Brain Stimulation and Robotics in Chronic Stroke Motor Recovery: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Brain Stimulation and Robotics in Chronic Stroke Motor Recovery (NCT03562663), a randomized na study. The primary outcome is Change From Baseline in Upper Limb Fugl Meyer Score.

2. Clinical Question

3. Trial Design

This was a randomized, double-masked, parallel-group trial listed as completed. The registry records an enrollment of 82 and identifies chronic stroke as the condition. Its listed interventions were transcranial direct current stimulation and upper-extremity robotics. The record describes active and sham stimulation, each given before robotic training; it does not describe a no-training group.

The active-group description specifies 20 minutes of active 2 mA stimulation over the motor cortex of the affected arm before robotic intervention. The sham group received 20 minutes of sham 2 mA stimulation over the same region before robotic training. The primary endpoint timeframe is baseline and after the 12-week intervention. The primary outcome population narrative indicates 41 enrolled in each group, while the posted outcome summaries include 40 in the active group and 37 in the sham group.

The record lists the study start as 2012-01 and primary completion as 2016-01. It lists no applicable phase. Randomization and double masking are recorded, but the method used to generate the allocation sequence, conceal allocation, or maintain masking is not reported in the registry record. Details about who was masked are also not reported. The protocol’s planned sample size and its justification are not reported in the registry record.

The outcome record includes one primary measure and no posted secondary outcomes. It records no sponsor analysis entries. Thus, the numerical comparison discussed in this analysis is based on the posted group summaries and an unadjusted recalculation, rather than an inferential analysis reported by the study sponsor.

4. Participant Flow and Accounting

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

Overall Study

Analysis population for the primary outcome, as defined in the registry: Of the 41 enrolled for active tDCS, 1 was lost due to unrelated illness and could not complete assessment after the 12-week intervention. Only 40 participant's data were included in the analysis. Of the 41 enrolled for Sham tDCS, 1 person was excluded due to Botox treatment, 2 people were excluded due to unrelated illness and 1 other person was excluded due to related illness. Only 37 participant's data were included in the analysis.

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: Between January 2012 and January 2016, 82 participants with chronic stroke were enrolled in the study across the two sites (65 Site 1, 17 Site 2), and were randomized to Robot-tDCS (n = 41) or Robot-Sham (n = 41) groups.

6. Primary Endpoint

The registry lists the primary outcome as Change From Baseline in Upper Limb Fugl Meyer Score, measured over Baseline and after the 12-week intervention.

The primary endpoint is change from baseline in the upper-limb Fugl-Meyer score after the 12-week intervention. The registry describes this score as a measure of upper-extremity motor weakness, with a range from 0 to 66 and higher scores indicating a better outcome. The reported unit is units on a scale.

A change score expresses how much a participant’s measured score differs from their own baseline. Comparing change between randomized groups can help address whether the groups experienced different average changes over the intervention period. The endpoint is relevant to the study’s stated focus on upper-limb motor recovery and the proposed combination of stimulation and robotic training.

The posted summaries give a mean change of 7.0 units for active stimulation and 7.7 units for sham stimulation. The corresponding standard deviations are 4.0 and 4.9. These summaries describe the analyzed participants, not everyone enrolled. The registry’s endpoint description does not provide further details about the exact assessment procedures, the scoring assessor, or how any missing baseline or follow-up measurements were handled. Longer-term follow-up results are not reported in the registry record, so the posted primary endpoint alone does not quantify whether any change was sustained beyond the stated assessment timeframe.

7. Results Posted in the Registry

• Active tDCS: mean 7.00 versus 7.70 on control; difference -0.70 (95% CI -2.71 to 1.31), standardized effect d = -0.16; z-test p = 0.494.

8. Statistical Interpretation

9. Statistical Methods Explained

The main numerical comparison is the difference between the average change in the active-stimulation group and the average change in the sham-stimulation group. It is an unadjusted recalculation from the posted means and standard deviations. The comparison uses active minus sham, so a negative estimate means the observed mean change was lower in the active group. This direction describes the arithmetic contrast and should not be taken as a judgment about clinical importance.

What does a mean difference represent?

For a continuous outcome, a group mean summarizes the average measured value or change in a group. A mean difference compares those averages on the original scale. Here the unit is a unit on the Fugl-Meyer scale, so the difference is expressed in score units rather than in a standardized unit. The group summaries are mean changes, not endpoint scores alone. The posted means are 7.0 for active stimulation and 7.7 for sham stimulation, and the recalculated mean difference is -0.7.

