size of an effect, or its practical importance. The registry record labels the reported sponsor analyses as superiority analyses.

Why does crossover structure matter?

In a crossover study, each participant may contribute outcome measurements under more than one condition. Analyses can use the pairing of those measurements, which separates within-person variation from variation between participants. A comparison that ignores pairing can have different precision from one that uses it. The record identifies the design as crossover and states that each participant had an active and a sham session, but it does not report the sponsor model specification beyond ANCOVA or the within-person covariance. The recalculated results should therefore be understood as simple, unadjusted re-calculations from posted summary statistics, not as a replacement for the trial's own analysis.

Period and carryover effects can also matter in crossover trials. A period effect occurs when outcomes differ by session timing; a carryover effect occurs when one condition influences outcomes in a later period. The registry record does not report whether such effects were assessed, how treatment sequence was handled, or whether a washout interval was used. No conclusion about those design features can be drawn from the posted group means alone.

Why can extra variation matter?

Over-dispersion means that observed variation is greater than a statistical model expects. When variation is underestimated, confidence intervals can be too narrow and tests can overstate evidence against a null hypothesis. This is a general statistical concern, especially when outcomes have more variability than a chosen model allows. The primary endpoint is continuous, and the record reports standard deviations, but it does not report a specific assessment of over-dispersion. It should not be assumed either to have occurred or to have been ruled out.

The sample-size illustrations use a normal approximation and equal allocation between two arms, as described in the registry-derived planning assumptions. That calculation is a planning exercise based on an observed effect and specified fractions of that effect. It does not account, in the displayed description, for every possible feature of a crossover design, such as within-person correlation or period effects. The original trial's sample-size method and justification are not reported in the registry record.

How should the separate groups be understood?

The sponsor reports separate ANCOVA analyses for cognitively intact participants and participants with MCI. The posted recalculations also include an MCI sham comparison against the cognitively intact sham group. These are distinct contrasts and answer different questions. Comparing treatment with sham within a population addresses a condition contrast; comparing MCI with cognitively intact participants under sham describes a difference between populations under that condition. The latter does not estimate the active-versus-sham effect.

Because multiple outcomes and analyses are listed in the record, multiplicity could be relevant when interpreting results across analyses. However, whether the sponsor adjusted for multiple comparisons, selected a primary contrast in advance, or performed any interim analyses is not reported in the registry record. The p-values should not be treated as if a multiplicity adjustment had been applied unless that is documented.

10. Confidence Intervals and Precision

Precision is reflected in the spread of plausible values around an estimate, as represented by its confidence interval. For the cognitively intact active-versus-sham comparison, the recalculated mean difference is -0.98 cm, and the 95% confidence interval runs from -3.002 to 1.042. The interval includes zero and includes both lower and higher mean error under active stimulation relative to sham. The estimate is therefore uncertain in direction as well as size.

For the MCI active-versus-sham comparison, the recalculated difference is 1.16 cm. Its confidence interval extends from a negative value to 2.65, also including zero. The interval permits values on either side of no difference, so the estimate does not precisely distinguish a lower average error from a higher average error. The confidence interval for the comparison of MCI sham with cognitively intact sham also includes zero and extends to 2.207.

Confidence intervals are more informative about effect size and precision than a p-value alone, but they depend on the method and assumptions used to calculate them. The recalculated intervals are unadjusted and based on posted summary statistics. Because the study is crossover and the within-person covariance is not reported in the registry record, these intervals may not match an analysis that uses the pairing of observations. The sponsor's ANCOVA confidence intervals are not reported in the registry record, so the precision of those adjusted estimates cannot be assessed from the reported p-values alone.

The record does not report a threshold for a meaningful change in location error. Thus, even if an interval excludes zero, statistical evidence alone would not establish whether the effect is important in everyday navigation. Here, the recalculated intervals include zero, while the sponsor's analyses report p-values without effect estimates or confidence intervals. Both the size and precision of the sponsor's adjusted effects remain unreported.

11. Planning a Similar Trial: Sample Size

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

The planning illustrations express required sample size as participants per arm, not total events. The event-count convention for time-to-event outcomes does not apply to this continuous endpoint. The rows describe planning for 100%, 75%, or 50% of the observed effect, with estimates shown for 80% and 90% power. The smaller assumed effects require more participants per arm than the larger assumed effects.

Power is the probability, under a particular assumed effect and model, of detecting an effect at the specified significance level. The 80% power column gives the planned participants per arm for a design with an 80% chance of detecting the assumed effect under the stated assumptions. The 90% column gives the corresponding planning figure for a 90% chance. Higher planned power generally requires more participants when other assumptions are held fixed. These are planning illustrations, not observed power.

The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. Because the effect is derived from the observed trial result, the planning values depend on that estimate and should not be treated as a definitive target for a future study. A smaller assumed effect needs more participants to detect with the same planned power.