A mean is informative about the center of a distribution, but it does not describe every participant’s outcome. The standard deviations, 4.0 in the active group and 4.9 in the sham group, describe how spread out individual changes were around their respective group means. They are not standard errors and are not confidence intervals. A larger standard deviation indicates more variability among observed participant values, not more uncertainty in the mean by itself.

How should the confidence interval be read?

A confidence interval represents uncertainty in an estimate under the statistical procedure used to calculate it. The recalculated 95% interval for the mean difference runs from -2.707 to 1.307. In general, a confidence interval is a range of values compatible with the data and the calculation’s assumptions; it is not a guarantee that the true value lies in that particular interval. Its width reflects both the observed variability and the amount of information in the analysis.

Because this interval includes zero, the data do not determine a clear direction for the group difference. Values on either side of zero remain compatible with the interval. That does not demonstrate equivalence: an equivalence conclusion requires a prespecified margin and an analysis designed to test whether the interval lies within that margin. Such a margin and an equivalence analysis are not reported in the registry record.

What does the p-value add?

The unadjusted p-value is 0.494. In general, a p-value measures how unusual data at least as incompatible with a null hypothesis would be under the null model and its assumptions. It is not an effect-size measure, and it does not state the probability that the null hypothesis is true. The p-value does not replace the estimated mean difference or its confidence interval: the estimate conveys direction and magnitude, while the interval conveys uncertainty across plausible values under the procedure.

No sponsor analysis entries are posted. Consequently, the numerical inferential comparison is an unadjusted recalculation from summary statistics, not a sponsor-reported model. The registry does not report covariate adjustment, a specific model for the primary comparison, or the original analysis plan. It is not possible to determine from this record whether any planned analysis differed from the unadjusted calculation.

Why can spread and sample size matter?

General statistical explanation: when individual outcomes vary substantially, a group mean is estimated less precisely unless the analysis contains more information. The standard deviation describes observed spread, while the standard error describes uncertainty in an estimated mean or contrast. The confidence interval is built from the estimate’s uncertainty and the statistical method. The posted recalculation includes group standard deviations and sample sizes, but the underlying participant-level data and analysis details are not reported.

General statistical explanation: over-dispersion occurs when data vary more than a statistical model assumes. If a model understates variability, its uncertainty estimates can be too small and its confidence intervals too narrow. The endpoint is continuous and is summarized by means and standard deviations; the registry does not report a model-based assessment of over-dispersion or other distributional diagnostics. Such a diagnostic should not be inferred from the summaries alone.

The record reports a parallel randomized design and a continuous endpoint, but the detailed statistical plan is not reported in the registry record. The planning illustration is based on the observed effect and specified assumptions; it is separate from the trial’s own design justification, which is not reported. The illustration should not be confused with evidence about the actual study’s power after its results were observed.

10. Confidence Intervals and Precision

The recalculated mean difference in change, active minus sham, is -0.7 units. Its 95% confidence interval extends from -2.707 to 1.307 units. This interval is the clearest summary of the uncertainty around the estimated contrast. It includes zero, so the posted data are compatible with no mean difference as well as with differences in either direction under the calculation’s assumptions.

Precision is not the same as whether a result is important. A narrow interval would constrain the range of plausible values more tightly; a wider interval would leave greater uncertainty. The interval spans negative and positive values, so it does not resolve whether the active group had a higher or lower mean change than the sham group. The registry does not report a clinically important difference threshold, which prevents assessing whether any particular value in the interval would be important to patients or researchers.

The standard deviations of the observed changes were 4.0 for active stimulation and 4.9 for sham stimulation. Those values indicate variability in individual changes within the groups. They help contextualize the spread of outcomes, but do not by themselves determine the precision of the between-group estimate. The analysis sample sizes are 40 and 37, and the original planned sample size and design assumptions are not reported in the registry record.

The interval and p-value are unadjusted recalculations from summary statistics, with no sponsor analysis posted. They should therefore be interpreted as results of that calculation, rather than as a complete account of every analysis that may have been planned or conducted. The registry does not report whether an adjusted analysis, sensitivity analysis, or alternative missing-data method was used.

11. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm, not total events. They illustrate the sample sizes that would be needed under the stated assumptions to detect specified fractions of the observed effect. The assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect.