The registry record does not report the trial's own original sample-size justification or design assumptions. The displayed planning approach is therefore not evidence that the original study was designed using these assumptions. The crossover structure and within-person correlation may also matter to an original trial calculation, but those details are not included in the stated planning assumptions.

12. How the Sample Size Is Derived

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

Formula

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

Worked calculation for this trial

1. Observed difference Δ = -0.980; pooled standard deviation σ = 3.421.
2. n = 2 × (1.96 + 0.842)² × 3.421² / -0.980² = 191.3, rounded up to 192 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 <- -0.98                      # observed difference in means
sigma <- 3.4212570789112                     # 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(1958437)
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 = 192 (80% power), 257 (90% power)
 75% of observed effect: n per arm = 341 (80% power), 456 (90% power)
 50% of observed effect: n per arm = 766 (80% power), 1,025 (90% power)
power.t.test: 192.3 
Simulated power at n = 192 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.

13. Analyses Reported by the Sponsor

The registry reports ANCOVA superiority analyses for active versus sham tDCS separately in cognitively intact participants and participants with MCI. The reported p-values are .048 and .063, respectively. The record does not provide the corresponding adjusted effect estimates, confidence intervals, model specification beyond ANCOVA, or additional details needed to reproduce those analyses.

The recalculated comparisons use the posted group means and standard deviations to form simple unadjusted estimates. For cognitively intact participants, that recalculation gives a mean difference of -0.98 cm and p = 0.342; for MCI, it gives a mean difference of 1.16 cm and p = 0.127. These results differ from the sponsor's reported p-values. Because the discrepancy flag is true, the sponsor's own analysis takes precedence over these recalculations when describing the trial's reported analysis.

That precedence does not make the sponsor results fully interpretable: without adjusted estimates and confidence intervals, their magnitude and precision are not available in the registry record. Nor do the reported p-values establish clinical importance. The recalculations remain useful as transparent descriptions of contrasts derived from posted summaries, but they are not substitutes for the sponsor's analysis and may not reflect the crossover pairing or ANCOVA adjustments.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists four outcome measures and eight analyses. The primary endpoint is the allocentric location accuracy measure described as distance in centimeters from the target. The posted sponsor analyses include separate ANCOVA superiority comparisons for cognitively intact participants and participants with MCI. Whether the sponsor adjusted for multiple outcomes or comparisons is not reported in the registry record.

Multiplicity arises when several hypotheses are tested: the chance of at least one apparently unusual result can increase across a collection of tests if no adjustment or other control strategy is used. This is a general statistical issue, not evidence that the sponsor did or did not use a particular procedure. No multiplicity strategy is reported in the registry record. The record also does not identify whether these analyses were prespecified, whether any outcomes or contrasts were selected after examining the data, or whether any interim analyses occurred.

The outcome description notes computer errors that caused missing data for a subset of participants, identified as n=4, and says those observations were omitted from the analyses. The registry does not report whether missingness was related to participant characteristics, treatment condition, outcome performance, or session order. It also does not describe imputation, sensitivity analyses, or a comparison of participants with and without missing data. Consequently, the possible influence of the omitted observations cannot be assessed from the record.

The analysis population is not described in enough detail to determine whether analyses followed an intention-to-treat approach, a per-protocol approach, or another population definition. The record does not report how crossover sequence, period, or carryover was handled in the sponsor's ANCOVA. These omissions matter because they affect what population and treatment contrast the reported results represent. They should be treated as unreported features rather than inferred from the study design label.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent non-serious adverse event terms

The registry reports zero serious adverse events in each of the four outcome groups: cognitively intact active, cognitively intact sham, MCI active, and MCI sham. The corresponding at-risk counts are 22, 22, 20, and 20. No deaths are reported in any group, and no serious adverse event terms are listed.

These are counts recorded for the groups in the registry; they do not establish that serious events could not occur or that the conditions have no risk. The record also lists other adverse events, with counts of 13 for cognitively intact active, 17 for cognitively intact sham, 15 for MCI active, and 12 for MCI sham, using the posted at-risk counts for those groups. The record does not provide further detail about the nature, severity, timing, or relatedness of those other events.

In a crossover study, the same participant may contribute to more than one condition, so group-level at-risk counts should not be read as separate sets of people. The registry record does not describe how adverse events were attributed across sessions or whether the event summaries account for repeated exposure. The figures are descriptive safety reporting, not a comparative estimate of risk.

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

The posted results describe location-error averages after active and sham tDCS sessions in cognitively intact participants and participants with MCI. The sponsor's ANCOVA reports p = .048 for cognitively intact participants and p = .063 for participants with MCI. The unadjusted recalculations produce different p-values and confidence intervals that include zero for both active-versus-sham comparisons. Given the recorded discrepancy, the sponsor's analysis is the primary reported analysis, while its effect estimates and confidence intervals are unavailable in the registry record.