The 80% power column means the planning calculation targets an 80% chance of detecting the chosen effect if that effect is the true one and the planning assumptions hold. The 90% power column uses a higher target chance of detection under the same general framework. These are design targets, not guarantees that a future study will detect an effect. For 100% of the observed effect, the illustration gives 636 participants per arm for 80% power and 852 participants per arm for 90% power. For 75% of the observed effect, it gives 1,131 and 1,514 participants per arm, respectively. For 50% of the observed effect, it gives 2,544 and 3,405 participants per arm, respectively.

Smaller effects require more participants to detect under the same assumptions, because a smaller difference is harder to distinguish from ordinary variation. These calculations use the observed effect as their starting point and are planning illustrations only. This is not observed power. The trial’s own original sample-size justification and assumptions are not reported in the registry record.

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 = -0.700; pooled standard deviation σ = 4.455.
2. n = 2 × (1.96 + 0.842)² × 4.455² / -0.700² = 635.8, rounded up to 636 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 <- -0.7                      # observed difference in means
sigma <- 4.45475027358437                     # 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(3562663)
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 = 636 (80% power), 852 (90% power)
 75% of observed effect: n per arm = 1,131 (80% power), 1,514 (90% power)
 50% of observed effect: n per arm = 2,544 (80% power), 3,405 (90% power)
power.t.test: 636.7 
Simulated power at n = 636 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. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary outcome measure and no posted secondary outcomes. It also lists no sponsor analysis entries. This leaves no registry-reported set of multiple outcome tests to assess for multiplicity, but it does not establish what analyses may have appeared in a protocol or in other reports. The analysis plan, including any multiplicity strategy, is not reported in the registry record.

Multiplicity arises when several hypotheses or outcomes are tested. Repeated testing can increase the chance of finding an apparently notable result by chance, so a prespecified approach may adjust interpretation or control error rates. Whether such an issue arose in this study cannot be determined from the posted record, because it does not give a full analysis plan, list of interim analyses, or complete set of analyses conducted.

The primary outcome summary includes 40 participants in the active group and 37 in the sham group. The accompanying population narrative says 41 were enrolled in each group. It states that one active-group participant was lost because of an unrelated illness and could not complete the post-intervention assessment. For the sham group, the narrative says one person was excluded due to Botox treatment and two people were excluded for a reason that is cut off in the registry description. The reason for those additional exclusions, and any further details about the analysis population, are not reported in the registry record.

The record does not state whether the primary analysis followed an intention-to-treat approach, whether participants were analyzed as randomized, or how missing outcome measurements were handled. It also does not report sensitivity analyses for missing data. Because the displayed results use fewer participants than the enrollment narrative, exclusion and missingness could affect interpretation; the extent and direction of any effect cannot be assessed from the available information.

14. Safety Results

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

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 records serious adverse events for 0 of 41 participants at risk in the active-stimulation group and 0 of 41 at risk in the sham-stimulation group. No serious adverse-event terms are listed. These figures describe the safety entries in the registry; they do not establish that no serious event occurred outside the period or definitions captured by the record.

For other adverse events, the record lists 12 affected participants among 41 at risk in the active group and 4 among 41 at risk in the sham group. These are the posted counts, not a causal comparison. The registry does not provide event descriptions, severity categories, timing, exposure duration, or an analysis comparing groups. Deaths are not reported in the registry record.

Adverse-event counts should be read in the context of how events were defined, collected, and attributed. Those details are not reported in the registry record. The counts alone do not show whether events were related to stimulation, robotic training, or other causes, and they do not establish a treatment effect or safety profile beyond the recorded information.

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

The primary posted comparison concerns average change in upper-limb Fugl-Meyer score after a 12-week intervention combining robotic training with either active or sham stimulation beforehand. The active group’s mean change was 7.0 units and the sham group’s was 7.7 units. The unadjusted recalculated difference was -0.7 units, and its 95% confidence interval ranged from -2.707 to 1.307. The interval includes zero and allows for possible differences in either direction.

These results do not establish that the groups are equivalent. They also do not establish that active stimulation improves or worsens outcome relative to sham. The estimated contrast is uncertain, and the registry does not provide a threshold for what magnitude of score difference would be clinically important. The p-value of 0.494 should not be read as the probability that there is no effect or as a measure of the probability that the observed difference arose by chance.

The groups both received robotic training, with active or sham stimulation beforehand. Therefore, the comparison does not estimate robotic training versus no robotic training. Nor does it isolate stimulation without robotic training. It addresses the difference between the two stimulation conditions within the training context recorded for the trial.