These findings do not establish that stimulation improves navigation, nor do they establish that it does not. A p-value alone does not convey the size or practical importance of a difference. The posted group means and unadjusted contrasts are descriptive and do not provide a complete account of the crossover analysis. The sponsor's p-values provide evidence within its specified ANCOVA analysis, but the model details and adjusted estimates are not reported, limiting interpretation of magnitude and precision.

The registry's scientific rationale distinguishes allocentric navigation, which uses landmarks and mental maps, from egocentric navigation, which relies on habitual feature-direction associations. The primary endpoint measures accuracy in placing a landmark, rather than all aspects of everyday navigation. The record does not report whether a change in this task translates to real-world navigation or whether any observed difference reaches a meaningful threshold for participants.

The findings are limited to the posted groups and endpoint. Although Alzheimer's disease appears in the listed conditions, an Alzheimer's disease outcome group is not included in the posted results. The registry also does not report the trial's original sample-size justification, multiplicity plan, handling of missing outcomes beyond omission, or details of crossover-period analyses. Those gaps prevent a broader or more definitive interpretation than the measured outcome and reported analyses support.

17. Why This Trial Matters Statistically

This trial illustrates how a crossover design changes the statistical information available from a study. When participants experience both active and sham conditions, the contrast can use within-person comparisons. Those comparisons may be more precise than analyses that treat conditions as independent groups, depending on how consistently participants' outcomes track across sessions. The registry identifies the crossover structure, but the posted summary statistics do not report the within-person covariance needed to reconstruct that paired analysis.

It also illustrates why estimates, confidence intervals, and analysis methods should be read together. The sponsor reports ANCOVA p-values, while the simple recalculations from group summaries give different estimates of statistical evidence. The discrepancy means the recalculations should not replace the sponsor's analysis. At the same time, the absence of sponsor effect estimates and confidence intervals makes it difficult to assess the adjusted results' magnitude and precision.

Finally, the endpoint is a continuous measure with a clear interpretation in centimeters, but a measurable difference is not automatically an important difference. No threshold for meaningful change is reported. The sample-size illustrations also show the general planning principle that a smaller target effect requires more participants under otherwise fixed assumptions, while remaining separate from the original design rationale. Together, these features make the record a useful example of the importance of transparent model reporting, outcome interpretation, and uncertainty in clinical research.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record omits details needed to reproduce the sponsor's ANCOVA, including the adjusted treatment estimates, confidence intervals, covariates, and model specification. The recalculated contrasts are unadjusted, and the within-person covariance for the crossover observations is not reported. Therefore, their uncertainty may not represent the sponsor's intended crossover analysis.

The record does not describe treatment sequence, period effects, carryover, washout, or how these issues were handled analytically. The primary outcome description says that the two sessions were estimated within 1 week of each other, but it does not establish whether that interval was applied consistently or whether it was a washout period. The original trial sample-size justification and assumptions are also not reported.

Computer errors caused missing outcome data for n=4 participants, whose data were omitted. The reason for the computer errors is given, but the relationship between missingness and condition, session, or outcome is not reported. No missing-data sensitivity analysis or analysis-population definition is reported. Multiplicity handling and any interim analyses are also not reported.

The posted primary outcome is a landmark-location task, so it does not by itself establish effects on everyday navigation. The record does not report a threshold for a meaningful difference. Alzheimer's disease is listed among the conditions, but the outcome groups do not include an Alzheimer's disease group; the relationship between that condition listing and the posted outcome population is not reported in the registry record. These limitations restrict conclusions to the groups and analyses explicitly described.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Enhancing Spatial Navigation Using Non-Invasive Brain Stimulation — NCT01958437.
• Registry record last updated 2018-08-31; status last verified 2018-08.
• Results first posted 2018-08-31.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

The registry record describes a completed, randomized, double-masked crossover study of active and sham tDCS, sponsored by the VA Office of Research and Development. Enrollment is listed as 44. The primary endpoint is allocentric navigation accuracy, measured as distance in centimeters between the actual and selected landmark locations after each of two sessions.

Posted outcome groups include cognitively intact participants and participants with MCI. The sponsor reports separate ANCOVA superiority p-values of .048 and .063 for the active-versus-sham analyses. Unadjusted recalculations from the posted summaries differ; because the discrepancy flag is true, the sponsor's own analysis takes precedence. The sponsor's effect estimates and confidence intervals, the original sample-size rationale, multiplicity handling, and several crossover-analysis details are not reported in the registry record.

Computer errors led to omission of data for n=4 participants. No serious adverse events or deaths are reported in the listed groups. The record supports a cautious description of the endpoint and analyses, not a conclusion about clinical importance or everyday navigation effects.