The outcome reflects assessment after the stated 12-week intervention. Although the study rationale discusses sustained functional change and cortical physiology, the registry record does not post results for longer-term follow-up or cortical physiology. Those questions cannot be answered by the posted primary score comparison.

Finally, the posted summaries are based on 40 active-group and 37 sham-group participants, while the outcome narrative says 41 were enrolled in each group. The sham exclusion narrative is truncated, and the analysis method and missing-data handling are not reported. This limits assessment of how well the analyzed groups represent all randomized participants. The appropriate conclusion is therefore narrow: the registry’s available score summaries and unadjusted recalculation do not precisely determine the direction or magnitude of the difference between active and sham stimulation before robotic training.

16. Why This Trial Matters Statistically

This trial raises a statistical question that differs from simply asking whether participants improved over time. Both groups received robotic training, and the randomized contrast is whether active stimulation before training was associated with a different average change than sham stimulation before training. Keeping that contrast in view prevents within-group change from being mistaken for evidence about the added contribution of active stimulation.

The outcome is continuous and is reported as a mean change with standard deviation for each group. That makes it possible to express the comparison in the original Fugl-Meyer score units. The estimated difference is -0.7 units, but its confidence interval extends across zero. The interval emphasizes that the observed group contrast is not estimated precisely enough to establish its direction from the posted summaries alone.

The trial also illustrates how interpretation depends on the analysis population. The record lists an enrollment of 82 and describes 41 enrolled in each group, while the outcome summaries include 40 and 37. One active participant is described as unable to complete assessment after an unrelated illness; the sham exclusions are only partly described. Missing-outcome and exclusion rules can influence both the analysis and how confidently it reflects the randomized comparison.

Finally, a planning illustration based on an observed effect should not be treated as a retrospective verdict on whether the trial was adequately powered. Its figures depend on explicit assumptions and differ from the trial’s own original design justification, which is not reported. Together, these features make the record useful for understanding the distinction between a point estimate, uncertainty, analysis population, and design planning, while also showing why registry summaries cannot replace a full statistical analysis report.

17. Limitations

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

The primary outcome population description is incomplete. It reports that 40 active-group participants were analyzed after one of 41 enrolled could not complete the post-intervention assessment because of unrelated illness. It says that one sham participant was excluded due to Botox treatment and that two others were excluded for a reason cut off in the record. The remaining explanation is not reported in the registry record, limiting assessment of exclusions and missingness.

The registry does not report the original sample-size calculation or its assumptions, the detailed statistical analysis plan, the method for handling missing data, or whether the primary analysis followed an intention-to-treat principle. It also does not report a clinically important difference threshold for the Fugl-Meyer score. As a result, the clinical importance and robustness of the estimated contrast cannot be fully assessed.

The inferential statistics discussed are unadjusted recalculations from posted summary statistics; the registry lists no sponsor analysis entries. There is no posted participant-level analysis, adjusted estimate, sensitivity analysis, or diagnostic information. The comparison therefore depends on the recalculation’s assumptions and cannot reveal whether a different prespecified analysis was conducted.

The posted primary timeframe is after the 12-week intervention. Longer-term outcome results and cortical physiology results are not reported in the registry record, despite their mention in the study rationale. The record also does not describe detailed eligibility criteria, the randomization procedure, who was masked, or the assessment procedures. These omissions constrain interpretation of generalizability, potential bias, and durability of any observed changes.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Brain Stimulation and Robotics in Chronic Stroke Motor Recovery — NCT03562663.
• Registry record last updated 2021-01-20; status last verified 2020-12.
• Results first posted 2021-01-20.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The registry describes a completed randomized, double-masked, parallel-group trial of active versus sham transcranial direct current stimulation before robotic training for chronic stroke. It records enrollment of 82 and a primary outcome of change from baseline in upper-limb Fugl-Meyer score after the 12-week intervention.

Mean change was 7.0 units in the active group and 7.7 units in the sham group. The unadjusted recalculated mean difference was -0.7 units, with a 95% confidence interval from -2.707 to 1.307 and p = 0.494. The interval includes zero and leaves uncertainty about the direction and size of the difference.

The registry lists no sponsor analysis entries or secondary outcome results. Its analysis-population description is partly truncated, and details about the original statistical plan, missing-data methods, longer-term follow-up, and clinically important score differences are not reported in the registry record.